# Monoclinic LaSb2 Superconducting Thin Films

Adrian Llanos  Department of Applied Physics and Materials Science, California
Institute of Technology, Pasadena, California 91125, USA.  Institute for
Quantum Information and Matter, California Institute of Technology, Pasadena,
California 91125, USA.  Giovanna Campisi  Department of Physics and W. M. Keck
Computational Materials Theory Center, California State University,
Northridge, Northridge, California 91330, USA.  Veronica Show  Department of
Applied Physics and Materials Science, California Institute of Technology,
Pasadena, California 91125, USA.  Institute for Quantum Information and
Matter, California Institute of Technology, Pasadena, California 91125, USA.
Jinwoong Kim  Department of Physics and W. M. Keck Computational Materials
Theory Center, California State University, Northridge, Northridge, California
91330, USA.  Reiley Dorrian  Department of Applied Physics and Materials
Science, California Institute of Technology, Pasadena, California 91125, USA.
Institute for Quantum Information and Matter, California Institute of
Technology, Pasadena, California 91125, USA.  Salva Salmani-Rezaie  Department
of Materials Science and Engineering, The Ohio State University, Columbus,
Ohio 43210, USA  Nicholas Kioussis  Department of Physics and W. M. Keck
Computational Materials Theory Center, California State University,
Northridge, Northridge, California 91330, USA.  Joseph Falson
<EMAIL_ADDRESS>Department of Applied Physics and Materials Science,
California Institute of Technology, Pasadena, California 91125, USA.
Institute for Quantum Information and Matter, California Institute of
Technology, Pasadena, California 91125, USA.

###### Abstract

Rare-earth diantimondes exhibit coupling between structural and electronic
orders which are tunable under pressure and temperature. Here we present the
discovery of a new polymorph of LaSb2 stabilized in thin films synthesized
using molecular beam epitaxy. Using diffraction, electron microscopy, and
first principles calculations we identify a YbSb2-type monoclinic lattice as a
yet-uncharacterized stacking configuration. The material hosts
superconductivity with a $T_{\mathrm{c}}$ = 2 K, which is enhanced relative to
the bulk ambient phase, and a long superconducting coherence length of 140nm.
This result highlights the potential thin film growth has in stabilizing novel
stacking configurations in quasi-two dimensional compounds with competing
layered structures.

Layered intermetallics featuring the square-net structural motif form a
versatile platformHoffmann and Zheng (1985); Kordyuk (2012); Klemenz et al.
(2019); Yumigeta et al. (2021) for engineering electronic phases through
chemical control over lattice symmetries Ru et al. (2008); Ni et al. (2008);
Lei et al. (2019) and stacking configurations.Straquadine et al. (2019) Using
common experimental tuning knobs such as chemical substitution, pressure
($P$), and temperature ($T$), it is known that structural configurations
compete and can be modified with a subsequent influence the flavor of
electronic ground state of the compound.DiMasi et al. (1996); Shin et al.
(2005); Huang et al. (2008); Xiang et al. (2020); Singha et al. (2021);
Weinberger et al. (2023) Antimony-based $Ln$Sb2 (Ln = lanthanide element)
materials form stoichiometric crystals and refined structural analysisWang and
Steinfink (1967) describes the unit cell as being formed by two quintuple
layer (QL) blocks, each consisting of two Ln-Sb corrugated layers sandwiching
a two-dimensional Sb square net sheet. Variations in electron count on the
square net Sb sites as determined by the rare-earth ionization state leads to
a variety of bonding and stacking arrangements.Papoian and Hoffmann (2000) In
the case of EuSb2, the Eu2+ valence state causes a distortion of the Sb square
net into zig-zag chains and a monoclinic crystal structure Hulliger and
Schmelczer (1978); Ohno et al. (2021) while the orthorhombic structure of
YbSb2 is stabilizedWang et al. (1966) due to a small admixture of Yb3+ ions
within a predominantly 2+ network.Tremel and Hoffmann (1987) Finally, in the
case of (La, Ce, Nd, Sm)Sb2 compounds, the 3+ valence again gives rise to an
orthorhombic crystal in the so-called SmSb2 structure type.Wang and Steinfink
(1967); Bud’ko et al. (1998) This latter structure differs from the YbSb2 most
notably in the stacking arrangement of QL along the $c$-axis direction, which
in this context, can be conceptualized by a displacement vector $\vec{d}$
within the $a$-$b$ plane, as illustrated in Figure 1a.

Figure 1: a.) Two QL building blocks of LaSb2, where the upper QL block is
shifted relative to the lower one by lateral displacement(b) $\theta/2\theta$
diffraction pattern from LaSb2. (c) Reciprocal space map taken along the $h\
=1$ rod. Splitting at finite $Q_{x}$ indicates a monoclinic tilt. (d)
Schematic unit cells of the orthorhombic and monoclinic crystal systems. (e)
Atomic arrangements obtained in transmission electron microscopy within
domains with an overlay of the calculated unit cell modified with experimental
lattice constant values.

LaSb2 stands out as a particularly sensitive structure which is susceptible to
electronic and structural instabilities when tuning $T$ and $P$. Bulk crystals
grown with the self-flux method Canfield and Fisk (1992) form large, micaceous
crystals with high residual resistivity ratios (RRR) Bud’ko et al. (1998);
Fischer et al. (2019) and non-saturating positive magnetoresistance
(MR).Bud’ko et al. (1998); Young et al. (2003) Pronounced hysteretic
electrical resistance when sweeping $T$ is resolved under ambient $P$
conditions.DiTusa et al. (2011); Luccas et al. (2015); Weinberger et al.
(2023); Palacio et al. (2023) Under application of moderate $P$, the
hysteretic feature is rapidly suppressed to low $T$ and is completely absent
by $P\approx 12$ kbar. Accompanying this suppression is a rapid sharpening of
the superconducting (SC) transition under $P$ and an increase in SC critical
temperature ($T_{\mathrm{c}}$) to a maximum of $T_{\mathrm{c}}$ $\approx$ 2
K.Bud’ko et al. (2023); Guo et al. (2011); Weinberger et al. (2023) However,
due to the micacity of crystals, reliable structural analysis at high $P$
remains challenging and therefore complicates a full understanding of
correlation between structural and electronic properties.

Molecular-beam epitaxy (MBE) as a synthesis technique has found much
application in the engineering of low-temperature electronic ground states
primarily through dimensional confinementWen-Hao et al. (2014); Shiogai et al.
(2016); Jeffrey Gardner et al. (2011); Falson et al. (2020) and epitaxial
strain.Bozovic et al. (2002); Ruf et al. (2021); Engelmann et al. (2013) Here,
we use this technique to synthesize and study LaSb2 thin films on MgO (001)
(SG: Fm$\bar{3}$m, a = 4.21Å). Despite the lattice constants being relaxed in
the (001)-oriented films, we discover a not previously observed crystal
structure derived from the YbSb2 structure type with an additional monoclinic
shear. First principles calculations suggest this layering arrangement as the
lowest energy state, even compared to the observed SmSb2 structure type of
LaSb2 single crystals commonly observed in bulk crystals. The electronic
structure is characterized as a multi-band system with one hole-like band
derived from the La-Sb corrugated layer and multiple electron-like bands from
the Sb sheet. The films display no resistance anomaly at high $T$ indicative
of a structural phase transition and are superconducting with a
$T_{\mathrm{c}}$ = 2.03 K, which is enhanced relative to the bulk ambient
where $T_{\mathrm{c}}$ $\approx$ 1 K. The ability to stabilize stacking
configurations of quasi-2D materials not observed in their bulk counterparts
emphasizes the extra degrees of freedom available to thin film synthesis of
this broad class of materials.

The structure of $Ln$Sb2 materials is composed of QL blocks which can form a
variety of stacking configurations depending on their relative
displacementWang and Steinfink (1967); Wang et al. (1966). This is depicted in
Figure 1a with the vector $\vec{d}$ which represents the displacement in the
$a$-$b$ plane. Each QL contains one rare earth site, in this case La (blue),
and two different Sb sites, noted as Sb1 (orange) and Sb2 (red) in Figure 1a.
Out-of-plane X-ray diffraction of films presented in Figure 1b shows a single-
phase, $c$-axis oriented film with a lattice parameter of $c=17.62$Å. This
value is compressed relative to the value found in bulk LaSb2 in the SmSb2
structure where $c=18.56$Å.Wang and Steinfink (1967) A film of thickness $t$ =
144nm was used for determination of the lattice parameters. Rocking curve
analysis reveals a full-width-half max of 0.03∘ indicating low mosaicity and a
phi-scan using the (0 1 9) reflection reveals an [100]${}_{LaSb_{2}}\ ||\
[100]_{MgO}$ epitaxial relationship with additional domains oriented
[100]${}_{LaSb_{2}}\ ||\ [110]_{MgO}$ (Figure S2).

Asymmetric reciprocal space mapping (RSM) (Figure 1c) along the $h=1$
truncation rod was used to determine the in-plane lattice constants. The data
reveals a twinned crystal structure with sets of spots corresponding to values
from the two different crystal axes. For reflections corresponding to the
$a$-axis, a pair of spots ((1 0 12) and ($\bar{1}\ 0\ 12)$) are observed,
whereas intensity at (0 1 11) is associated with diffraction from the
$b$-axis. To simplify comparison with similar, bulk crystal polymorphs, we
adopt a setting where the $c$-axis is always taken to be the long axis. The
corresponding $a$ and $b$ axis lattice constants and were found to be
$a=4.52$Å and $b=4.43$Å. The similarity of the lattice constant values for the
grown film ($\frac{a-b}{a}\approx 2\%$) and their $\approx 6\%$ mismatch with
the cubic MgO substrate result in a relaxed film with twinned domains wherein
both $a$ and $b$ axis predominantly align with the $<100>$ directions of the
substrate. For comparison, the bulk ambient phase adopts the SmSb2 structure
(space group No.64 $Cmca$) with $a=b=4.42\text{\AA},\gamma=91.27$.foo (a);
Wang and Steinfink (1967)

The distribution of the (1 0 12) and ($\bar{1}\ 0\ 12$) spots along
$\vec{Q_{z}}$ reveals a monoclinic structure for the crystal, which can be
understood by referring to Figure 1d. When a crystal distorts from
orthorhombic to monoclinic, the $\vec{a*}$ reciprocal lattice vector forms a
finite angle with $\vec{a}$ so as to maintain orthogonality with $\vec{c}$.
The reduced symmetry of the monoclinic structure relative to the MgO substrate
leads to domains oriented 180∘ with respect to each other and the appearance
of both $(h0l)$ and $(-h0l)$ reflections along the same direction. Thus a
single spot corresponding to $(h0l)$ in the case of an orthorhombic crystal
appears to “split” along $\vec{Q_{z}}$ into two spots corresponding to the two
rotated domains. The angle between either of these spots and the horizontal
can be used to determine the monoclinic tilt which we find to be $\beta$ =
85.95∘.

Observed extinction conditions (Figure S3) imply an A-centered monoclinic cell
and are consistent with three possible space groups ($A2/m$, $A2$, $Am$).Flack
(2016) In Figure 1e we present a pair of scanning transmission electron
microscopy (TEM) images labelled by the zone axis of the crystalline material.
An extended set of micrographs is presented in the supplementary information,
showing that domains occur in varying proportions randomly in the sample,
consistent with the X-ray data. Energy dispersive x-ray spectroscopy taken in
the TEM allows for chemical identification of the atoms in the unit cell
(Figure S10) and confirms the 1:2 La:Sb stoichiometry within an accepted
tolerance of $\approx$10% for EDX in STEM.Lugg et al. (2015); MacArthur et al.
(2017) Line cuts along Sb layers (Figure S11) reveal that Sb sheets form
planar layers in contrast to the puckered layers found in the YbSb2
structure.Wang et al. (1966) Our proposed crystal structure was obtained from
density functional theory calculations, the details of which will be discussed
in the next section. In Figure 1(e) we overlay the calculated structure on the
TEM images, with lattice parameters taken from experiment, which confirms the
proposed atomic arrangements. The space group for the LaSb2 films was
determined to be $A2/m$ (No. 12).

t

Figure 2:  (a) Energy landscape of sliding two LaSb2 QL building blocks in Figure 1a on the two-dimensional $(d_{x},d_{y})$ displacement space. The global energy minima are denoted by $Y^{\pm}$ and the saddle points by $S^{\pm}$ and $Y^{0}$. (b) - (d) Schematic top-view of three LaSb2 building blocks with different stacking sequences. The cell with label 1 denotes the bottom block. (b) Sm-type orthorhombic structure with alternating stacking sites of $[S^{+}S^{-}]$; (c) Yb-type orthorhombic structure with a sole stacking site of $[Y^{0}]$; and (d) Yb-like monoclinic structure with a sole stacking site of $[Y^{+}]$ resulting in a tilted out-of-plane lattice vector. (e) Total energies versus volume for the four crystal structures, where the solid curves are fits to the Birch-Murnaghan equation of state.  Table 1:  Calculated relative total energies, lattice constants, and angles of several LaSb2 bulk phases corresponding to different stacking sequences. SG indicates the space group. The Sm-type structure is a base-centered orthorhombic cell and the lattice constants, $a$ and $b$, are equivalent to the distance from the corner to the center of the conventional cell base. System | Stacking sequence | SG |  $\Delta E$ (meV/La) |  $a$ (Å) |  $b$ (Å) |  $c$ (Å) |  $\alpha$ (∘) |  $\beta$ (∘) |  $\gamma$ (∘)
---|---|---|---|---|---|---|---|---|---
Sm-typefoo (a) | $\cdots S^{+}S^{-}S^{+}S^{-}[S^{+}S^{-}]\cdots$ | 64 | 29 | 4.470 | 4.470 | 18.628 | 90.0 | 90.0 | 91.1
Yb-type | $\cdots Y^{0}Y^{0}Y^{0}Y^{0}Y^{0}[Y^{0}]\cdots$ | 63 | 45 | 4.477 | 4.546 | 17.607 | 90.0 | 90.0 | 90.0
Yb-alt | $\cdots Y^{+}Y^{-}Y^{+}Y^{-}[Y^{+}Y^{-}]\cdots$ | 58 | 4 | 4.555 | 4.480 | 17.717 | 90.0 | 90.0 | 90.0
Yb-mono | $\cdots Y^{+}Y^{+}Y^{+}Y^{+}Y^{+}[Y^{+}]\cdots$ | 12 | 0 | 4.562 | 4.483 | 17.711 | 90.0 | 86.3 | 90.0
Bulk exp.foo (a); Wang and Steinfink (1967) |  | 64 |  | 4.42 | 4.42 | 18.56 | 90.0 | 90.0 | 91.2
This work |  | 12 |  | 4.52 | 4.43 | 17.62 | 90.0 | 85.96 | 90.0

The stacking arrangements for these materials can be constructed from QL
building blocks as shown in Figure 1(a), where the upper block is shifted
relative to the lower one by a displacement vector
$\vec{d}=(d_{x}a_{0},d_{y}b_{0})$. This construction or interpretation is
possible because of the relatively weak bond between neighboring La-Sb layers,
substantiated by the lower cleavage energy (Figure S4) and the longer inter-
block La-Sb bond length ($>3.5$ Å) compared to those of the intra-block bonds.
The energy landscape of the two LaSb2 building blocks on the two-dimensional
$(d_{x},d_{y})$ displacement space is shown in Figure 2(a). This is obtained
using a relaxed unit block slab where $a_{0}=b_{0}=4.50$ Å are the calculated
equilibrium in-plane lattice constants, and shifting it relative to an
adjacent slab, with subsequent relaxation of the atomic positions. The
calculations reveal (i) four global energy minima, $Y^{\pm}$ and (ii) six
saddle points, $Y^{0}$ and $S^{\pm}$. The symbols mark half of them and
$C_{4}$ rotation covers the unmarked special stacking sites. It is evident
that the vertical stacking $(d_{x},d_{y})=(0,0)$ is not favored. The $S^{\pm}$
sites, $(d_{x},d_{y})=(\pm 0.25,\pm 0.25)$, correspond to the displacement of
the Sm-type LaSb2 structure (space group $No.64,Cmca$) consisting of building
blocks with stacking sequence of $\cdots S^{+}S^{-}S^{+}S^{-}\cdots$ (see also
Table 1). The Yb-type structure (space group $No.63,Cmcm$) can also be
explained with the stacking sequences of $\cdots Y^{0}Y^{0}Y^{0}Y^{0}\cdots$.
The two displacements between three consecutive building blocks are
illustrated in Figure 2(b) and (c) for the Sm- and Yb-type structures, where
the successive lateral displacements are compensated and both Sm- and Yb-type
structures preserve orthorhombicity. We note that the energy map preserves the
$C_{4}$ rotational symmetry, inherited from the building block
($a_{0}=b_{0}$). The broken tetragonal symmetry of Sm- and Yb-type LaSb2 is
thus related to the displaced stacking sites that breaks the $C_{4}$ symmetry
of the building block. Both phases, however, do not contain the lowest energy
stacking sites $Y^{\pm}$ according to these calculations. Figure 2(d) shows
one potential structure with repeating $Y^{+}$ stacking, $\cdots
Y^{+}Y^{+}Y^{+}Y^{+}\cdots$, where the non-compensating displacement along the
$\hat{x}$ direction leads to shear deformation of the out-of-plane lattice
vector rendering the system monoclinic. To further validate this method, we
also have applied it to the SmSb2 and YbSb2 structures and have found that in
each case, the expected stacking arrangements are reproduced (Figure S5).

Table 1 lists the calculated relative total energies of the different stacking
sequences, as well as experimentally obtained values for bulk crystalsWang and
Steinfink (1967) and our thin films. The calculations point to the monoclinic
structure (Yb-mono) as the ground state, with the previously synthesized Sm-
type or proposed Yb-type phases exhibiting higher total energies. We note
however, that this is the energy at $T=0$, and therefore is distinct from the
free energy at elevated temperatures which contains phononic, magnetic, and
electronic entropic contributions. The novel Yb-mono phase is consistent with
the MBE-grown LaSb2 structure where all the calculated lattice constants and
monoclinic angle $\beta$ agree well with the diffraction data within an error
of 1%. Combining diffraction, calculation and microscopy results, we can
umambiguously confirm the novel Yb-mono polymorph has been stabilized.

Interestingly, the calculations also reveal a new orthorhombic phase (Yb-alt
in Table 1, space group $No.58,Pnnm$) with alternating stacking sequences of
$\cdots Y^{+}Y^{-}Y^{+}Y^{-}\cdots$, which is close in energy to the ground
state Yb-mono structure. In order to study the relative stability of the four
crystal structures under hydrostatic pressure, we show in Figure 2(e) the
calculated total energies as a function of volume. We find that the Yb-mono
structure remains the ground state under hydrostatic pressure, which on the
other hand, induces a structural phase transition from the Sm-type to the Yb-
type structures at 0.749 GPa, which is close to the calculated value in Ref
[Weinberger et al., 2023] of $\simeq$ 0.5 GPa.

Figure 3: (a) Temperature-dependent longitudinal resistance. (b) Longitudinal
magnetoresistance at different temperatures. (c) Brillouin zone and relevant
high symmetry points of the monoclinic structure. (d) Hall resistance curves
at different temperatures, offset for clarity. (e) Calculated band structure
with color coded dispersion features associated with projections on various
atomic sites, along with the corresponding DOS (total DOS scaled by
$\frac{1}{4}$).

In Figure 3a we present temperature dependence of resistivity for a film of
thickness $t=144$ nm. The films show metallic $\rho(T)$ with an RRR
(R300K/R2K) of 26. No features with sharp changes in $d\rho/dT$ are observed
up to $T$=400 K which would indicate the presence of a CDW transition or
first-order structural transition. Comparison of the data during both warming
and cooling shows slight increase in sample resistivity and slightly degraded
RRR (Figure S6) but no other anomalies. In Figure 3b and 3d, the symmeterized
magnetoresistance (MR) and anti-symmeterized Hall resistivity up to fields of
$B$=9 T for several temperatures are given. The clear curvature of the Hall
resistance indicates multiple carrier types while the MR displays linear
behavior at high fields at low temperature, similar to bulk crystal data both
in ambient conditions and under applied pressure, albeit with a reduced
magnitude compared to bulk crystals.Young et al. (2003); Bud’ko et al. (1998)
It was observed that while the behavior of the Hall resistivity was reasonably
captured by a simple Drude two carrier model using the formulas in Ref.Luo et
al. (2015), the magnetoresistance could only be fit by this model for higher
temperature scans, indicating that scattering mechanisms beyond the simple
Drude picture are relevant as temperature is reduced (Figure S7).

In Figure 3c we plot the Brillouin zone of the monoclinic crystal structure
with the relevant high symmetry points. The band structure along the high
symmetry directions (orange path in (c)) and the corresponding orbital-
projected density of states (DOS) are displayed in Figure 3e, where the blue,
orange, and red colors denote projections on the La-5$d$, Sb1/5$p$ and
Sb2/5$p$ orbitals (Sb1 are on the La/Sb corrugated layer and Sb2 are on the 2D
Sb sheets in see Figure 1(a)). The relatively flat bands along the Z-$\Gamma$,
X-F and A-C-Y directions indicate lower carrier mobility along the
z-direction, in contrast to the more dispersive Sb1/5p and Sb2/5p bands
crossing the Fermi level along the $\Gamma$-X and F’-Z directions, indicating
higher carrier mobility along the in-plane directions similar to those in the
bulk orthorhombic LaSb2 structureRuszala et al. (2020); Qiao et al. (2022);
Palacio et al. (2023) and in other topological square-net materials.Klemenz et
al. (2019) The presence of both hole-like and electron-like pockets at the
Fermi level is in agreement with the observation of multiple carrier types
from the Hall measurements.

In Figure 4a we present data showing the presence of a sharp superconducting
transition with resistive $T_{\mathrm{c}}$ $\approx$ 2.05 K. The films display
zero resistance and clear flux expulsion, as evidenced by a drop in voltage on
the secondary coil in a mutual inductance experimental geometry (inset of 4a).
The measured Tc in the two experiments agree within 1%. In Figure 4b, the
critical magnetic field $H_{\mathrm{c2}}$ for fields applied along the
$c$-axis with current applied parallel to the $a-b$ plane is plotted.
Determination of Hc2 was performed by fitting the transition isotherms to a
sigmoid function $\rho=\frac{1}{1+exp(-k(H-H_{c2}))}$ where k, A and $H_{c2}$
were fitting parameters. This fit implies that $H_{c2}$ is given by the
intersection with half the normal state resistance. The full set of critical
field isotherms and fits is given in S12. Data were taken every 25mK between
2.05K and 1.71K. In 4b, we fit the critical field data using a single-band,
Ginzburg-Landau modelTinkham (2004) to obtain estimates of the in-plane
coherence length $\xi_{ab}=140$ nm. This value is also in agreement with the
findings in bulk crystals under pressure.Guo et al. (2011)

Figure 4: (a) Superconductivity measured in a 144 nm film via resistance (red)
and mutual inductance (blue) methods. (b) Critical field as a function of
reduced temperature, yielding an estimate of the in-plane coherence length.

One possibility for the stabilization of the monoclinic LaSb2 is related to
epitaxial strain or other perturbations induced by the substrate. The square
symmetry of the MgO substrate would tend to favor layers with reduced
orthorhombicity and lattice mismatch with the substrate. In the monoclinic
phase, the $a$ and $b$ axes differ by $\approx$1.8% compared to approximately
$\approx$2.5% for the ambient phase structure. When comparing the lattice
mismatch between the two structures and the substrate, it would appear that
the orthorhombic SmSb2 foo (b), with mismatches $\approx$6% and $\approx$3%
for the $a$ and $b$ axes, would be favored over the monoclinic phase which
shows mismatches of $\approx$7% and $\approx$5%. However in both cases, these
lattices mismatches are so large, that is it unlikely that coherent strain
persists in the epilayer beyond the first 1-2 QL. Taken together, these
findings indicate that while layer-by-layer growth stabilizes the monoclinic
LaSb2, this observation is unlikely to be the result of epitaxial strain.
Another possibility for the observation of the monoclinic phase in thin films,
yet not in the bulk crystals, is the lower growth temperature used in the MBE
growth processes ($\approx$500oC $<T_{\mathrm{melt}}$ = 630∘C).Okamoto (2019)
During flux growth, crystals are obtained by slowly cooling the melt from the
liquidus temperature ($\approx$1000oC), over a period of tens of hours and
decanting the liquid flux slightly above the solidification temperature of the
desired phase.Canfield and Fisk (1992) Given the results of the 0 K DFT
simulations, monoclinic LaSb2 may therefore form a low-temperature crystalline
phase that would be preferentially stabilized by the vapor-solid reaction of
MBE.

We finally note that as of the time of writing this report, we are unaware of
single-crystal diffraction data reported for bulk-LaSb2 at high $P$. The
micacity of crystals makes such experiments challenging. Previous
studiesWeinberger et al. (2023) have proposed YbSb2 or EuSb2 as candidate
structures for the high-$P$ phase on the basis of DFT calculations. Our
calculations agree that while the YbSb2 structure is more stable compared to
the SmSb2 structure under pressure, the monoclinic $Y^{+}$ structure is the
ground state. We therefore propose that the application of pressure results in
a structural transition to either the $Y^{+}$ polymorph or perhaps a similar
orthorhombic structure labelled $[Y^{+}Y^{-}]$ which is nearly degenerate. The
association of the $Y^{+}$ phase with the high-pressure phase of the bulk
crystal is further bolstered by the qualitative features of transport and
superconducting behavior, namely, the absence of resistance anomalies at high
temperature and a sharp superconducting transition at 2K. In bulk LaSb2, the
superconducting transition is broad, with onset temperatures of about $T$=2 K,
yet only reaching a fully superconducting state at $T$=0.4 $\sim$0.5KGuo et
al. (2011). The transition sharpens with $P$ with concomitant suppression of
the high temperature resistance anomaly.Weinberger et al. (2023); Bud’ko et
al. (2023) A maximum T${}_{c}\approx$ 2 K was observed under applied pressure
of 4.5kbar at which point the anomaly is completely absent.Guo et al. (2011);
Weinberger et al. (2023) We note that the strongly 2D-like dispersion in the
other square-net systems such as SmSb2-type LaSb2 is significantly different
in our structure (Figure S8 for discussion), which may play a role in the
suppression of the resistance anomaly associated with a structural transition
that competes with superconductivity. Further investigations into the
superconducting phase will form the basis of future studies.

In summary, we have experimentally and theoretically presented a newly stable
polymorph of in the family of rare-earth diantimonides in thin films of LaSb2
deposited on MgO (001). The films are superconducting with a critical
temperature enhanced relative to reports on bulk crystals under ambient
conditions. The coherence length of the superconductor is comparable to the
film thickness, pointing towards this family of materials as a promising
platform to study superconductivity with varying lattice motifs and layering
orders which may be inaccessible or difficult to characterize in bulk samples.

## Acknowledgements

We thank Paul Canfield and Sergey Budko for helpful conversations and critical
reading of the manuscript. J.F acknowledges funding provided by the the Air
Force Office of Scientific Research (Grant number FA9550-22-1-0463), the
Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant number GBMF10638),
and the Institute for Quantum Information and Matter, an NSF Physics Frontiers
Center (NSF Grant PHY-1733907). The work at CSUN acknowledges support from the
NSF-PREP CSUN/Caltech-IQIM Partnership (Grant number 2216774) and NSF-PREM
(Grant number DMR-1828019). We acknowledge the Beckman Institute for their
support of the X-Ray Crystallography Facility at Caltech. Electron microscopy
was performed at the Center for Electron Microscopy and Analysis (CEMAS) at
The Ohio State University.

## Conflict of Interest

The authors declare no conflict of interests.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

##

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### Supplementary Data

##  I Experimental Section

Molecular beam epitaxy: Films were prepared using a molecular beam epitaxy
(MBE) apparatus at a base pressure of $\approx 10^{-10}$ Torr. Films were
grown upon MgO (001) ($a$=0.421 nm) substrates which were thermally prepared
using a home-built CO2 laser heating apparatus,Llanos et al. (2023) and then
later transferred to the growth chamber equipped with a conventional resistive
SiC coil. La and Sb were both provided from conventional effusion cells. All
growths begin with a low temperature buffer layer with La and Sb codeposited
at beam flux pressures of 6.5$\times 10^{-9}$ mbar and 1.5$\times 10^{-7}$
mbar, at growth temperature 315∘C. The buffer layer is annealed at 615∘C for 5
minutes before being cooled to 520∘C, where the rest of the film is grown with
La and Sb codepositing at beam flux pressures of 1$\times 10^{-8}$ mbar and
1.5$\times 10^{-7}$ mbar. Growth rate was estimated using Laue fringes
observed in lower thickness films and was found to be 0.033 Å/s. To reduce
degradation in air, all films were capped with amorphous Ge in-situ at room
temperature. Reflected high energy electron diffraction (RHEED) was obtained
at an accelerating voltage of 20 kV. RHEED and AFM images from a 24nm film can
be found in S1. RHEED patterns are streaky high-contrast indicating good
crystallinity. Images also reveal a 2x1 surface reconstruction. AFM was used
to asses the quality of the surface where it can be seen that the surface
consists of large, flat regions punctuated by deeper cavities.

X-ray diffraction: X-ray diffraction data was obtained using a Rigaku Smartlab
diffractometer using a 2-bounce Ge (220) monochromator and Cu-$K\alpha 1$
radiation.

Transmission electron microscopy: Scanning Transmission Electron Microscopy
(STEM) measurements were performed on a cross-sectional lamella prepared
through focused ion beam (FIB) lift-out using a FEI Helios NanoLab 600
DualBeam. The samples underwent thinning with 5 kV Ga ions, followed by a
final polish at 2 kV to minimize surface damage. The imaging was conducted
using the Thermo Scientific Themis Z S/TEM operating at 300 kV, featuring a
semi-convergence angle of 30 mrad. A High-Angle Annular Dark-Field (HAADF)
detector with an angular range of 64-200 mrad was utilized to capture HAADF-
STEM images. This imaging process involved acquiring a series of 20 images
(200 ns per frame), which were subsequently averaged to produce images with a
high signal-to-noise ratio. STEM- Energy dispersive X-ray spectroscopy (EDX)
data is acquired using a Super-X EDX detector.

First principles calculations: The first principles calculations are performed
by using the Vienna $ab$ $initio$ simulation package. The wave functions and
pseudopotentials are treated with the projected augmented wave method. The
exchange-correlation functional is described with Perdew-Burke-Erenzhoff
approach. The plane wave basis cut-off energy is set to 500 eV and the
momentum space is sampled with $\Gamma$-centered $16\times 16\times 1$ and
$16\times 16\times 6$ meshes for the slab and bulk calculations, respectively.
All structures are relaxed within energy convergence criteria of $10^{-5}$ eV.
Spin-orbit coupling is not included. The single building block is fully
relaxed first with vacuum layer thicker than 15 Å. The energy landscape upon
displacement is then calculated with a sampling width of $\Delta d_{x,y}=0.05$
and interpolated by using spline method. The in-plane lattice constants of the
building block and the displaced in-plane coordinates of ions are fixed and
only out-of-plane coordinates are relaxed.

Transport Measurements: Electrical data was obtained using four-point van der
Pauw geometry measurements in a Quantum Design Dynacool system. Samples were
cut in approximately square shape and sheet resistance was obtained by
numerically solving the van der Pauw equation. For superconducting
measurements, $T_{c}$ was determined to be the temperature at which the sheet
resistance crosses half the value of the normal state sheet resistance by
fitting a sigmoid function ($\rho=\frac{1}{1+exp(-k(H-H_{c2}))})$ to the
transition.

Mutual Inductance Measurements: The LaSb2 film was held upright on the
cryostat puck via a 3D printed housing. Two solenoids (5 mm in length, 2.5 mm
in diameter) were inserted into the housing centered co-axially on either side
of the film, and the sample was thermally and electrically grounded by a gold
wire soldered to the corner of the film. An AC driving current (50 $\mu$A at
10.13 kHz) was passed through one coil using an SR830 lock-in amplifier while
the first-harmonic pickup voltage was measured in the second coil with the
same lock-in (300 ms time constant). An out-of-plane magnetic field of 10 Oe
was applied to compensate for trapped flux in the cryostat system’s magnet.
While sweeping the sample’s temperature at 10 mK/minute through its
superconducting transition, the onset of the Meissner effect was observed as a
substantial drop in the induced voltage across the pickup coil, indicating
screening of the drive coil’s magnetic field by the superconducting film.

Figure S1: a) RHEED taken at the end of grown along [100] b) [110]. c) AFM of
surface of 24nm film. Figure S2: a) Rocking curve of (003) peak showing FWHM
of 0.03∘ b) Phi-scan demonstrating the epitaxial relationship described in the
main text. Minor domains rotated 45∘ can be seen. Figure S3: Additional
reciprocal space maps used to verify the extinction conditions and determine
the space group of the grown film. The above maps and those in the main text
imply k+l = 2n for general h,k,l; l = 2n for h, k = 0, l; k+l = 2n for h = 0,
k, l. Comparing with the listings in the international tables (International
Tables for Crystallography (2016). Vol. A, Section 1.6.5, pp. 114–128.), these
conditions, along with the identification as a monoclinic crystal imply 3
possible space groups: A2, Am, A2/m. Of these, A2/m is determined on the basis
of TEM measurements which confirm the atomic arrangement predicted by DFT
calculations. Figure S4: Calculated total energy difference, $\Delta$E, versus
cleavage separation, $\Delta$L, between two LaSb2 unit building blocks in the
Y± ground-state configuration [Figure 2(a)] for separation between (a) two
successive La-Sb corrugated layers (red circles) shown in the left atomic
structure and (b) successive La-Sb corrugated layer and the square Sb sheet
(blue circles), shown in the right atomic structure, respectively. $\Delta$E
converges to the ideal cleavage energy as the separation between the
neighboring building blocks increases. The substantially lower cleavage energy
for two successive La-Sb corrugated layers compared to that for the La-Sb
corrugated layer and the square Sb sheet, clearly demonstrates that the
interlayer bonding between two successive La-Sb corrugated layer is weaker,
thus allowing their easier glide. Figure S5: Energy surfaces for the SmSb2
structure and YbSb2 structure generated in the same manner as that used in the
main text. Results indicate that the expected structures are the most stable
for these compounds. Figure S6: Comparison of warming and cooling curves up to
400 K. Data show no anomalies associated with CDW or other structural
transition.  Figure S7: (a) fits to two-carrier Drude model for increasing
temperature.
$\rho_{xx}=\frac{1}{e}\frac{(n_{h}\mu_{h}+n_{e}\mu_{e})+(n_{h}\mu_{e}+n_{e}\mu_{h})\mu_{h}\mu_{e}B^{2}}{(n_{h}\mu_{h}+n_{e}\mu_{e})^{2}+(n_{h}-n_{e})^{2}\mu_{h}^{2}\mu_{e}^{2}B^{2}}$,
$\rho_{xy}=\frac{B}{e}\frac{(n_{h}\mu_{h}^{2}-n_{e}\mu_{e}^{2})+(n_{h}-n_{e})\mu_{h}^{2}\mu_{e}^{2}B^{2}}{(n_{h}\mu_{h}+n_{e}\mu_{e})^{2}+(n_{h}-n_{e})^{2}\mu_{h}^{2}\mu_{e}^{2}B^{2}}$.
(b), (c) variation with temperature of charge density and mobility,
respectively Figure S8: Fermi surface (FS) projections for (a) thin film
Yb+-type LaSb2 and (b) bulk Sm-type LaSb2. Suppression of a competing CDW is
thought to lead to enhancement of superconductivity in monoclinic LaSb2. In
this system, there is strong hybridization with Sb1-p which introduces band
dispersion along the $k_{z}$ direction and breaks 2D like features. Overall,
the FS of the monoclinic structure is distinct from the highly nested FS
sheets of the orthorhombic Sm-type structure and could be a possible origin of
CDW suppression and enhancement of the superconducting Tc.  Figure S9: Wide
area TEM showing the presence of a-b axis twinning and rotated domains
oriented parallel to [110], close to the interface. Figure S10: Elemental
mapping of films, including the monoclinic structure for reference. The survey
HAADF and EDX elemental maps in shows the monoclinic (C2/m) LaSb2 structure
with zig-zag of Sb and La and Sb sheets. The La/Sb ratio with absorption and
ionization cross-section correction for the foil with a thickness of 30 nm is
0.566. The structure with Sb and La atoms all aligned along [100] direction is
unique to the monoclinic structure. MgO is beam sensitive structure and the
structure is damaged while collecting EDX data. The EDX elemental maps
acquired from a wide field of view shows uniform distribution of La and Sb
with similar La/Sb ratio for different regions.  Figure S11: Line profiles on
atomically resolved images along the [100] zone axis. The uniform ampltide
across the Sb sheet indicates an absence of distortion along the c-axis
direction, in contrast to the YbSb2 structure Figure S12: a) Critical field
isotherms showing the increase in Hc2 vs temperature. Estimation of Hc2 was
performed by fitting the transition to a sigmoid function
$\rho=\frac{1}{1+exp(-k(H-H_{c2}))}$ where k, A and $H_{c2}$ were fitting
parameters. Fits are displayed along with raw data. b) extrapolation of the
Ginzburg-Landau fit to zero temperature