# Electronic Structure and Superconductivity of FeSe-Related Superconductors

Xu Liu1, Lin Zhao1, Shaolong He1, Junfeng He1, Defa Liu1, Daixiang Mou1, Bing
Shen1, Yong Hu1, Jianwei Huang1 and X. J. Zhou1,2,∗
1National Lab for Superconductivity, Beijing National Laboratory for Condensed
Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing
100190, China
2Collaborative Innovation Center of Quantum Matter, Beijing, China

(November 24, 2014)

###### Abstract

The FeSe superconductor and its related systems have attracted much attention
in the iron-based superconductors owing to their simple crystal structure and
peculiar electronic and physical properties. The bulk FeSe superconductor has
a superconducting transition temperature (Tc) of $\sim$8 K; it can be
dramatically enhanced to 37 K at high pressure. On the other hand, its cousin
system, FeTe, possesses a unique antiferromagnetic ground state but is non-
superconducting. Substitution of Se by Te in the FeSe superconductor results
in an enhancement of Tc up to 14.5 K and superconductivity can persist over a
large composition range in the Fe(Se,Te) system. Intercalation of the FeSe
superconductor leads to the discovery of the AxFe2-ySe2 (A=K, Cs and Tl)
system that exhibits a Tc higher than 30 K and a unique electronic structure
of the superconducting phase. The latest report of possible high temperature
superconductivity in the single-layer FeSe/SrTiO3 films with a Tc above 65 K
has generated much excitement in the community. This pioneering work opens a
door for interface superconductivity to explore for high Tc superconductors.
The distinct electronic structure and superconducting gap, layer-dependent
behavior and insulator-superconductor transition of the FeSe/SrTiO3 films
provide critical information in understanding the superconductivity mechanism
of the iron-based superconductors. In this paper, we present a brief review on
the investigation of the electronic structure and superconductivity of the
FeSe superconductor and related systems, with a particular focus on the FeSe
films.

###### Contents

  1. 1 Introduction
  2. 2 Electronic Structure of Bulk Fe(Se,Te) System and Intercalated FeSe
    1. 2.1 Bulk Fe(Se,Te)
    2. 2.2 Intercalated FeSe system
  3. 3 Electronic Structure and Superconductivity of FeSe Films
    1. 3.1 Electronic structure and superconductivity of FeSe films grown on graphene substrate
    2. 3.2 Electronic structure and superconductivity of FeSe films grown on SrTiO3 and related substrates
    3. 3.3 Transport and magnetic measurements of FeSe/SrTiO3 films
  4. 4 Implications and theoretical understanding
    1. 4.1 Implications
    2. 4.2 Theoretical understanding
  5. 5 Summary and Perspective

##  1 Introduction

The iron-based superconductors discovered in 2008Kamihara  represent the
second class of high temperature superconductors after the discovery of the
first class of high-Tc cuprate superconductors in 1986Bednorz . The
superconducting transition temperature (Tc) has reached $\sim$55 KXHChen ;
NLWang ; ZARenSm ; ZAXu  that is beyond the generally-believed McMillan limit
of the conventional superconductors. Indications of even higher Tc have
emerged in the single-layer FeSe filmsQYWangCPL ; DFLiu ; SLHe ; STan . Since
the discovery of the cuprate superconductors, understanding the high
temperature superconductivity mechanism remains a prominent and challenging
task facing the condensed matter physics community. The discovery of the iron-
based superconductors provides an opportunity to compare and contrast with the
cuprate superconductors that may lead to uncover the clue of high temperature
superconductivity. Great progress has been made in materials preparation,
experimental investigation, and theoretical understanding of the iron-based
superconductorsKIshida ; Johnston ; Paglinone ; Stewart ; FWang ; Hirschfeld ;
DXMouReview ; PCDai ; Chubukov ; Dagotto .

So far, several families of the iron-based superconductors have been
discovered that can be mainly categorized into ‘11’MKWu , ‘111’XCWang ,
‘122’MRotter  and ‘1111’Kamihara ; XHChen ; NLWang ; ZARenSm  systems
according to their crystal structure (Fig. 1)Paglinone . Similar to the
cuprate superconductors, the iron-based superconductors are quasi-two-
dimensional in their crystal structure. The FePn (Pn=As or Se) layer is an
essential building block that is believed to be responsible for the
superconductivity in the iron-based superconductors. Different from the
cuprate superconductors where the CuO2 plane is basically co-planar, the FePn
(Pn=As or Se) unit consists of three layers with the central Fe layer
sandwiched in between two adjacent Pn (Pn=As or Se) layers. This results in
the doubling of the unit cell in the iron-based superconductors and the
folding of the corresponding electronic structure (Fig. 2). Most
significantly, different from the cuprate superconductors where the low-energy
physics is mainly dominated by the single Cu d${}_{x^{2}-y^{2}}$ orbital, in
the iron-based superconductors, all the five Fe 3d orbitals participate in the
low-energy electronic structuresFJMaFPC ; TYildirim ; FJMaPRB ; FJMaPRL .
Generally, there are multiple bands crossing the Fermi level that form hole-
like Fermi surface sheets near the Brillouin zone center and electron-like
Fermi surface sheets near the zone cornerFChen ; YLubashevsky ; JMaletz ;
AAKordyuk ; LZhao ; GDLiu ; HYLiuPRB ; HYLiuPRL . The multiple-orbital nature
(Fig. 2)SGraser ; YZhangorbital  plays an important role in understanding the
physical properties and superconductivity mechanism in the iron-based
superconductors.

Among all the iron-based superconductors, the FeSe superconductor and its
related systems have gained particular attention due to their simple crystal
structure and peculiar electronic and physical properties. The FeSe
superconductor has a simple crystal structure consisting of the FeSe layer
that is the essential building block in the iron-based superconductors; such a
simple structure is ideal for theoretical and experimental study of the
superconductivity mechanism. The bulk FeSe superconductor has a
superconducting transition temperature (Tc) of $\sim$8 KMKWu ; it can be
dramatically enhanced to 37 K at high pressureSMedvedev . On the other hand,
its cousin system, FeTe, possesses a unique antiferromagnetic ground state but
is non-superconductingWBao . Substitution of Se by Te in the FeSe
superconductor results in an enhancement of Tc up to 14.5 K and
superconductivity can persist over a large composition range in the Fe(Se,Te)
systemMHFangPRB ; Nkatayama . Intercalation of the FeSe superconductor leads
to the discovery of the AxFe2-ySe2 (A=K, Cs and Tl) system that exhibits a Tc
higher than 30 KJGuo ; MFang ; MHFangEPL ; XLChenSR  and unique electronic
structure of the superconducting phaseDLFengIFS ; HDingIFS ; DXMouReview . The
latest report of possible high temperature superconductivity in the single-
layer FeSe/SrTiO3 films with a Tc above 65 K has generated much excitement in
the communityQYWangCPL ; DFLiu ; SLHe ; STan . This pioneering work opens a
door for interface superconductivity to explore for high Tc
superconductorsQYWangCPL . The distinct electronic structure and
superconducting gap, layer-dependent behavior and insulator-superconductor
transition of the FeSe/SrTiO3 films provide critical information in
understanding the superconductivity mechanism of the iron-based
superconductors.

In this paper, we will present a brief review on the investigation of the
electronic structure and superconductivity of the FeSe superconductor and
related systems. We will put particular focus on the FeSe films that is an
exciting and fast-growing field. The paper is organized as follows: In Section
2, bulk FeSe and related materials are first introduced. In Section 3, we will
discuss the electronic properties of the FeSe films, including Fermi surface,
band structure, gap symmetry and the evolution of electron structure with
annealing. The implications and theoretical understandings are presented in
Section 4. In Section 5, we end with further issues to be investigated and a
future perspective.

##  2 Electronic Structure of Bulk Fe(Se,Te) System and Intercalated FeSe

###  2.1 Bulk Fe(Se,Te)

Bulk FeSe superconductor with a Tc of 8 K was first discovered in 2008 in a
tetragonal phase $\beta$-FeSe with PbO-structure at ambient pressure (Fig.
3a)MKWu . It has been found that excess Fe is inevitable to stabilize the
crystal structure of Fe1+δSe and the superconductivity is very sensitive to
its stoichiometry ($\delta$)TMMcQueen . The FeSe superconductor exhibits a
dramatic pressure dependence (Fig.3c), in particular, its Tc can be enhanced
to 36.7 K under high pressureSMedvedev . At ambient pressure, FeSe
superconductor undergoes a structural transition from tetragonal to
orthorhombic around 90 K but without a magnetic transitionYMizuguchi ;
TMMcQueen . This is distinct from many other iron-based parent compounds where
the structural transition is usually accompanied by a magnetic phase
transitionPCDaiTransition ; JZhaoTransition ; YChen ; JZhao1111 ; JZhao122 ;
AIGoldman ; QHuang . However, under high pressure, static magnetic order is
observed in superconducting FeSeMBendele . Short range spin fluctuation has
also been reported in FeSe superconductor that is enhanced under high
pressureImai .

As Se is gradually replaced by Te in FeSe, superconductivity with a maximum Tc
around 14.5 K can be observed in a large composition range (x) in the
Fe1+δSe1-xTex system (Fig. 3d)MHFangPRB ; NTakayama . Again, the excess Fe
content ($\delta$) has a big effect on the physical properties and
superconductivity in this caseTMMcQueen . The excess Fe is found to be located
at the interstitial sitesWBao . Fe1+δTe is present at the other end of the
Fe1+δ(Se1-xTex) phase diagram (Fig. 3d). It undergoes a phase transition
between 60-75 KMHFangPRB ; GFChenFeTe  and no superconductivity is observed in
the bulk Fe1+δTe. Signature of superconductivity is reported in the FeTe films
but is likely due to the incorporation of oxygensLXCao ; YFNie ; MZheng . At
low temperature, Fe1+δTe shows an antiferromagnetic order of bi-collinear
structure (Fig. 3b, upper panel) that is distinct from the usual collinear
magnetic structure observed in many other parent compounds like BaFe2As2 (Fig.
3b, lower panel)WBao ; SLLiFeTe .

The band structure and Fermi surface of the bulk FeSe superconductor (Fig. 4a
and 4b) from the band structure calculations show similar behaviors as other
iron-based superconductors, i.e., the low energy electronic states originate
mainly from the iron 3d orbitals, and there are two hole-like Fermi surface
sheets at the zone center and two intersecting electron-like Fermi surface
sheets around the zone cornerASubedi . Direct ARPES measurements on the FeSe
superconductors has been hindered due to the difficulty in obtaining FeSe
single crystals. With the latest progress on growing high-quality FeSe single
crystalsJYLin ; AEBoehmer ; KKhuynh ; FZhou , several ARPES measurements on
the FeSe superconductor have become availableJMaletz ; KNakayama ; TShimojima
.

The ARPES results on FeSe single crystals reported so far give a basically
consistent pictureJMaletz ; KNakayama ; TShimojima , as exemplified in Fig. 4.
First, at low temperature below the structural transition ($\sim$90 K), the
$\Gamma$ point is dominated by two hole-like bands (Fig. 4f), while near the M
point, an electron-like band crossing the Fermi level and a hole-like band at
higher binding energy are observed. Second, the measured electronic structures
show a significant difference from the band structure calculations; the bands
undergo a pronounced orbital-dependent renormalization. Third, there is an
obvious change of the electronic structure across the structural phase
transitionKNakayama ; TShimojima . An energy splitting of bands up to 50 meV
around the M point is observed below the structural transition. This is
interpreted as the splitting of the dyz and dxz orbital bands (Fig. 4e),
indicating the orbital ordering. In particular, the Fermi energy for both the
hole-like bands near the zone center and the electron-like band near M is
rather small. These are consistent with the quantum oscillation
measurementsTTerashima ; AAudouard  and STM measurementSKasahara  of the FeSe
crystals. The comparable energy scale of the Fermi energy, superconducting
gap, and Zeeman energy in FeSe superconductor also provides a window to look
into the BCS-BEC crossover regimeSKasahara .

FeTeMHFangPRB ; GFChenFeTe , as a cousin of FeSe, shows quite different
behaviors. It is non-superconducting and undergoes a strutural/magnetic
transition around TMS=70 KMHFangPRB ; GFChenFeTe  (Fig. 5e). It is
semiconductor-like above the transition while becomes metallic below the
transition (Fig. 5e). Initial ARPES measurements reveal a pair of nearly
electron-hole compensated Fermi pockets, strong Fermi velocity
renormalization, and an absence of a spin-density-wave gapYXia . The measured
electronic structure is qualitatively similar to other iron-pnictides although
the antiferromagnetic structure in FeTe is different and 45 degrees rotated
when compared with that in other iron-pnictide parent compounds. This is not
consistent with the Fermi surface nesting picture for the formation of spin-
density-wave (SDW) below the transition temperature. Further work studied the
Fermi surface and band structure of FeTe both in the paramagnetic state and
the SDW stateYZhangFeTe . As shown in Fig. 5, above the magnetic transition
temperature, the spectral weight mainly concentrates near $\Gamma$ point and M
point (Fig.5a) (as noted by ZKLiuFeTe , there may be a 45 degree rotation on
the Brillouin zone definition in YZhangFeTe ). The $\Gamma$ point is dominated
by two hole-like bands while there are two electron-like bands near the M
point. Upon decreasing the temperature below TMS, the spectral weight
distribution experiences an obvious change. The spectral weight around M and X
point is suppressed that is interpreted as the spectral weight transfer from
low binding energy to high binding energyYZhangFeTe . Detailed temperature-
dependent ARPES measurements on FeTe reveal coherence quasipartical peak near
the Fermi level below the transition, accompanied with a hump structure
located at higher binding energy and a dip in between these two features (Fig.
5h and i)YZhangFeTe ; ZKLiuFeTe . Such a “peak-dip-hump” structure bears a
strong resemblance to that observed in manganites and the heavily underdoped
cuprates that can be explained in terms of polaron formationZKLiuFeTe . The
hump feature is interpreted as from incoherent excitation of electron strongly
coupled to bosons while the qusipartical feature is related with coherent
polaron motion. In this picture, the coherent polaron motion at low
temperature may explain the metallic transport in the spin-density-wave
stateZKLiuFeTe .

Extensive ARPES measurements have been carried out on Fe(Se,Te) system to
investigate its electronic structure and superconducting gapKNakayamaFST ;
FChen ; ATamai ; YLubashevsky ; HMiaoFeTeSe ; KOkazakiFeTeSe ; KOkazakiSRep ;
EIeki . Typical results are summarized in Fig. 6. There are three hole-like
bands around the $\Gamma$ point with two bands crossing the Fermi level
(labeled as $\beta$ and $\gamma$) and the third band (labeled as $\alpha$)
barely touching the Fermi level, while there are two electron-like bands
around M point in Fe(Se,Te) (Fig. 6c-e)FChen . The measured Fermi surface is
sketched in Fig.6f. Taking advantages of the photoemission matrix element
effect by performing ARPES measurements under different polarization geometry,
the $\alpha$ band is assigned as from dxz/dyz orbitals, the $\beta$ band is
mainly from d${}_{xz},d_{yz}$ and some from dxy orbital, and the $\gamma$ band
is assigned as from d${}_{x^{2}-y^{2}}$ orbitalFChen . Direct comparison
between measurements and band structure calculations indicates a strong
orbital-selective renormalization in the normal stateATamai . Such strong
renormalizaiton is consistent with the recent theoretical calculations to show
that the 11 system exhibits a stronger correlation effect in the iron-based
superconductorsZPYin .

In the optimally-doped FeTe0.55Se0.45 superconductor, the measured
superconducting gap is nearly isotropic both near the zone center and the zone
corner (Fig. 6g)HMiaoFeTeSe . Further high-resolution measurements indicate
that the superconducting gap around the Fermi surface near $\Gamma$ is
anisotropic which can be represented by cos(4$\varphi$) modulation
(Fig.6h)KOkazakiFeTeSe . These ARPES results are consistent with the STM
measurement on Fe(Te,Se) that points to an unconventional s-wave (S±-wave
symmetry) superconducting gapHanaguriFeTeSe . In Fe(Se,Te) superconductors,
like in FeSe superconductor caseSKasahara , the Fermi energy is comparable to
the superconducting gap; this system thus provides an opportunity to explore
the BCS-BEC crossover phenomenon in a superconducting materialYLubashevsky ;
KOkazakiSRep .

###  2.2 Intercalated FeSe system

The attempt to intercalate FeSe with potassium (K) resulted in a successful
preparation of the KxFe2-ySe2 superconductor with a Tc higher than 30 KJGuo .
Later on, it was found that FeSe can be intercalated with many other
intercalates including Cs, Rb, Tl, Li, Na, Sr, Ca, Yb, Eu and even
moleculesMFang ; AKMaziopaAFeSe ; CHLi ; HDWangAFeSe ; XLChenSR ; MBLucas .
This system is complicated with the coexistence of different phases. For
reviews on this topic, one may refer to Refs.DXMouReview ; Dagotto .

For the completeness of the review, here we present the main ARPES results on
the AxFe2-ySe2 (A=K, Cs, (Tl,K), (Tl, Rb)) systemDLFengIFS ; TQianAFeSe ;
DXMouPRL ; LZhaoAFeSe ; DXMouReview ; XWangAFeSe ; FChenAFeSe ; MXu ; XPWangG
. Although the intercalates can vary, the electronic structure of the
superconducting phase in the AxFe2-ySe2 system turned out to be similar. As
shown in Fig. 7, the measured Fermi surface consists of two electron-like
Fermi surface sheets ($\alpha$ and $\beta$ in Fig. 7g) around $\Gamma$ and one
electron pocket around M ($\gamma$ in Fig. 7g) that includes two nearly
degenerate Fermi surface sheets. The bands around $\Gamma$ (Fig. 7a and 7b) is
dominated by two electron bands $\alpha$ and $\beta$: the bottom of the
$\alpha$ band just touches the Fermi level while the origin of the $\beta$
band remains unclearDXMouPRL . Around the M point, a clear electron band is
observed in the vicinity of Fermi level and a hole-like band with its top
about 100 meV below the Fermi level (Fig. 7c and 7d). More detailed
measurements indicate that there are two electron bands with similar Fermi
momenta but different band bottoms around M (Fig. 7e and f)DXMouReview .

It was proposed that the interband scattering between the hole-like bands near
$\Gamma$ and electron-like bands near M gives rise to electron pairing and
superconductivity in the iron-based superconductorsKuroki ; Nesting ; FWangPRL
; AVChubukov ; VStanev ; FWangEPL ; IIMazinNP . The distinct Fermi surface
topology in the AxFe2-ySe2 superconductor presents a serious challenge to this
picture since there is no hole-like Fermi surface present near the $\Gamma$
point. An alternative scattering mechanism between the electron pockets was
proposedKuroki ; TAMailer ; FWangEEScattering ; TDas . In this case, the
inter-electron pocket scattering tends to produce d${}_{x^{2}-y^{2}}$ gap
symmetry. Nearly isotropic superconducting gap is observed around the $\gamma$
electron pocket at the M point (Fig. 7h)DLFengIFS ; TQianAFeSe ; DXMouPRL ;
LZhaoAFeSe ; DXMouReview . In particular, the electron Fermi pockets around
the zone center provide a good opportunity to distinguish among various gap
symmetries. Nearly isotropic superconducting gap is observed on the small
$\alpha$ electron pocketMXu ; XPWangG  and nearly isotropic superconducting
gap was also observed around the larger $\beta$ electron-pocket around
$\Gamma$DXMouReview . These results are not consistent with the d-wave gap
symmetry in the AxFe2-ySe2 system with only electron Fermi surface.

##  3 Electronic Structure and Superconductivity of FeSe Films

###  3.1 Electronic structure and superconductivity of FeSe films grown on
graphene substrate

High-quality crystalline FeSe films can be grown on graphene substrate by a
molecular beam epitaxy (MBE) methodCLSong . The graphene substrate used in
this case is double-layer graphene formed on the SiC(0001) surface and the
FeSe films grow as islands on the graphene layer. The grown FeSe films are
along the (001) direction. One unit cell consists of one Fe layer and two Se
layers (one above the Fe layer and the other below) (see Fig. 1) (loosely
speaking, we will call this one unit cell of FeSe as single-layer in the
following). The interaction between the FeSe film and the underlying graphene
substrate is very weak so the lattice constant of the FeSe film is the same as
the bulk FeSe (3.76 $\AA$). Also because of this weak interaction, the FeSe
films form domains with different orientations within the (001) plane. In this
case, several STM works have been done on the FeSe/graphene filmsCLSongScience
; CLSongBoundary ; CLSongMode , but no ARPES measurement can be done due to
the multi-domain nature of the films.

The superconductivity of the FeSe/graphene films behaves in a usual manner,
i.e., its superconducting transition temperature decreases when the films get
thinner (Fig. 8)CLSong . Fig. 8a shows a series of normalized tunneling
conductance spectra on an 8-layer FeSe/graphene film. Clear coherence peak
associated with superconductivity is observed and the gap size ($\Delta$) can
be obtained by measuring the distance between the two peaks (2$\Delta$). It is
2.1 meV at 3 K for the 8-layer FeSe/grahene film with a corresponding
superconducting temperature (Tc) at 8 K. In comparison, bilayer FeSe/graphene
film shows a lower Tc that is only 3.7 K (Fig. 8b). The superconducting gap
and Tc are determined for the FeSe/graphene films with different layers, as
shown in Fig. 8c which plots the variation of Tc with the film thickness. Tc
is found to be linearly proportional to the inverse of the film thickness 1/d.
This is consistent with the usual expectation that Tc of the ultra-thin films
decreases with the decrease of the film thickness: Tc(d)=Tc0 (1-d/dc) with Tc0
being the bulk transition temperature and dc being the critical thickness
where superconductivity emergesJSimonin . Similar behaviors are also observed
in ultra-thin PbUltraPb  and ultra-thin YBa2Cu3O7-δYBCOTc  films. Note that no
superconductivity is observed in single-layer FeSe/graphene film above 2.2 K.
The extrapolated Tc0 from the layer-dependence of Tc is $\sim$9.3 K that is
consistent with the Tc of the bulk FeSe superconductorCLSong .

In an atomically flat and defect-free (001) surface of the FeSe/graphene film
(about 30 unit cell thick) with large terraces (Fig. 9a), the topmost layer is
Se-terminated (Fig. 9b)CLSongScience . The scanning tunneling spectroscopy
(STS) probes the quasiparticle density of states and measures the
superconducting gap at the Fermi energy (EF) (Fig. 9c). The maximum of the
superconducting gap is measured as $\Delta$0 = 2.2 meV. The most striking
feature of the spectra at 0.4 K is the V-shaped dI/dV curve and the linear
dependence of the quasiparticle density of states on energy near EF. This
feature is similar to that found in the d-wave cuprate superconductors with
gap nodesOFisher  and in contrast to the U-shaped dI/dV curve observed in bulk
Fe(Se,Te) superconductorHanaguriFeTeSe . This V-shaped feature in the
FeSe/graphene film explicitly indicates the existence of line nodes in the
superconducting gap functionCLSongScience . Further Fermi surface topology
examination (Fig. 9d) suggests that the line nodes may be related to the
component of the extended s±-wave form $\Delta_{2}$(coskx + cosky) that gives
rise to nodes near M points. The reason why the Cooper pairing is nodal in
FeSe/graphene films but nodeless in bulk Fe(Se,Te) remains a theoretical
challenge although it is suggested that the pnictogen height may introduce a
switch between the nodal and nodeless pairingsKurokipnictogen .

In the FeSe/graphene films, the electron pairing with twofold symmetry,
instead of four-fold symmetry, was demonstrated by direct imaging of
quasiparticle excitations in the vicinity of magnetic vortex cores, Fe
adatoms, and Se vacanciesCLSongScience . The twofold pairing symmetry was
further supported by the observation of striped electronic nanostructures in
the slightly Se-doped samples. The anisotropy was explained in terms of the
orbital-dependent reconstruction of electronic structure in FeSe. It was also
discovered that, in the FeSe/graphene films, superconductivity near the twin
boundaries is suppressed, which also provides a measure of the superconducting
coherence length on the order of 5.1 nmCLSongBoundary . Such a
superconductivity suppression is linked to the increased Se height in the
vicinity of twin boundariesCLSongBoundary . STM/STS also revealed signatures
of a bosonic mode in the local quasiparticle density of states of the
superconducting FeSe/graphene filmsCLSongMode .

###  3.2 Electronic structure and superconductivity of FeSe films grown on
SrTiO3 and related substrates

The FeSe films grown on the SrTiO3 substrate exhibit surprising and different
behaviors from those grown on graphene substrateLLWangReview . When a single-
layer FeSe film was grown on SrTiO3 (001) substrate by a MBE method (Fig. 10),
four pronounced peaks were identified at $\pm$20.1 mV and $\pm$9 mV in the
tunneling spectrum at 4.2 K that are symmetric with respect to the Fermi level
(Fig. 10b)QYWangCPL . The gap at 20.1 meV, when taken as a superconducting
gap, would correspond to a superconducting transition temperature near 80 K if
one assumes the similar ratio between the superconducting gap and Tc as in the
FeSe/graphene filmsCLSongScience . The temperature dependence of the gap, the
observation of magnetic field-induced vortex state, and the transport
measurement all indicate that the single-layer FeSe/SrTiO3 film is likely
supercondctingCLSongScience . This pioneering work has generated a great
excitement in the community and many experimental and theoretical works
follow. On the other hand, it was found that the two-layer FeSe/SrTiO3 films,
grown under the same condition, show a semiconducting behavior (Fig.
10d)QYWangCPL .

The immediate ARPES measurements on a superconducting single-layer FeSe/SrTiO3
film reveal a simple and distinct electronic structureDFLiu . The observed
Fermi surface (Fig. 11a) consists of only electron pocket near the zone corner
M without any Fermi surface crossing near the zone center $\Gamma$. This Fermi
surface topology is the simplest among all the observed Fermi surface in the
iron-based superconductors (Fig. 11); it is also dramatically different from
the calculated Fermi surface of the bulk FeSe (Fig. 11d). Considering two
electron-pockets around M point due to two-Fe-sites in a unit cellRPengPRL ;
JJLee , the carrier concentration of this particular sample can be estimated
by the area of the electron-pocket; it corresponds to $\sim$0.10 electrons per
Fe. The band structure near the zone center (left panel of Fig. 11e) is
dominated by a hole-like band with its top about 80 meV below the Fermi level.
The band structure across the zone corner (M point) consists of an electron-
like band with its bottom about 60 meV below the Fermi level. An effective
mass of $\sim$3me can be estimated for this particular electron-like bandDFLiu
.

ARPES also provides an alternative approach to examine whether the single-
layer FeSe/SrTiO3 is superconducting or not and its superconducting transition
temperature by directly measuring the possible superconducting gap opening and
its temperature dependenceDFLiu . The temperature-dependent photoemission
spectra are shown in Fig. 12a; sharp peaks develop at low temperature and
become gradually broadened with increasing temperature. The symmetrized
photoemission spectra is shown in Fig.12b in order to visually inspect
possible gap opening and remove the effect of Fermi distribution function near
the Fermi level. There is a clear gap opening at low temperature. The gap size
decreases with increasing temperature and closes at 50$\sim$55 K. The
variation of the gap size as a function of temperature (Fig.12e) follows a
standard BCS form. Momentum dependent measurements (Fig.12c and d) indicate
that the gap is nearly isotropic without any sign of zero gap (node) around
the Fermi surface. Since the single-layer FeSe film is highly two-dimensional,
it avoids complications from three-dimensional Fermi surface. In this case, it
is definitive to claim that the gap along the electron-like Fermi surface near
M is s-wave like without nodes. The near-EF band back-bending at low
temperature (Fig. 12g, right panel), the sharp coherence peaks at low
temperature (Fig. 12a), the BCS-form-like temperature dependence of the gap
(Fig. 12e), and the momentum dependence of the gap (Fig. 12c) provide strong
evidence to indicate that the gap observed here is a superconducting gap.

In the electronic phase diagram of both the high temperature cuprate
superconductors and the iron-based superconductorsPALee ; JPaglione , it is
clear that the physical properties depend strongly on the carrier
concentration, and superconductivity can be optimized at a particular carrier
concentration. It is tempting to ask whether one can establish a similar phase
diagram for the single-layer FeSe/SrTiO3 system, and whether it is possible to
optimize its superconductivity. Such an idea is motivated by the MBE growth
process where the single-layer FeSe/SrTiO3 film is first grown at a relatively
low temperature which is non-superconducting; then it becomes superconducting
only after the film is annealed in vacuum at a relatively high
temperatureQYWangCPL ; WHZhangPRB ; ZLiSTM . To keep track on how the
evolution from the as-grown non-superconducting single-layer FeSe/SrTiO3 film
to the vacuum-annealed superconducting film occurs, extensive ARPES
measurements were carried out on the as-grown single-layer FeSe/SrTiO3 film
that was vacuum-annealed in situ by many sequences at different temperatures
and different timesSLHe . The main results are summarized in Fig. 13. For the
as-grown non-superconducting single-layer FeSe/SrTiO3 film, its electronic
structure (Fig. 13(e-h)) is distinct from that of the superconducting films
(Fig. 13(a-d)). In this case, the underlying Fermi surface shows four strong
spots around the M point (Fig. 13e). A hole-like band is present near the
$\Gamma$ point but its top is closer to the Fermi level compared to that in
the superconducting film. A pronounced hole-like band is observed along the
$\Gamma$-M direction near the M point that is totally different from the
electron-like band in the superconducting film. The distinct electronic
structures between the as-grown non-supercoucting films and the
superconducting films indicate there are two different phases present in the
single-layer FeSe/SrTiO3 films (Fig. 13(a-h)), for convenience, the phase with
the electronic structure similar to the as-grown films is called “N”-phase
while the one with the electronic structure similar to the superconducting
FeSe films is called “S”-phaseSLHe . It turned out that the evolution proceeds
in three stages during the vacuum-annealing process.SLHe . For the as-grown
non-superconducting film, after initial first-stage mild annealing, it stays
in the pure N-phase (left pink region in Fig. 13i). Further annealing leads to
the emergence of the S phase; the S phase increases with the annealing process
at the expense of the N phase. This gives rise to the second stage of the
mixed phase region (middle light blue region in Fig. 13i). After extensive
annealing at sufficiently high temperature and long time, the film can convert
to pure S phase in the final third stage (right bright green region in Fig.
13i).

The annealing process also made it possible to tune the superconductivity of
the single-layer FeSe/SrTiO3 film by varying the carrier concentrationSLHe .
The carrier concentration of the S phase during the annealing process can be
obtained by calculating the area of the electron-like Fermi surface near M. It
has been shown that during the vacuum annealing process, the S phase gets more
and more electron-doped, with the electron concentration increasing from 0.07
to 0.12 electrons per FeSLHe . The corresponding gap measurements indicate
that the gap size and the gap closing temperature increase with the annealing
process (Fig. 13i). A gap of $\sim$19 meV and a gap closing temperature of
$\sim$ 65 K were achieved for the annealed single-layer FeSe/SrTiO3 film (Fig.
13i)SLHe . This provides first electronic evidence of superconductivity at
$\sim$65 K in the single-layer FeSe/SrTiO3 films that was also confirmed by
other groupsSTan ; JJLee . Such a gap increase with vacuum annealing was also
observed in the STM/STS measurementsWHZhangPRB .

Since the S phase appears in the early stage of vacuum annealing of the
single-layer FeSe/SrTiO3 films which coexists with the N phaseSLHe , it is
intriguing to ask whether the S phase becomes superconducting as long as it
appears. To address this issue, the evolution of the electronic structure and
the energy gap as a function of the carrier concentration is studied for the S
phase of the single-layer FeSe filmsJFHe . It was found that, at low
temperature, there is a gap opening along the underlying electron-like Fermi
surface near M at low carrier concentration, as seen from the symmetried
photoemission spectra around the Fermi surface (Fig. 14b). As the carrier
concentration of the S phase increases, the gap size decreases and reaches
zero at a critical carrier concentration around 0.089 electrons/Fe (Fig. 14a
and 14b). Further increase of the carrier concentration results in another gap
opening at low temperature. From the appearance of the coherence peak and the
gap closing with increasing temperature (Fig. 14d), this high carrier
concentration gap is apparently the superconducting gap we have discussed
before. For the low carrier concentration gap, it shows quite different
behaviors from the high carrier concentration superconducting gap. The broad
photoemission peaks, weak temperature dependence of the gap (Fig. 14c) and its
relatively large size compared to the superconducting gap are similar to those
observed in the insulating heavily-underdoped cupratespyy . We believe the low
carrier concentration energy gap is consistent with an insulating gap.
Therefore, there is an insulator-superconductor transition across the critical
carrier concentration of 0.089 in the S phase of the single-layer FeSe/SrTiO3
filmsJFHe . It was noted that such a transition exhibits many similar
behaviors as that found in the heavily underdopd cupratespyy . At present, the
origin of this insulator-superconductor transition remained to be understood
which may be associated with the two-dimensionality that enhances electron
localization or correlation. In a multi-orbital system like the iron-based
compounds, the carrier density-induced Mott transition may be realized in an
orbital-selective fashionRYuOrbitalS . Such an orbital-selective Mott
transition has been examined in AxFe2-ySe2 superconductorMYi . In the S phase
of the single-layer FeSe/SrTiO3 films, it is possible that the same mechanism
is at operation for the observed carrier concentration-induced insulator-
superconductor transitionJFHe .

The electronic structure and superconductivity of the FeSe/SrTiO3 films show
drastically different layer-dependence from that of the FeSe/graphene films
(Fig. 8)CLSong , as well as FeSe films grown on the MgO substrateRSchneider .
For the FeSe/SrTiO3 films, while single-layer FeSe/SrTiO3 film can become
superconducting, STM/STS does not find signature of superconductivity in the
second and multiple-layer FeSe/SrTiO3 films regardless of how the samples are
annealedQYWangCPL ; ZLiSTM . Such a dramatic difference between the single-
layer, double-layer and multiple-layer FeSe/SrTiO3 films is surprising if one
considers the usual layer-dependence found in the FeSe/graphene filmsCLSong .
To address this issue, a comparative investigation between the single-layer
and double-layer FeSe/SrTiO3 films is carried out by performing a systematic
angle-resolved photoemission study on the samples annealed in vacuumXLiu . The
as-prepared double-layer FeSe/SrTiO3 film exhibits electronic structure that
is similar to the N phase of the single-layer FeSe/SrTiO3 film (Fig. 15). The
double-layer FeSe/SrTiO3 film shows a quite different doping behavior from the
single-layer film. It is hard to get doped and remains in the
semiconducting/insulating state even under an extensive annealing condition.
However, after sufficient vacuum annealing, the double-layer FeSe/SrTiO3 film
may follow similar doping trend as in the single-layer film although
superconductivity has not been realized. Such a behaviour is understood as
originating from the much reduced doping efficiency in the bottom FeSe layer
of the double-layer FeSe/SrTiO3 film from the FeSe-SrTiO3 interface when the
dominant doping process comes from the electron transfer from the SrTiO3
surfaceXLiu .

Detailed ARPES study on the layer-dependence of the electronic structure for
the FeSe/SrTiO3 films have been reported in STan ; JJLee  and typical results
are shown in Fig. 16STan . It is found that the electronic structure of the
FeSe/SrTiO3 films becomes similar when the number of layers is above two. In
this case, the Fermi surface is quite different from the S phase of the
superconducting single-layer FeSe/SrTiO3 film in that: the Fermi surface of
the multi-layer FeSe/SrTiO3 films consists of four strong spots near the M
point, and there are bands crossing the Fermi level around the $\Gamma$ point
(Fig. 16a). It was also found that the multi-layer FeSe/SrTiO3 films
experience a transition at a high temperature where the electronic structure
exhibits a change above and below the transition temperatureSTan . The
transition temperature increases as the number of FeSe layers decreases (Fig.
16b). Such a transition is attributed to the spin-density-wave formation and
the layer-dependent transition temperature is associated with the strain
difference in samples with different layersSTan .

We note that the N phase of the single-layer FeSe/SrTiO3 film is not observed
in STan ; JJLee . Also there are discrepancies on the electronic structure of
the double-layer FeSe/SrTiO3 films between different groupsXLiu ; STan ; JJLee
. The difference can be attributed to the different preparation conditions
used and possible mixing of the single-layer and double-layer FeSe/SrTiO3
films. In our case, we have clearly observed pure N phase in both the single-
layer and double-layer FeSe/SrTiO3 filmsSLHe ; XLiu . In fact, the electronic
structure of the N phase in the single-layer and double-layer FeSe/SrTiO3
films is rather similar to that found in multi-layer filmsSTan ; JJLee  except
for some qualitative band position difference. The electronic structure of the
N phase in the single-layer and double-layer FeSe/SrTiO3 films also experience
a transition at high temperature (Fig. 17), the transition temperature in
single-layer FeSe/SrTiO3 is the highest among all the FeSe/SrTiO3 films and
basically follows the trend found for multi-layer FeSe/SrTiO3 filmsSTan . Such
a transition is reminiscent of the electronic structure change in the parent
compound BaFe2As2 across the structural/magnetic transition temperature
($\sim$140 K for BaFe2As2)(Fig. 17e and 17f)GDLiu . In bulk FeSe, there is a
structural transition near 90 KTMMcQueen . Recently, an electronic structure
change is also reported in the ARPES stiudy of the bulk FeSe crystals across
this structural transtionKNakayama ; TShimojima . Since there is no static
magnetic transition found in bulk FeSe, whether the electronic structure
transition in the FeSe/SrTiO3 films is caused by spin-density-wave formation
needs further investigations and direct magnetic measurements.

The dramatic difference of superconductivity between the FeSe/SrTiO3 films and
the FeSe/graphene films points to the key role played by the growth substrate.
Furthermore, as the superconductivity of the FeSe superconductor is found to
be sensitive to pressure in the bulk formSMedvedev  or strain in the thin film
formYFNieFeSe ; FNebashima , it is natural to ask whether the strain may play
the key role in enhancing superconductivity in the FeSe/SrTiO3 films. As the
bulk FeSe has a lattice constant of 3.76 $\AA$ and SrTiO3 has a lattice
constant of 3.90 $\AA$, when FeSe films are epitaxially grown on the SrTiO3
substrate, the FeSe films will experience a tensile stress from the underlying
SrTiO3 substarteQYWangCPL . To check on the effect of strain on the
superconductivity of the FeSe films, different substrates with disparate
lattice constants have been used to grow FeSe filmsRPengPRL ; RPengNC . With
the substrate varying from SrTiO3 to SrTiO3/KTaO3 (SrTiO3 buffer-layers grown
on KTaO3 substrate as the substrate for FeSe films), to BaTiO3/KTaO3 (BaTiO3
buffer layers grown on KTaO3 substrate as the substrate for FeSe films), there
are changes on the corresponding electronic structures of the FeSe films (Fig.
18a and 18b), but the gap closing temperature shows little change within the
range of (70$\pm$5) KRPengPRL ; RPengNC . This seems to indicate that the
tensile stress on the FeSe films exerted from the underlying substrate does
not affect superconductivity of the FeSe films significantly.

The latest episode sees the observation of replica band in the band structure
of the superconducting single-layer FeSe/SrTiO3 films (Fig. 19)JJLee . As
shown in Fig. 19, the main hole-like band near $\Gamma$ point (band d in Fig.
19b), the electron-like band (band a in Fig. 19c) and hole-like band (band b
in Fig. 19c) all produce weak “replica” bands that are $\sim$100 meV below the
original bands. Such replica bands persist above the gap opening
superconducting temperature (Fig. 19d-g). The replica bands appear weak in
other measurementsDFLiu ; SLHe ; STan  possibly because of the photoemission
matrix element effect causes by different measurement conditions. These
replica bands have been understood as due to the presence of bosonic modes,
most probably optical phonons in SrTiO3, that couple to the FeSe electrons
with only a small momentum transferJJLee . It was also suggested that such
interfacial coupling could assist superconductivity in most channels and this
coupling is responsible for the Tc enhancement in the single-layer FeSe/SrTiO3
filmsJJLee .

###  3.3 Transport and magnetic measurements of FeSe/SrTiO3 films

Although ARPES and STM/STS have observed gap opening and the behaviors of the
gap are consistent with the superconducting gap such as the sharp coherence
peak, the BCS form of the gap size as a function of temperature, and the
particle-hole symmetry around the Fermi surfaceQYWangCPL ; DFLiu ; SLHe ; STan
, direct evidence from the transport and magnetic measurements is necessary to
establish whether the FeSe/SrTiO3 films are truly superconducting or not. Such
measurements on ultra-thin films are challenging because of the complication
of the sample deterioration to the air, SrTiO3 substrate conductance and very
weak magnetic signal. Initial transport measurement on a five-layer
FeSe/SrTiO3 film covered by 20-nm-thick amorphous silicon protection layer saw
a transition with an onset temperature of $\sim$53 K (Fig. 20a)QYWangCPL .
Later on, the single-layer FeSe/SrTiO3 film was better protected by covering a
10-layer FeTe film followed by a 30-nm-thick amorphous silicon layer so that
the sample can be stable at ambient condition for a relatively long time. The
resistance as a function of temperature clearly reveals the appearance of
superconductivity: the resistance begins to drop at 54.5 K and reaches zero at
23.5 K with an onset Tc of 40.2K (Fig. 20b)WHZhangCPL . Magnetic measurement
on the same sample reveals a diamagnetic response with an abrupt change of
both in-phase and out-of-phase signal at 21 K (Fig. 20d) that is consistent
with the zero resistance critical temperature from the transport measurement
(Fig. 20b). This has unambiguously demonstrated that the single-layer
FeSe/SrTiO3 film under measurement is superconducting although the measured Tc
is not as high as that expected from the STM/ARPES measurements. This is
understandable because it is known that the superconducting transition
temperature of the FeSe/SrTiO3 films is sensitive to the carrier
concentrationSLHe . Also the protection layer may affect the superconductivity
of the single-layer FeSe/SrTiO3 film, in particular, FeTe is known to be
magnetic at low temperature that may suppress the superconductivity of the
adjacent FeSe film. Superconductivity is also reported in double-layer
FeSe/SrTiO3 films from the transport measurementsYSun . Hints of higher
transition temperatures are spotted in some FeSe/SrTiO3 filmsLZDeng  that need
further investigations.

It is ideal to carry out in situ transport and magnetic measurements on the
FeSe/SrTiO3 films in order to remove the effect of sample damage and
protection layers. The in situ transport measurements have been performed
lately on the single-layer FeSe/SrTiO3 filmJFGe . Surprisingly, the measured
zero resistance temperature reaches as high as 109 K (Fig. 20c) that is well
above the Tc$\sim$80 K expected from the 20.1 meV gap from the STM/STS
measurementsQYWangCPL  and the Tc$\sim$65 K from ARPES measurementsSLHe ; STan
. Further measurements are needed to reproduce and confirm this exciting
result.

##  4 Implications and theoretical understanding

###  4.1 Implications

The discovery of high temperature superconductivity in the single-layer
FeSe/SrTiO3 films has important implications in understanding the
superconductivity mechanism and the pairing symmetry in the iron-based
superconductors. In most of the iron-based superconductors, the Fermi surface
consists of hole-like Fermi surface sheets near the Brillouin zone center
($\Gamma$ point) and electron-like Fermi surface sheets near the zone corner
M($\pi$,$\pi$) point (Fig. 2)DJSingh . It has been proposed that the electron
scattering between the hole-like bands around $\Gamma$ and electron-like bands
near M is responsible for electron pairing and superconductivity of the iron-
based superconductors has a dominant s$\pm$ superconducting order
parameterKuroki ; Nesting ; FWangPRL ; AVChubukov ; VStanev ; FWangEPL ;
IIMazinNP . The absence of Fermi surface near $\Gamma$ in the superconducting
single-layer FeSe/SrTiO3 filmDFLiu , together with that only electron-like
Fermi surface sheets are observed in the intercalated AxFe2-ySe2
superconductorsDLFengIFS ; TQianAFeSe ; DXMouPRL , rules out the necessity of
the electron scattering between the hole-like bands near $\Gamma$ and
electron-like bands near M in this “Fermi nesting” picture.

The observation of the nearly isotropic superconducting gap around the
electron-like Fermi surface near M point (Fig. 12c)DFLiu  also provides
crucial information in understanding the pairing symmetry of the iron-based
superconductors. With the absence of hole-like Fermi surface near $\Gamma$,
electrons can only scatter across the Fermi surface sheets between M points
which is predicted to result in a d-wave superconducting gapKuroki ; TAMailer
; FWangEEScattering ; TDas . The dxy-like superconducting order parameter is
obviously ruled out because it will produce zero gap on the electron-like
Fermi surface near M. With an alternative d${}_{x^{2}-y^{2}}$-like
superconducting order parameter that can avoid the direct gap nodes, it is
argued that two Fermi surface sheets around a given M point with opposite
phases can also give rise to gap nodes around the Fermi surfaceIMazinNode . In
this case, it remains not consistent with the observation of nodeless gap on
the electron-like Fermi surface near M point. The superconducting pairing
symmetry in the single-layer FeSe/SrTiO3 films and the AxFe2-ySe2 system
remains puzzling that asks for further experimental and theoretical efforts.

The different behaviors between the FeSe/graphene and FeSe/SrTiO3 films
clearly indicate the critical role played by the interface in giving rise to
the high temperature superconductivity. The discovery of high temperature
superconductivity in the single-layer FeSe/SrTiO3 films represents the first
clear case of interface-enhanced superconductivity. Interface (and surface)
superconductivity has a long history which is expected to increase
superconducting temperatureGinzburg . Superconductivity has been reported in
various interface systems, including those between two insulatorsNReyren ,
between one insulator and one metalAGozar , and between one metal and one
semiconductorTZhang . However, in all these cases, the observed Tc in the
interface is not obviously higher than the maximum Tc of its individual
constituents. In the single-layer FeSe/SrTiO3 films, its superconducting
transition temperature is much higher than the maximum Tc of either FeSe
system or SrTiO3 system, thus establishing a convincing case of interface
superconductivity. This discovery proves the concept of interface-enhancement
of superconductivity and opens a door to further explore for new
superconductors with higher Tc.

###  4.2 Theoretical understanding

The FeSe/SrTiO3 films have attracted much theoretical attention, in regard to
understanding its unique electronic structure, carrier doping mechanism and
the possible origin of high temperature superconductivityKLiu ; YYXiang ;
TBazhirov ; FWZheng ; HYCao ; QQYe ; JBang ; TBerlijn ; NNHao . By using
first-principles calculations, the atomic and electronic structures of the
single-layer and double-layer FeSe/SrTiO3 films were studiedKLiu . The band
structure of free single-layer FeSe film shown (Fig. 21a) is similar to that
of the bulk FeSe (Fig. 4)ASubedi . It is found that both single-layer and
double-layer FeSe films on the SrTiO3 substrate behave like a slightly doped
semiconductor with a collinear antiferromagnetic order on the Fe ions and a
Dirac cone-like band around the $\Gamma$ point (Fig. 21b)KLiu . These results
show difference from the measured results, for both the N phase and S phase of
the single-layer and double-layer FeSe/SrTiO3 filmsDFLiu ; SLHe ; STan ; XLiu
. It was further shown that the SrTiO3 substrate-induced tensile strain tends
to stabilize the collinear antiferromagnetic state in FeSe thin film by
enhancing of the next-nearest-neighbor super-exchange antiferromagnetic
interaction bridged through the Se atomsHYCao . The calculated Fermi surface
considering the collinear antiferromagnetic order and electron-doping can be
consistent with experimental observations that the hole-like Fermi surface
sheets near $\Gamma$ disappearHYCao . In the presence of constrained
magnetization, it was also shown that the observed Fermi surface can be
described by the checker-board antiferromagnetic spin patternTBazhirov ;
FWZheng . In this case, it was found that the system has a considerable charge
transfer from SrTiO3 substrate to the FeSe layer, and so has a self-
constructed electric field. The disappearance of the Fermi surface around the
$\Gamma$ point can also be explained by the antiferromagnetic checkerboard
phase with charge doping and electric field effectsFWZheng . These results
show considerable consistency with the behavior of the N phase of the
FeSe/SrTiO3 filmSLHe ; XLiu . So far, most theoretical calculations involve
antiferromagnetic order, and overall show some qualitative agreement with the
experimental observations. However, we note that, the ARPES results are only
suggestive that the N phase of the FeSe/SrTiO3 films may be magneticSLHe  or
the low temperature form of the multi-layer FeSe/SrTiO3 films may be in the
spin-density-wave stateSTan , further direct evidence is needed to pin down on
their magnetic nature.

It is clear from ARPES measurements that the superconducting S phase of the
single-layer FeSe/SrTiO3 films is electron-dopedDFLiu ; SLHe ; STan ; JJLee .
The origin of the electron-doping may have two possibilities: oxygen vacancy
formation on the SrTiO3 surface that gives rise to electron doping, and the
formation of Se vacancies in the FeSe filmDFLiu . Further ARPES results
substantiate the picture of the oxygen vacancy formation on the SrTiO3
surfaceSTan ; XLiu . The role of the oxygen vacancy on the top layer of the
SrTiO3 substrate was also investigated by first principles calculationsJBang .
It shows that the oxygen vacancies strongly bind the FeSe layer to the
substrate giving rise to a (2$\times$1) reconstruction, and also serve as the
source of electron doping. Theoretical investigation on the doping effect of
Se vacancies in the FeSe/SrTiO3 films leads to a somehow counter-intuitive
result that, in terms of the Fe-3d bands, Se vacancies behave like hole
dopants rather than electron dopants as usually expectedTBerlijn . Such
results are considered to exclude Se vacancies as the origin of the large
electron pockets measured by ARPESTBerlijn .

The most prominent issue concerning the superconductivity of the single-layer
FeSe/SrTiO3 films is on the origin of its dramatic Tc enhancement. The
discovery of high temperature superconductivity in the single-layer
FeSe/SrTiO3 films was motivated by the idea that strong electron-phonon
coupling can enhance superconductivityQYWangCPL . Subsequent study on the
effects of screening due to the SrTiO3 ferroelectric phonons on the Cooper
pairing in FeSe shows that it can significantly enhance the energy scale of
Cooper pairing and even change the pairing symmetryYYXiang . It was shown that
the role of the SrTiO3 substrate in increasing the electron-phonon coupling
and the resulting higher Tc is two-fold. First, the interaction of the FeSe
and TiO2 terminated face of SrTiO3 prevents the single-layer FeSe from
undergoing a shearing-type (orthorhombic) structural phase transition. Second,
the substrate allows an antiferromagnetic ground state of FeSe which opens
certain electron-phonon coupling channels within the single-layer that are
prevented by symmetry in the non-magnetic phaseQQYe . The replica bands
observed in the superconducting single-layer FeSe/SrTiO3 films provide
experimental evidence on the coupling of electrons in FeSe layer with the
SrTiO3 phononsJJLee . Further theoretical analysis suggests that such
interfacial electron-phonon coupling assists superconductivity in most
channels, and is responsible for raising the superconducting temperature in
single-layer FeSe/SrTiO3 filmsJJLee .

##  5 Summary and Perspective

In this brief review, we have shown that the FeSe superconductor and related
systems have exhibited rich and fascinating phenomena and physical properties.
Since the report of possible high temperature superconductivity in the single-
layer FeSe/SrTiO3 filmsQYWangCPL , great progress has been made in
understanding related issues both experimentally and theoretically. Some
questions are answered, and more questions are asked. Since this is a
burgeoning and fast-evolving field, it is natural that many issues remain to
be addressed. Here we briefly list some further issues that are either
particular to the FeSe/SrTiO3 systems or more general to the iron-based
superconductors.

(1). Interface superconductivity? So far many experiments point to the
interface superconductivity in the single-layer FeSe/SrTiO3 films. More
decisive evidence is needed to pin down on the nature of the interface
superconductivity. What new effects can be expected from an interface
superconductivity system?

(2). Doping mechanism? It has been shown that during the vacuum annealing
process, the single-layer FeSe/SrTiO3 films can be electron-doped. It has also
been proposed that oxygen vacancies on the SrTiO3 surface may play the role of
electron-dopingDFLiu ; SLHe ; STan . How to directly prove the role of oxygen
vacancies in electron-doping? Recent STM measurements on the vacuum annealed
single-layer FeSe/SrTiO3 film found thatWHZhangPRB , there are some extra Se
adatoms on the surface of the as-prepared FeSe film and the sample is
insulating. In the initial stage of the annealing process, these extra Se
adatoms are gradually removed. Further annealing leads to the formation of Se
vacancies. What are the role of these Se adtoms and Se vacancies on the doping
of FeSe films?

(3). Role of electron-phonon coupling? There is experimental evidence to show
the existence of electron-phonon coupling in the FeSe/SrTiO3 filmsJJLee .
There are theoretical arguments that such electron-phonon coupling can enhance
superconductivityQYWangCPL ; YYXiang ; QQYe ; JJLee . However, more
experimental evidence is needed to prove that such an electron-phonon coupling
is the cause of the Tc enhancement in the single-layer FeSe/SrTiO3 films.

(4). Pairing mechanism? The observation of the distinct Fermi surface topology
in the superconducting FeSe/SrTiO3 filmsDFLiu  has ruled out the possibility
of Fermi surface nesting picture in giving rise to superconductivity in the
single-layer FeSe/SrTiO3 films. With only electron-pockets present near M
point, what is the pairing mechanism then?

(5). Pairing order parameter? With only electron pockets present near M points
in the single-layer FeSe/SrTiO3 filmsDFLiu ; SLHe ; STan ; JJLee , it is
predicted that d-wave pairing may dominateKuroki ; TAMailer ;
FWangEEScattering ; TDas  which is not consistent with the experimental
results of nearly isotropic nodeless superconducting gapDFLiu . What can be
the superconducting order parameter for the superconducting single-layer
FeSe/SrTiO3 films?

(6). Theoretical understanding of electron structure. The unique electronic
structure of the N phase and S phase of the single-layer FeSe/SrTiO3 film and
the multi-layer FeSe/SrTiO3 films poses a challenge to band structure
calculations and theoretical understandings. More efforts are needed to
understand the electronic structure by including the effect of the substrate,
vacancy and disorder, electron correlation, the spin-orbit coupling and so on.

(7). Inconsistency of superconductivity measurements. There are
inconsistencies among different measurements on the superconducting properties
of the FeSe/SrTiO3 films. First, transport measurements on the single-layer
FeSe/SrTiO3 films give different Tc, varying from 23.5 K (zero
resistanceWHZhangCPL ) to 109 KJFGe . Second, there is an obvious difference
of Tc on single-layer FeSe/SrTiO3 films between transport
measurementsQYWangCPL ; WHZhangCPL ; YSun ; JFGe  and STM/ARPES
measurementsQYWangCPL ; DFLiu ; SLHe ; STan . Third, for multi-layer
FeSe/SrTiO3 films, STM/STS and ARPES indicate they are not
superconductingQYWangCPL ; XLiu . However, transport measurements show sign of
superconductivity in double-layer FeSe/SrTiO3 filmYSun ,five-layer FeSe/SrTiO3
filmQYWangCPL . How to reconcile these differences?

(8). Nature of the N phase and S phase in the single-layer FeSe/SrTiO3 films.
With vacuum annealing, two different phases (N phase and S phase) with
distinct electronic structures are clearly observedSLHe . It remains unclear
about the real difference between the N phase and S phase, i.e., whether the
electronic structure difference is caused by the difference in crystal
structure, composition or the carrier concentration. It is also not clear how
the N phase and S phase distribute in a real space.

(9). Magnetic state? ARPES has provided suggestions that the N phase of the
single-layer FeSe/SrTiO3 film may be magneticSLHe , and the low-temperature
form of the multi-layer FeSe/SrTiO3 films may be in the spin-density-wave
stateSTan . Direct evidence is needed to pin down on their magnetic nature.

(10). Further enhancement of Tc? The superconducting transition temperature of
the FeSe/SrTiO3 film is sensitive to carrier concentrationSLHe . Tc has not
reached the maximum in the doping range studied; more electron doping may
result in even higher TcSLHe . For double-layer or multi-layer FeSe/SrTiO3
films, it has been found that the absence of superconductivity is related to
the insufficient electron dopingXLiu . It is interesting to explore, if
sufficient electron doping is provided, whether double-layer or multi-layer
FeSe/SrTiO3 films can become superconducting or exhibit even higher Tc than
the single-layer case. So far, SrTiO3 and related BaTiO3 substrate are proven
to be magic in producing high temperature superconductivity in the single-
layer FeSe films. Are there other substrates present that can produce similar
effect and even higher Tc?

The surprising discovery of high temperature superconductivity in the
FeSe/SrTiO3 films has provided a new platform for investigating interface
superconductivity, superconductivity mechanism of the iron-based
superconductors, and opened a new path in exploring for new high temperature
superconductors. Theoretical calculations suggest robust topological phases
may be realized in the single-layer FeSe/SrTiO3 films which is intertwined
with superconductivityNNHao . The ultra-thin nature of the FeSe/SrTiO3 films
is also ideal for making heterostructuresWLWang ; the topological
insulator/superconductor heterostructure has been proposed as a prototype to
detect Majorana fermionsLFu . The ideal two-dimensional character, dichotomy
between single-layer and double-layer films, and high Tc superconductivity
open a door for potential device fabrication and applications. We have already
witnessed surprises brought up by the single-layer FeSe films, we can expect
more surprises to come in the near future.

∗Corresponding author<EMAIL_ADDRESS>
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Acknowledgement We thank Wenhao Zhang, Yun-Bo Ou, Fansen Li, Chenjia Tang,
Qing-Yan Wang, Zhi Li, Lili Wang, Xi Chen, Xucun Ma, Qikun Xue, Jiangping Hu,
Q. M. Si and Dunghai Lee for collaborations and helpful discussions. XJZ
thanks financial support from the NSFC (11190022,11334010 and 11374335) the
MOST of China (973 program No: 2011CB921703 and 2011CBA00110) the Strategic
Priority Research Program (B) of the Chinese Academy of Sciences (Grant No.
XDB07020300).

Figure 1: Several major classes of the iron-based superconductors. All of
these iron-based superconductors contain FeSe or FeAs building blocks (the
iron ions are shown in red and the pnictogen/chalcogen anions are shown in
gold) that are essential for the occurrence of superconductivity. Reprinted
from JPaglione . Figure 2: Brillouin zones of the iron-based superconductors
containing one iron and two irons in a unit cell and the orbital-related
electronic structure. (a) FeAs lattice indicating As above and below the Fe
plane. Dashed green and solid blue squares represent 1- and 2-Fe unit cells,
respectively. (b) Schematic two-dimensional Fermi surface in the 1-Fe
Brillouin zone whose boundaries are indicated by a green dashed square. The
arrow indicates folding wave vector to convert from 1-Fe zone to the 2-Fe
zone. (c) Fermi sheets in the folded Brillouin Zone whose boundaries are now
shown by a solid blue square. In this case, the size of the first Brillouin
zone is half of that of the 1-Fe case (dashed green squeare). Reprinted from
Hirschfeld . (d) A typical orbital characters of the bands in the iron
pnictides as shown in Ref.SGraser ; YZhangorbital . (e) The corresponding
Fermi surface sheets of the five-band model for the undoped compound in
Ref.SGraser . Figure 3: Crystal structure, magnetic structure and phase
diagram of bulk Fe1.01Se and the phase diagram of the Fe1+ySexTe1-x system.
(a) Schematic crystal structure of $\beta$-FeSe. Four unit cells are shown to
reveal the layered structure. Reprinted from MKWu . (b) Magnetic structures of
$\alpha$-FeTe (upper panel) and BaFe2As2 (lower panel), which are shown in the
primitive Fe square lattice. Reprinted from WBao . (c) Phase diagram of
Fe1.01Se as a function of pressure. Reprinted fromSMedvedev . (d) Phase
diagram of Fe1+ySexTe1-x with y $\sim$0 as a function of x and T. Reprinted
from Nkatayama .

Figure 4: Fermi surface and band structure of the bulk FeSe from band
structure calculations and angle-resolved photoemission measurements. (a) (b)
LDA calculated Fermi surface and band structure of bulk FeSe from ASubedi .
(c) (d) ARPES intensity and corresponding EDCs, respectively, along the
$\Gamma$-M cut at T = 30 K. (e) Schematic band diagram around the M point
below/above the structural transition temperature Ts. Red and blue curves
indicate the dyz and dzx orbitals, respectively. Solid and dashed curves
represent the band dispersion along the (0, 0)-($\pi$, 0) and (0, 0)-(0,$\pi$)
directions (longer Fe-Fe and shorter Fe-Fe directions) of the untwined
crystal, respectively. (f) (g) Comparison of the second-derivative plot of the
near-EF ARPES intensity around the $\Gamma$ point between T = 30 and 120 K.
(h) Experimental band dispersion around the $\Gamma$ point at T = 30 K (blue
circles) and 120 K (red circles), extracted by tracing the peak maxima of the
EDCs divided by the Fermi-Dirac function. Reprinted from KNakayama . Figure 5:
Fermi surface and band structure of FeTe. (a)-(f) Electron structure of
Fe1.06Te in paramagnetic state above the magnetic transition. (a) Fermi
surface of Fe1.06Te measured at 135 K. (b) The spectral weight distribution
around EF. (c) and (d) The EDCs along cut 1 and 2 labelled in (a),
respectively. (e) The temperature dependence of the resistivity for Fe1.06Te.
(f) The photoemission intensities along the M-$\Gamma$-X high-symmetry line in
the paramagnetic state. (g)-(j) Electron structure of Fe1.06Te in the magnetic
state. (g) Fermi surface of Fe1.06Te measured at 15 K. (h) and (i) The EDCs
along cut 1 and cut 2 labelled in (g), respectively. (j) The photoemission
intensities along the M-$\Gamma$-X high-symmetry lines in the magnetic state.
Reprinted from YZhangFeTe . (k) Plot of the EDCs at the M point at various
temperatures. (l) Plot of the M band binding energy and linewidth at the M
point together with the (0.5, 0, 0.5) antiferromagnetic Bragg peak intensity
versus temperature. Reprinted from ZKLiuFeTe .  Figure 6: Fermi surface, band
structure and superconducting gap of Fe(Te,Se). (a) Fermi surface of
Fe1.04Te0.66Se0.34. (b) The Fermi surfaces are constructed based on the
measured Fermi crossings. (c) The photoemission intensity along the cut 1 in
the $\Gamma$-M direction and (d) its second derivative with respect to energy.
(e) The data in panel c is re-plotted after dividing the angle integrated
energy distribution curve. (f) The calculated Fermi surface of
Fe1.04Te0.66Se0.34. Reprinted from FChen . (g) Three-dimensional
representation of the superconducting gap with the Fermi surface topology of
FeTe0.55Se0.45. Reprinted from HMiaoFeTeSe . (h) Fermi surface-angle
dependence of superconducting gap size of FeTe0.6Se0.4. Reprinted from
KOkazakiFeTeSe  Figure 7: Band structure, Fermi surface and superconducting
gap of AxFe2-ySe2. Band structure and photoemission spectra of AxFe2-ySe2
superconductors measured along two high symmetry cuts. Cut locations are
illustrated in the top-left and top-right inserts. (a)(c) Measured band
structure of (Tl0.58Rb0.42)Fe1.72Se2 along cut1 and cut2, respectively. (b)(d)
Their corresponding EDC second derivative images. (e)(f) Fine measurement of
the band structure in red square of (c) and its corresponding EDC second
derivative images. (g) Fermi Surface of (Tl0.58Rb0.42)Fe1.72Se2. (h) Momentum
dependent superconducting gap size for the $\beta$ Fermi surface sheet around
$\Gamma$ and $\gamma$ Fermi surface sheet around M, respectively. Reprinted
from DXMouPRL ; DXMouReview .  Figure 8: Normalized tunneling conductance
spectra and Tc as a function of the film thickness in the FeSe/graphene films.
Normalized tunneling conductance spectra on (a) 8-layer and (b) 2-layer
FeSe/graphene films measured at different temperatures. (c) Superconducting
transition temperature Tc vs the inverse of the film thickness d. Reprinted
from CLSong .  Figure 9: STM/STS measurements on an as-grown FeSe/graphene
films about 30-layer thick. (a) Topographic image of the FeSe/graphene film.
The step height is 5.5 $\r{A}$. (b) Atomic-resolution STM topography of the
FeSe/graphene film. The bright spots correspond to the Se atoms in the top
layer. a and b correspond to either of the Fe-Fe bond directions. (c)
Temperature dependence of differential conductance spectra at different
temperatures. (d) Schematic of the unfolded Brillouin zone and the Fermi
surface (green ellipses). The nodal lines for coskxcosky and (coskx+cosky )
gap functions are indicated by black and red dashed lines, respectively.
Reprinted from CLSongScience .  Figure 10: Discovery of possible high
temperature superconductivity in single-layer FeSe/SrTiO3 film. (a) Schematic
structure (side-view) of the FeSe films on the SrTiO3 substrate along the
c-axis. (b) Tunneling spectrum taken on the single-layer FeSe/SrTiO3 film at
4.2 K revealing the appearance of superconducting gap. Four pronounced
coherence peaks appear at $\pm$20.1mV and $\pm$9mV, respectively. (c) The STM
image of the FeSe film with both single-layer (1UC) and double-layer (2UC)
FeSe/SrTiO3 films. (d) Tunneling spectrum taken on the double-layer
FeSe/SrTiO3 films. Reprinted from QYWangCPL . Figure 11: Distinct Fermi
surface and band structures of the superconducting single-layer FeSe/SrTiO3
Film. (a) Fermi surface mapping of the single-layer FeSe/SrTiO3 film measured
at 20 K. (b) Fermi-surface mapping of (Tl,Rb)xFe2-ySe2 superconductor (Tc = 32
K)DXMouPRL . (c) Fermi-surface mapping of Ba0.6K0.4Fe2As2 superconductor (Tc =
35 K)GDLiu . (d) Fermi surface of $\beta$-FeSe by band-structure calculations
for kz = 0 (blue thick lines)ATamai . For convenience, the four equivalent M
points are labelled as M1($\pi$, $\pi$), M2(-$\pi$, $\pi$), M3(-$\pi$, -$\pi$)
and M4($\pi$, -$\pi$). (e) Band structure along the cut crossing the $\Gamma$
point (left panel) and along the cut crossing the M3 point (right panel). The
pink dashed line in the left panel shows schematically a hole-like band near
the $\Gamma$ point with its top at 80 meV below the Fermi level. The purple
dashed line in the right panel shows schematically an electron-like band with
its bottom at 60 meV below the Fermi level. Reprinted from DFLiu . Figure 12:
Temperature and momentum dependence of the superconducting gap in the
superconducting single-layer FeSe/SrTiO3 film. (a) Photoemission spectra
(EDCs) at the Fermi crossings of the electron-like $\gamma$ Fermi surface near
M and their corresponding symmetrized spectra (b) measured at different
temperatures. (c) Momentum dependence of the superconducting gap along the
$\gamma$ Fermi surface. (d) The Fermi surface mapping near M3 and the
corresponding Fermi crossings. The violet circle represents the Fermi surface.
The red solid circles represent measured Fermi momenta that are labeled as P1
to P15. (e) Temperature dependence of the superconducting gap. Reprinted from
DFLiu . (f) (g) Band structure along $\Gamma$-M cut measured at 70 and 23 K,
respectively. The corresponding MDCs (momentum distribution curves) at the
Fermi level for the two measurements are shown in (h). The two MDC peaks show
little change in their positions above and below the gap opening temperature.
Reprinted from SLHe .

F

Figure 13: Electronic structure of the S phase and the N phase and phase
diagram of the single-layer FeSe/SrTiO3 film with vacuum annealing. (a) Fermi
surface of the S phase of the single-layer FeSe/SrTiO3 film. (b-d)
Corresponding band structure of the S phase along the $\Gamma$, M2 and M3
cuts, respectively. (e) Fermi surface of the N phase of the single-layer
FeSe/SrTiO3 film. (f-h), Corresponding band structure of the annealed single-
layer FeSe/SrTiO3 film along the $\Gamma$, M2 and M3 cuts, respectively. The
band structures shown in (b,c,d) and (f,g,h) are second derivative of the
original band with respect to energy. (i) Schematic phase diagram of the
single-layer FeSe film during the annealing process. The inset shows the Fermi
surface corresponding to each stage. Reprinted from SLHe . Figure 14: Evidence
of an insulator-superconductor transition in the single-layer FeSe/SrTiO3
film. (a) Phase diagram of the S phase in the single-layer FeSe/SrTiO3 film
that shows the decrease of the insulating energy gap (black solid diamond)
with increasing doping at low doping side and the increase of the
superconducting gap (red solid triangle) and the corresponding superconducting
transtion temperature Tc (blue empty square) with increasing doping at high
doping side. There is an insulator-superconductor transition near $\sim$0.09
doping level. (b) Doping-evolution of the symmetrized EDCs at a Fermi momentum
kF along the cut crossing M2 point. (c) (d) The variation of the energy gap at
different temperatures at low doping level and high doping level,
respectively. Reprinted from JFHe . Figure 15: Fermi surface and band
structure evolution of the double-layer FeSe/SrTiO3 film annealed at a
constant annealing temperature of 350∘C in vacuum for different times. (a)
Fermi surface and band structure evolution of the double-layer FeSe/SrTiO3
film annealed at a constant annealing temperature of 350 ∘C in vacuum for
different times. The sequences 1 to 6 correspond to an accumulative time of
15, 30.5, 46.5, 66.5, 87.5, and 92.5 hours, respectively. (a) Fermi surface
evolution as a function of the annealing time. (b-d) Band structure evolution
with annealing time for the momentum cuts across $\Gamma$ (b), M2 (c) and M3
(d). (e) Band structure of the annealed double-layer FeSe/SrTiO3 film
(corresponding to the sequence 6) measured at 23 K (left panel) and 70 K
(right panel). The photoemission images are divided by the corresponding Fermi
distribution function to highlight opening or closing of an energy gap. (f)
Corresponding symmetrized EDCs on the Fermi momentum measured at different
temperatures. Reprinted from XLiu . Figure 16: Layer dependent Fermi surface
and band structure in the FeSe/SrTiO3 films. (a) The thickness dependence of
the Fermi surface as represented by the photoemission intensity map at the
Fermi energy at 30 K. (b) (c) The thickness dependence of band structure along
the cut crossing $\Gamma$ point and M point respectively. (d) Phase diagram of
the FeSe-related systems. Values of Tc and TA for FeSe are plotted against the
lattice constant. The dashed line represents the extrapolated values of TA,
suggesting the existence of spin-density-wave (SDW) order in bulk FeSe under
pressure. Values of Tc for other iron selenides are also plotted in the
elliptical region. Reprinted from STan . Figure 17: Temperature dependence of
the band structure of the N phase in the single-layer and double-layer
FeSe/SrTiO3 films. (a),(c) and (e) are the Fermi surface of single-layer
FeSe/SrTiO3 film, double-layer FeSe/SrTiO3 film and BaFe2As2, respectively.
(b), (d) and (f) Temperature dependence of the band structure measured along
the M3 cut for the single-layer FeSe/SrTiO3 film, double-layer FeSe/SrTiO3
film and BaFe2As2, respectively. (g) The transition temperature as a function
of the number of FeSe layers in the FeSe/SrTiO3 films. Here the transition
temperature for the single-layer and double-layer FeSe films (red squares) is
determined from the temperature dependence of the band structure where the
hole-like bands begin to disappear. The temperature for other films (violet
triangles) with more FeSe layers is taken from STan . Reprinted from XLiu .
Figure 18: Band structure of the single-layer FeSe films grown on various
substrates. (a,b) The photoemission intensity along $\\#$BU1, $\\#$BR1,
$\\#$SX1 and $\\#$S1 across $\Gamma$, and the corresponding second derivative
with respect to energy to highlight the dispersions for FeSeBU, FeSeBR, FeSeSX
and FeSeS, respectively. For the definition of different substrates, refer to
RPengNC . (c) Comparison of the dispersion of band $\alpha$ from ARPES data
and the DFT calculated band structures along the $\Gamma$-M’ direction. (d)
The energy separations between the $\alpha$ and $\omega$ bands at $\Gamma$
versus a. (e) Effective mass m∗ of band $\alpha$ as a function of in-plane
lattice constant a, where me is the free-electron mass. Reprinted from RPengNC
. Figure 19: Replica bands observed in the single-layer FeSe/SrTiO3 films and
their temperature dependence. (a) EDCs at M shown as a waterfall plot, with
markers indicating band peaks. (b) (c) Second derivatives in energy of the
high symmetry cuts from $\Gamma$ cut and M cut. An additional weaker replica,
labelled c, can now be seen at M in (c), sitting 50 meV below a, and at the
$\Gamma$ point in (b) we see the hole band and a corresponding replica,
labelled d and d , respectively. (d-g) Temperature dependence of the replica
bands, which persist at temperatures higher than the gap-opening temperature.
Reprinted from JJLee . Figure 20: Transport and magnetic measurements of the
superconductivity in the FeSe/SrTiO3 films. (a) Temperature dependence of
square resistivity (Rsq) of a 5-layer FeSe/SrTiO3 film from 0 to 300 K. Upper
inset: Rsq$C$T curves at various magnetic fields along the c-axis. Lower
inset: the Rsq$C$T curve from 0 to 80 KQYWangCPL . (b)The temperature
dependence of resistance under zero field, showing Tonsetc =40.2K and Tzeroc
=23.5 K. Inset: a schematic structure for the transport measurements in the
heterostructure of 30nm amorphous
Si/(10-layer)FeTe/(1-layer)FeSe/SrTiO3WHZhangCPL . (c) Temperature dependence
of the resistance in situ measured on a single-layer FeSe/SrTiO3 filmJFGe .
The inset shows the temperature dependence of resistance taken on a bare
SrTiO3 surface. (d) The diamagnetic response measured by a two-coil mutual
inductance system. Inset: the data near the superconducting transition in an
amplified view showing the formation of diamagnetic screening at 21
KWHZhangCPL .

Figure 21: Band structure Calculations of single-layer FeSe film with
different magnetic orders. (a) and (b) The calculated band structure of
single-layer FeSe/SrTiO3 film in nonmagnetic state and collinear
antiferromagnetic state respectivelyKLiu . (c) The calculated band structure
of single-layer FeSe film in checkboard antiferromagnetic stateFWZheng .