# mmSense: Detecting Concealed Weapons with a Miniature Radar Sensor

###### Abstract

For widespread adoption, public security and surveillance systems must be
accurate, portable, compact, and real-time, without impeding the privacy of
the individuals being observed. Current systems broadly fall into two
categories – image-based which are accurate, but lack privacy, and RF signal-
based, which preserve privacy but lack portability, compactness and accuracy.
Our paper proposes mmSense, an end-to-end portable miniaturised real-time
system that can accurately detect the presence of concealed metallic objects
on persons in a discrete, privacy-preserving modality. mmSense features
millimeter wave radar technology, provided by Google’s Soli sensor for its
data acquisition, and TransDope, our real-time neural network, capable of
processing a single radar data frame in 19 ms. mmSense achieves high
recognition rates on a diverse set of challenging scenes while running on
standard laptop hardware, demonstrating a significant advancement towards
creating portable, cost-effective real-time radar based surveillance systems.

$\mathsection$$\mathsection$footnotetext: Equal Contribution

Index Terms—  Real-time signal processing, mmWave radars, Vision Transformer

##  1 Introduction

Radar solutions developed on Frequency Modulated Continuous Wave (FMCW)
technology have shown promising success through their ability to serve as a
capable and versatile basis for computational sensing and short range wireless
communication systems [1]. Such radars, operating at millimeter wave (mmWave)
frequency, can be used for robust gesture generation and recognition [2, 3],
and even measure distances with mm accuracy [4]. Furthermore, mmWave radars
have the potential to serve as a basis for concealed metallic object detection
(e.g. knives, guns etc) which presents a novel and most importantly, privacy-
preserving manner of real-time surveillance. The principles of mmWave metal
detection rely on the underlying physics of RF waves- radio frequency (RF)
waves that fall in the $30$–$300$ GHz range between microwaves and terahertz
waves. This frequency band corresponds to wavelengths of $1$–$10$ mm. Within
various forms of spectral imaging (e.g. IR, UV), one chooses the waveband that
interacts with the object/scene to be imaged, whilst ignoring any obfuscating
features. The same is true when detecting metals concealed on humans, where
the mmWave waveband is appropriate because the waves from a mmWave RF source
pass through the thin layers of clothes, and are reflected highly by the body,
plus any hidden objects between the two [5]. Figure 1 depicts this concept
empirically. We believe there is a niche in the security field for a portable
technology that can screen for illegal metallic weapons, whilst still allowing
people to maintain their freedom and privacy in public without security
bottlenecks and conventional image-capturing cameras.

Fig. 1:  The RF waves from a Google Soli reflect from a person standing $1.5$m
away from the radar with and without a knife. To mitigate the variations in
specular reflection, the subject rotated through 90∘ and an average over 60s
was used in each scene. The reflected signal received via receiver 2 (of 3) of
the Soli is converted into a range profile by computing an FFT over it, and
plotted here. The difference between the two range profiles shows the
potential of using mmWave radars like the soli, for detecting metallic
objects.

This work is not the first to propose mmWave sensing for metal detection.
Fusion of mmWave radar and vision data has already helped create accurate and
effective object detection systems for autonomous driving applications [6].
The comparison in performance of Convolutional and Recurrent Neural Networks
(CNNs and RNNs) for metal detection using magnetic impedance sensors has been
extensively evaluated in [7]. Their system is compact, however they need to
scan the complete scene, and restrict themselves to large metal sheets that
are visible in the Line-of-Sight (LOS) of their sensor. [8] use mmWave radar
sensors to alert robots to the presence of humans. Of most relevance to our
study are [9, 10]\- the former study, [9] provides a comprehensive guide on
the metal detection capabilities of a $77-81$GHz radar chip but do so by
comparing intensities of the reflected signal with the intensities of their
own model of a body without the presence of the metallic object. Their work
does not look at concealed metallic objects but ones that are already visible.
[10] created an AI powered metal detection system capable of working in real-
time. The system, however, processes their data differently, is prohibitively
expensive, and is considerably bulkier than ours. One fundamental advantage
our system has over all existing mmWave systems proposed for similar
applications is the use of a radar sensor that has the widest Field of View
(FOV), smallest form factor and least power consumption amongst its
competitors. The Soli is capable of illuminating its surroundings with a
$150^{o}$ FOV radar pulse. The lower power consumption of the Soli is due to
the fact that it transmits 16 chirps at a pulse repetition frequency of $2000$
Hz in a single burst (each burst is transmitted at $25$Hz), and then stops
transmitting until the next burst to save power [3]. This saves considerable
power compared to mmWave radars used in existing works that continuously
transmit chirps. Compared to current radar based surveillance systems, our
technology does not need to sweep a scene to work, but provides inference on-
the-fly by illuminating the scene with RF waves and processing the received
signal.

Fig. 2: The mmSense set up is shown in (a). The individual components of the
set up, and exemplar visualizations of the imaged scenes are shown for the
Soli, and the Intel RealSense D435 in (b) and (c). The knife, gun, and metal
sheet, used for the experiments are shown in (d).

Our work is intended to disrupt the trend of specialised surveillance and
imaging systems which are becoming increasingly expensive to install and
operate, by using an inexpensive, compact device capable of being mounted in
various locations throughout open spaces, which can function in real time. To
this end, we present the use of a commercial mmWave radar transceiver to
detect the presence of concealed objects on people in real time, in a privacy
preserving manner. We focus on high frequency ($60$GHz), short range (up to
$3$m) sensing using Google’s Soli sensor, primarily due its miniature form
factor, low power consumption, portability, and novel sensing characteristics.
The Soli is designed for Human-Computer Interaction applications, and has
shown success in ’macro’ radar-based computational imaging tasks (detecting
motion, gestures etc). Its application to detecting objects within the
movement is unexplored and challenging. The Soli captures a superposition of
reflected energy from different parts of a scene using high frequency RF
waves: this results in poor lateral spatial resolution, while detecting even
the smallest amount of motion. This makes metal detection challenging when
there is plenty of movement in the scene i.e., in all practical real world
scenarios. To mitigate this challenge, we propose a novel, real-time Vision
Transformer model that can exploit semantic sequential relations in the
preprocessed radar data and recognize the presence of a concealed metallic
object on a person in a scene while ignoring objects such as wallets, keys,
belts and mobile phones.

The following are our main contributions: $(1)$ We present mmSense \- a novel,
end-to-end framework capable of detecting concealed metallic objects on people
in a scene using only raw radar data without any human intervention. $(2)$
mmSense is real-time, and can potentially use off-the-shelf commercially
available hardware making it easy to replicate and deploy. $(3)$ We open
source mmSense including all our datasets and models with the hopes of
facilitating further research in this novel field of Artificial Intelligence
powered concealed metal detection with mmWave RF signals.

##  2 mmSense

Fig. 3: TransDope (shown here) processes the radar data stream while
preserving time-dependent information throughout.

Our mmSense pipeline comprises of three components – a Google Soli radar for
data acquisition, an Intel RealSense D435 Time-of-Flight (TOF) camera for
visualizing results, and an API capable of acquiring and processing radar data
streams in real-time. A single burst of the Soli’s transmitted signal is
received across 3 antennas. For each RF illumination of the scene by the
radar, it receives back a signal $I\in\mathbb{R}^{P\times C}$ where $I$ is the
imaged scene as perceived by the radar and $P$ is the number of chirps
received by the radar across its $C(=3)$ antennas. We operate the Soli at a
frequency of $60$GHz with $1$GHz, the maximum permitted bandwidth $BW$. This
gives us a range resolution $R_{r}=\frac{c}{2BW}=15$cm, where $c$ refers to
the speed of light. This is the minimum distance that the radar can separate
in its LOS between two distinct points. The Soli transmits and receives a
series of chirps that are grouped into bursts- we define the number of chirps
for our system to be $16$, and collect bursts at $25$Hz, giving us 25 bursts
of Soli data in one second. In this configuration, we can detect up to a
maximum range of $9.6$m.

The Soli hardware has a corresponding API provided by Google and implemented
in C++. We built a C++ application around this API which allows us to
interface with the Soli radar in real-time (e.g. selecting a range profile)
and receiving the bursts generated from the radar. Our application supports
streaming the Soli bursts directly to a Python script using the ZeroMQ1
messaging framework. The bursts are relayed immediately upon being received by
the device with no additional buffering, and are ultimately parsed by a Python
module which extracts both the parameters associated with the burst (e.g. a
hardware-supplied timestamp) and the raw radar data. 11footnotetext:
https://github.com/zeromq/cppzmq

After parsing the raw chirps and their timestamps, we create a Range Doppler
[11] transformation of the signal. This is done via a series of Fast Fourier
Transforms (FFT) applied to the data. First, we calculate the complex value
range profile (RP) of the radar signal. This is done via an FFT of the radar
chirps received by the 3 antennas. As the Soli’s signal is a superposition of
reflections from a scene, the RP data can be interpreted as how well the
separate contributions of the RF scatters in the scene are resolved. This
gives us an estimate of the geometry of the scene. A Complex Range Doppler
(CRD) plot is then calculated as an FFT over each channel of the radar’s
complex value range profile. Here, the range represents the distance of the
object in a scene from the Soli, and the Doppler corresponds to the radial
velocity of the object towards the Soli. We use the magnitude of the CRD for
our experiments, which is obtained in the following way,
$\texttt{ARD}(r,d)=|\texttt{CRD}(r,d)|$, where ARD refers to the Absolute
Range Doppler, $r$ and $d$ are the range and doppler bins, and $|\cdot|$ is
the absolute value.

The ARD plots are processed using our novel Deep Neural Network, TransDope
(Doppler Transformer, figure 3), capable of accurate real time classification
of the input data stream. The input is a sequence of 8 ARD frames. TransDope
contains two Time Convolution layers pretraind on a large collected dataset of
ARD plots, an embedding layer to create a transformer compatible embedding of
the convolution features, and transformer layers to learn long range time-
dependent semantic features in the data. We first collect a large dataset of
ARDs from various scenes with and without concealed metallic objects on
actors. We then train a model with two Time Convolution and Max Pooling
layers, the output of which is flattened and fed to a classification layer.

Following training, we discard the output layer, and use the two time
convolution layers with the pre-trained weights as an initialization. Unlike
standard convolutions that apply a weight kernel across all 8 ARDs
concurrently, we apply convolutions sequentially to the 8 ARD frames to
extract time-dependent features from them, and hence call them time
convolutions. We then reshape the output of the last Max Pooling layer to
create an embedding of the features. We also add positional encoding to each
of the 8 ARD frames to preserve their sequence. Following this, we pass the
embedding through 3 TransDope layers that extract semantic dependencies within
the ARD’s feature representation. These layers are the same as ViTs [12]
encoder layers with the exception of having a convolutional layer following
the multi head attention layer, instead of the dense layers, to reduce
parameter size. We use global average pooling to reduce the transformer
layer’s features to a vector, which are then passed into the output layer. Our
Time Convolution layers have $32$ filters and a kernel size of $3\times 3$.
Our transformer layer has an embedding size of $128$ and uses $2$ attention
heads. TransDope contains $0.8$ million parameters, and can process a single
ARD frame in $19$ milliseconds on an Intel i$9$ $8$-core CPU. We train our
model in TensorFlow 2 for 50 epochs, with a batch size of $8$, and a learning
rate of $1e-2$ which inversely decays after every 10 epochs. During inference,
we feed $1$ batch of 8 ARD frames through the model to get a classification.

##  3 Experiments

P S | A | B | C | D | E | F
---|---|---|---|---|---|---
Object | M | K | K | G | G | G
People | 1 | 5 | 1 | 2 | 1 | 1
Dist. (m) | 2.0 | 2.0 | 2.0 | 2.85 | 1.5 | 2.0
Closed | ✗ | ✗ | ✗ | ✗ | ✓ | ✓
Accessories | ✓ | ✓ | ✗ | ✗ | ✗ | ✗
Acc. (%) | 95.1 | 86.9 | 88.4 | 89.0 | 74.6 | 79.2
Table 1: Distinct properties (P) of the scenes (S) we collected, along with
the accuracy of TransDope to identify the object for that scene. Here, K, G
and M refer to the Knife, Gun and Metal Sheet respectively, people is the
number of individuals in the scene and distance (in metres) is the maximum
distance from the Soli that the individuals in the scene walk up to. Closed
refers to a scene where the walls are close to the radar, and the RF signal
can bounce off adjacent walls. Accessories are everyday items belts, wallets,
keys and phones that the people in the scene carry.

To test the accuracy and flexibility of our technique, we collected 6
different scenes with varying characteristics, as depicted in table 1. Data
was acquired in 4 instances for each scene: 2 with a metallic object hidden on
a person, and 2 without. Each acquisition contains approximately 1500 frames
of data. Before training our machine learning model, we collected roughly
15,000 frames of Soli data equally split into the two classes in various
scenes, to pre-train the TransDope time convolutions. For each scene, we then
trained TransDope, to predict a binary class for each ARD.

We carefully curated different scenes to portray real world situations where
our system can be deployed. Scene A was an initial proof of concept where we
used the metal sheet as the hidden object to verify the capabilities of our
system. We were able to predict the presence of the sheet with $95.1\%$
accuracy. Scene B replicates a crowded expansive scenario, such as an airport
terminal. Here we crowded the scene with 5 people walking up to 2m away in
radius from the setup. Each person in the scene was carrying everyday objects
such as phones, keys, wallets, and belts; only one of these individuals had a
knife on their person. Even in such a challenging setting, our system detected
the presence of the knife with up to $86.9\%$ accuracy. In Scenes C and D, we
observed the effects of changing the hidden object from a knife to a gun. This
is important as different objects have different characteristic specular
reflections. As seen from our results, the performance of our system held when
switching the metallic object from the knife to the gun. Scenes A to D were
all open scenes, i.e. the data was not acquired with constricting walls. This
results in no multipath RF signals received by the Soli receiving antennas. In
Scenes E and F, we tested the effects of keeping our set up in a closed
setting and noticed performance decreased. Our results are summarized in table
1 and visualized in figure 4.

Ablations. Table 5 shows the effect of varying the amount of sequential
information provided to TransDope, as well as varying the various blocks of
TransDope. The experiments show that each individual component in our model
contributes to performance boosts in terms of metal detection accuracy. We
chose $8$ ARD frames per sequence as the input to TransDope due to it
providing the best accuracy versus execution time. Having multiple sequences
of ARDs does further boost performance, but it also doubles (for 2 ARD
sequences of 8 ARD frames - $2*8$), and quadruples (for $4*8$) the execution
time for only minor gains in performance.

Fig. 4: Results for Scene C where the person has a knife hidden under a
jacket. On the left are the ARDs for the three receiver antennas, and on the
right is the output visualization. The red TOF output denotes the knife being
detected, and the black is the misclassification due to the specular
reflection from the knife not providing a strong signal. Fig. 5: Effects of
varying the number of frame sequences and model layers on performance on Scene
C.

##  4 Conclusions and Limitations

Our paper proposed mmSense, an AI assisted concealed metal detection system
whose technology is centred on an mmWave transceiver. mmSense can detect the
presence of concealed weapons capable of mass harm even when scenes are
crowded. It does so in real-time, and without compromising the privacy of the
individuals in the scene. Our system however, has certain limitations in terms
of performance degradation due to the effects of multipath RF waves at the
receiver that occurs in close walled areas, as well as the inherent lack of
spatial context from which commercial mmWave sensors suffer. We believe that
investigating multi-modal sensor fusion of the radar and TOF data to add
spatial awareness to the ’sensing’ ability of mmSense may help to alleviate
these drawbacks, and would be a fitting next step to extend this technology.

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#  Strong Pressure Dependent Electron-Phonon Coupling in FeSe

Subhasish Mandal  Geophysical Laboratory, Carnegie Institution of Washington,
Washington D.C. 20015, USA  R. E. Cohen  Geophysical Laboratory, Carnegie
Institution of Washington, Washington D.C. 20015, USA  Department of Earth
Sciences, University College London, Gower Street, WC1E 6BT, London, United
Kingdom  K. Haule  Department of Physics, Rutgers University, Piscataway, New
Jersey 08854, USA

###### Abstract

We have computed the correlated electronic structure of FeSe and its
dependence on the $A_{1g}$ mode versus compression. Using the self-consistent
density functional theory - dynamical mean field theory (DFT-DMFT) with
continuous time quantum Monte Carlo (CTQMC), we find that there is greatly
enhanced coupling between some correlated electron states and the $A_{1g}$
lattice distortion. Superconductivity in FeSe shows a very strong sensitivity
to pressure, with an increase in Tc of almost a factor of 5 within a few GPa,
followed by a drop, despite monotonic pressure dependence of almost all
electronic properties. We find that the maximum $A_{1g}$ deformation potential
behaves similar to the experimental $T_{c}$. In contrast, the maximum
deformation potential in DFT for this mode increases monotonically with
increasing pressure.

###### pacs:

74.70.Xa, 74.25.Jb, 75.10.Lp

So far there is no predictive theory for superconductivity in the cuprate and
iron-superconductors, hence these superconductors can be classified as non-
conventional superconductors, since there is a well-developed, predictive
theory for electron-phonon superconductors whose normal state is well-
represented by conventional density functional theory (DFT) Loa  _et al._
(2012); Yin  _et al._ (2006); Cohen  _et al._ (1990). The unconventional
superconductors are very sensitive to applied pressure, so pressure provides a
control to test theories and develop a better understanding Medvedev  _et al._
(2009); Torikachvili  _et al._ (2008); Takahashi  _et al._ (2008). Here we
study superconductivity under applied pressure in pure FeSe; unlike cuprates,
superconductivity in FeSe arises without doping. FeSe is an ideal system to
study the electron pairing mechanism due to the simplicity of its crystal and
electronic structure. It shows a very strong enhancement of $T_{c}$ upon
application of modest pressure with dramatic increase of $T_{c}$ from 8K to
$\sim$ 37KMedvedev  _et al._ (2009); Margadonna  _et al._ (2009); Imai  _et
al._ (2009) and then decreases upon further application of pressure. Why does
$T_{c}$ increase with pressure and then decrease for rather small lattice
compression? This question was addressed in Ref. Imai  _et al._ , 2009, where
it was found that applied pressure (P) intensified antiferromagnetic spin
fluctuations (SF). However, this did not explain the decrease in $T_{c}$ with
further compression.

The discovery of the iron superconductors showed that high Tc is not specific
to the cuprates, and suggests a wider field of potential high Tc materials
Mazin (2010). Although DFT gives many properties reasonably accurately for
both cuprates Pickett  _et al._ (1990); Cohen  _et al._ (1989); Pickett  _et
al._ (1992) and Fe-superconductorsSubedi  _et al._ (2008); Johannes  _et al._
(2010); Mazin  _et al._ (2008a), there is also significant indication of the
importance of correlations and fluctuating local moments beyond DFT specially
for the Fe-superconductors which are paramagnetic metals in room temperature,
and Dynamical Mean Field Theory (DMFT) has proved to be a good approximation
Kotliar  _et al._ (2006); Kotliar and Vollhardt (2004); Schafgans  _et al._
(2012); Liu  _et al._ (2012); Yin  _et al._ (2011a, b); Kuneš  _et al._
(2008).

While most studies suggest a spin fluctuation coupling mechanism for SC in Fe-
superconductors similarly to cupratesMazin  _et al._ (2008b); Dai  _et al._
(2008); Jin  _et al._ (2011), strong coupling phonons have also been proposed
to play a role in both sets of materials Anisimov  _et al._ (1992); Cohen
(1994); Boeri  _et al._ (2010); Alexandrov and Mott (1994a); Cohen  _et al._
(1990); Chen  _et al._ (2007); *Dewaele:2009ur. The study of strong electron-
phonon coupling in correlated solids is in its infancy due to extreme
computational complexity. Only in the non-self-consistent Hubbard I and LDA+U
approximations has it proved tractable so far Savrasov and Kotliar (2003);
*Floris:2011ca. The role of lattice vibrations in the mechanism of SC in
unconventional superconductors is still controversial. The observation of
strong electron-phonon and spin-phonon coupling, both in cuprates Liu  _et
al._ (2009); Krakauer  _et al._ (1993, 1992); Lee  _et al._ (2006) and iron
superconductorsLanzara  _et al._ (2001); Chu  _et al._ (2013); Kim  _et al._
(2012); Gnezdilov  _et al._ (2011); Kumar  _et al._ (2010a); Liu  _et al._
(2013) indicates that the electron-phonon coupling (EPC) may play an important
role in the unconventional superconductors, at least to explain the observed
Fe-isotope effectKhasanov  _et al._ (2010), the anomalous temperature
dependence of the local Fe-As displacementHigashitaniguchi  _et al._ (2008),
gap anisotropy, and the correlation of $T_{c}$ with the Fe-anion height Okabe
_et al._ (2010). These observations also suggest polaron and/or bipolaron
driven superconductivity in this material Bussmann-Holder and Keller (2008);
Bussmann-Holder  _et al._ (2009); Zhao  _et al._ (1997); Salje  _et al._
(2005); Alexandrov (2003); Bussmann-Holder  _et al._ (2008).

Here we examine the effects of pressure on the electronic structure and
electron-phonon interaction (EPI) in FeSe using DMFT in combination with the
DFT as implemented in Haule  _et al._ (2010).

Figure 1:  (Color online) Pressure evolution of DFT-DMFT spectral function
(left panel, a-c) and the Fermi surface on the $k_{z}$=0 plane (right panel,
d-f). The Fermi surface is colored in red, green, and blue according to its
dominating orbital character of xy, xz, and yz respectively. (g) Quasiparticle
weight as a function of pressure for the Fe-$d$ orbitals.

Electronic and magnetic properties of FeSe are very sensitive to the position
($z_{Se}$) of the selenium layers with respect to the iron layersMoon and Choi
(2010); Okabe  _et al._ (2010); Grechnev  _et al._ (2012); Kuroki  _et al._
(2009); Yin  _et al._ (2008); Essenberger  _et al._ (2012); Mazin  _et al._
(2008a). The magnetic ordering is found to be strongly affected by the
chalcogen heightMoon and Choi (2010). An accurate estimation of $z_{Se}$ is
essential to study the electronic structure of FeSe. We optimized $z_{Se}$ for
P=0, 3.4, 7.2, and 11 GPa and notice a monotonic increase with P. The reported
experimental values of $z_{Se}$ at ambient pressure are consistently estimated
to $z_{Se}$ = 0.267Phelan  _et al._ (2009). Our DFT+DMFT computations give
value of $z_{Se}$=0.27 at ambient pressure (Fig. S2 in Supplementary
Information), whereas LDA and spin-polarized GGA give 0.234Subedi  _et al._
(2008) and 0.26 respectively. The inclusion of local spin fluctuations by DMFT
is hence crucial to describe the structural properties in the disordered
paramagnetic state, and has similar effect on $z_{Se}$ as the presence of long
ranged order in standard DFT.

We compute the DFT-DMFT spectral function ($A(\omega,k)$) and the Fermi
surface (FS) for the optimized value of $z_{Se}$ at different pressures and
summarized them in the Fig. 1. A dramatic change in $A(\omega,k)$ is noticed
when the pressure is increased from 0 to 3.4 GPa. There are three DFT-DMFT
bands crossing the Fermi energy ($E_{F}$) from $\Gamma$ to $X$-point at P=0,
while there are only two bands crossing $E_{F}$ at P=3.4 GPa. The strong 3D
band which crosses $E_{F}$ from $\Gamma$ to $Z$ at P=0, does not cross $E_{F}$
above 3.4 GPa. Further, we consider the orbital resolved FS at $k_{z}$=0 plane
as a function of pressure. From Fig. 1(d-f) we notice that the electron
pockets (e1 and e2) at the M point do not change much with increasing the
pressure whereas the hole pockets (h1, h2, and h3) at the $\Gamma$ point
changes significantly. The number of hole pocket􀀀 reduces from three to one by
increasing the pressure. The outer hole pocket h3 are mainly of xy character,
while the inner hole pockets h1 and h2 consists of xz and yz character. With
increasing pressure three hole pockets behave differently. The outer hole
pocket h3 expands, while the inner hole pocket h2 shrinks with increasing
pressure. The inner hole pocket h1, which shows most $k_{z}$ dependence,
vanishes above P=3.4 GPa.

Figure 2: (Color online). (a)Maximum and Fermi surface average of deformation
potentials ($\mathcal{D}$) for the A1g distortion computed in DFT-DMFT and DFT
as a function of pressure indicates the presence of strong EPC in FeSe; inset
shows deformation potential as a function of $E_{F}$ at P=0. (b)Demonstration
of huge local electron-lattice coupling for the A1g distortion in our DFT-DMFT
computations at P=0GPa for a selective part of the BZ; red and blue lines
represent GGA bands. The common Fermi energy is considered for the equilibrium
position and denoted by the single horizontal line for both DFT and DFT-DMFT
methods.

It is important to know how the electron correlation changes with increasing
pressure. In order to investigate the degree of correlation, we calculated
$Z_{A}=(1-\frac{\delta\Sigma}{\delta\omega})^{-1}_{\omega=0}$. In a Fermi-
liquid it is the quasiparticle weight, which is unity for non-interacting
system, and is much smaller than unity for strongly correlated system. We have
calculated $Z_{A}$ for all the Fe-d orbitals and plotted them as a function of
P in Fig. 1(g). Though the $d_{z^{2}},d_{x^{2}-y^{2}}$ orbital becomes less
correlated with the increase of P, the $t_{2g}$ orbitals ($d_{xz}$, $d_{yz}$,
and $d_{xy}$) remain correlated and in particular the $d_{xy}$ orbital, which
carries more magnetic moment, becomes even more correlated with increasing
pressure. The predicted $Z_{A}$ of 0.41 for $d_{xy}$ orbital at P=0 GPa and at
T=300 K differs from 0.287 calculated at T = 116 K in Ref.Yin  _et al._
(2011b) due to the use of slightly different lattice parameters and $z_{Se}$.
By comparing results with Ref. Yin  _et al._ (2011b), we found that among
other $t_{2g}$ orbitals, $d_{xy}$ shows the strongest temperature dependence
in $Z_{A}$ at P=0GPa.

Calculated electron density of states, optical conductivity both along ab-
plane and c-axis shows a monotonic behavior as a function of compression
(details in Supplementary). We now turn our discussion to the electron-phonon
coupling and polaron formation in FeSe. The coupling between electronic states
and atomic displacements (the electron-phonon matrix element) and hence
$\lambda$ is directly related to the shift in the energy eigenvalues at
$E_{F}$. We calculate this shift by calculating $\delta E$ (details in
Supplementary Information ). We estimate the average as well as the maximum
value of the deformation potential ($\mathcal{D}=\frac{\delta E}{\delta Q}$)
upon Se atom displacement ($\delta Q$) in $z_{Se}$ of a particular phonon mode
(A1g distortion) for the entire FS. In Fig. 2(a) we have plotted the
deformation potential for both DFT and DFT-DMFT methods. The equation of
states (pressure points on the axis) are obtained from the experimentKumar
_et al._ (2010b). First we notice that the average $\mathcal{D}$ increases in
DFT-DMFT over that obtained in DFT for all pressure. At P=0 the average
$\mathcal{D}^{2}$ increases $\sim$1.5 times in DFT-DMFT; $\mathcal{D}$ is 0.84
eV/$\AA$ in DFT-DMFT while 0.69 eV/$\AA$ in GGA. A similar increase was found
by Boeri et al. Boeri  _et al._ (2010) when magnetic softness was included in
their calculations. At P=3.4 GPa the average $\mathcal{D}^{2}$ increases
$\sim$ 2.25 times in DFT-DMFT. However this is still not sufficient to obtain
37 K but not small enough to ignore as suggested earlier by Boeri et al.Boeri
_et al._ (2010). More interesting is the pressure dependence of the maximum
$\mathcal{D}$. At ambient pressure we notice that the maximum deformation
potential ($\mathcal{D}^{m}$) in DFT-DMFT is about 3 times higher than that
obtained in GGA. One band is very sensitive to this deformation; it crosses
the $E_{F}$ for P=0, 1.4, 2.6 and -2.0 GPa ( indicated by h1 in the Fig. 1d
for P=0). This sensitive pocket gives a very high value of $\mathcal{D}^{m}$
for this pressure range within DFT-DMFT method, where the experimental $T_{c}$
is also observed to be high. $\mathcal{D}^{m}$ obtained from the GGA is found
to be very small at P=0. We found that the $\mathcal{D}$ obtained from DFT-
DMFT is different for different parts of the FS (details in the Supplementary
Information). For example at P=0, h1 gives $\mathcal{D}^{m}$ of $\sim$ 4.4 eV/
$\AA$, while e1 gives only $\sim$ 1.5 eV/$\AA$ with DMFT method. The largest
contribution in the enhanced deformation potential is from the hole pocket
(h1), located in the $\Gamma$-region. A nonuniform and anisotropic nature of
the electron phonon coupling has also seen in the cuprates, where the average
EPC was found to be one order of magnitude smaller than the maximum Devereaux
_et al._ (2004). This is consistent with our results.

With increasing pressure, maximum value of the deformation potential within
DFT-DMFT then decreases and remains almost unchanged after P=3.4 GPa; whereas
the maximum $\mathcal{D}$ within DFT for this mode is insensitive to
increasing pressure except at P=11 GPa, where the experimental $T_{c}$ is
found to decrease. At P=11 GPa, the sensitive band crosses the $E_{F}$ for the
GGA, which leads to a high $\mathcal{D}^{m}$ for GGA. For pressure above 3.4
GPa, we notice that the maximum $\mathcal{D}$ in DMFT is from the electron
pocket centered at $M$-point. $\mathcal{D}^{m}$ also strongly depends on the
$E_{F}$. The inset of Fig. 2(a) shows the behavior of maximum and average
value of $\mathcal{D}$ as a function of $E_{F}$ at P=0 calculated with DFT-
DMFT. So the movement of $E_{F}$ due to defect or pressure can significantly
change the FS topology and hence the $\mathcal{D}$. The momentum resolved
spectral function $A(\omega,k)$ is shown in Fig. 2(b) for both equilibrium
position and $A_{1g}$ distortion between the high symmetric points, where the
most sensitive band crosses the $E_{F}$. The solid red and blue lines
represent corresponding GGA bands for equilibrium position and $A_{1g}$
distortion respectively. From the Fig. 2(b), we notice that at P=0, the shift
in energy ($\delta E$) over the atomic displacement of 0.0276 $\AA$ is $\sim$
0.12 eV in DFT-DMFT and $\sim$ 0.04 eV in GGA, respectively. So as reflected
from Fig. 2, the $\mathcal{D}$ is about three times higher in DFT-DMFT for
this particular region of the BZ. If we notice carefully in Fig. 2(b), the
shift of the bands due to $A_{1g}$ distortion is very non-uniform in DFT-DMFT;
a strong deformation potential is noticed only in $\Gamma$ to Z region while
for the other part of the BZ, deformation potential is found to be small. This
leads to a strong non-uniform EPC at P=0, which is reflected in Fig. 2(a)
where maximum $\mathcal{D}$ is found to be about three times higher than the
average. We found this similar non-uniform EPC for P=1.4, 2.6, and -2.0 GPa.

We estimate $\lambda$ using $\mathcal{D}$ (Supplementary Information for
details). While the average $\lambda$ is still small, the maximum $\lambda$ in
DFT-DMFT is found to be 0.98 at P=0. At P=2.6 GPa, the maximum $\lambda$
reaches 1.159. We found that only certain electronic states have very strong
$\lambda$ while the average $\lambda$ is not strong enough to explain 37K. So
a conventional electron-phonon mechanism seems unlikely. On the other hand,
this also indicates that local EPC can be important and one can use polaron
model, where a single electron can strongly couple with the lattice and form
polarons. Formation of polaron has been experimentally found in both Fe-
superconductorsLiu  _et al._ (2013); Núñez-Regueiro (2009); Oyanagi and Zhang
(2010) and cupratesZhao  _et al._ (1997). The anomalous temperature dependence
of the local Fe-As displacement, observed in Ref. Higashitaniguchi  _et al._
(2008) indicates that local rather than global electron-lattice interaction is
present in Fe-based superconductors and as suggested in Ref. Bussmann-Holder
_et al._ (2009), polaron formation is responsible for the observed
anomaliesHigashitaniguchi  _et al._ (2008). Though the formation of polaron
depends on a lot of factors, like the band-filling, temperature, EPC strength,
phonon frequency etc, our results suggest to use a polaron model. We consider
the electronic state corresponding to maximum $\lambda$ ($\sim$ 1) forms a
polaron, which is a quasiparticle consisting of electron and the surrounding
lattice distortion. Then the polaronic binding energy ($E_{p}$) will linearly
depend Alexandrov and Mott (1994b); Ercelebi and Senger (1994) on maximum
$\lambda$ and hence on square of the maximum deformation potential. Taking the
polaronic band into account, Alexandrov and Mott Alexandrov and Mott (1994b)
described that $T_{c}$ exponentially depends on function of $E_{p}$. Under
hydrostatic pressure, we found that electronic properties change monotonically
while only $|\mathcal{D}^{m}|^{2}$ (and hence $E_{p}$) initially grows (to 3.4
GPa) and then drops, similarly to experimental $T_{c}$. This indicating that a
strong local EPC plays an important role in Fe-based superconductors.

It is important to mention that $T_{c}$ was found to increase rapidly for the
low pressure range (0-3 GPa) and can reach up to 27K at 1.48 GPaMizuguchi  _et
al._ (2008). The disagreement in the pressure dependence of experimental
$T_{c}$ and our DFT-DMFT calculation of maximum $\mathcal{D}$ can be due to
the presence of the mixed phase in low temperature crystal structure in
experiment while our calculations are based on room temperature tetragonal
(PbO-type) structure.

The behavior of the DFT-DMFT deformation potential with pressure hints that
superconductivity in FeSe may have partially phonon or polaron origin and
local EPI plays a very important role in superconductivity in the
unconventional superconductors. Analysis of the contributions of each many-
body state reveals that charge fluctuations due to correlations and charge
transfer from Fe to Se are coupled to the A1g mode.

Our computations predict that applied pressure significantly changes the FS
around $\Gamma$-point. We show the Fermi surface average of the deformation
potential is enhanced up to 50 % in DFT-DMFT when compared with standard DFT,
and is still not high enough to give high $T_{c}$ in FeSe. This reflects and
confirms that a simple electron-phonon coupling mechanism seems unlikely as
relevant from many experimental findings. Calculated electronic properties
show a monotonic behavior with applied pressure. We found a strong enhancement
of the coupling between correlated electronic states along high symmetric
$\Gamma$ point and $A_{1g}$ lattice distortion. The maximum deformation
potential within GGA for this mode is almost insensitive to increasing
pressure except at high pressure where the experimental $T_{c}$ is found to
decrease. The corresponding DFT-DMFT deformation potential behaves similarly
to experimental $T_{c}$, which increases first and then decrease after a
certain pressure.

To explain high Tc by conventional strong coupling EPI enhanced in DFT-DMFT
method, these enhancements would need to be on average just as large for all
modes. More importantly the difference (addition) between interband and
intraband coupling has to be enhanced to support the $s_{\pm}$ ($s_{++}$)
pairing symmetry. Alternatively, as shown here, if only certain modes become
very strongly coupled with certain electronic states, this could give
sufficient coupling for polaron formation which requires only certain modes to
have extreme coupling leading to condensation of either polaronic and/or
bipolaronic states or Cooper pairs Salje  _et al._ (2005); Zhao  _et al._
(1997); Alexandrov and Mott (1994a); Liu  _et al._ (2013). For high $T_{c}$
cuprates, Müller et al. showed that the normal state polaron can form Cooper
pairs and can be responsible for superconductivityZhao  _et al._ (1997). Such
polaronic states may involve spin as well as charge fluctuations Alexandrov
and Mott (1994a), leading to a problem that still requires significant
development for a predictive theory. Even if the giant correlated EPI we
predict is not directly responsible for superconductivity, it should help
explain some experimental observations, such as significant and unusual
isotope effects Chen  _et al._ (2007); Shirage  _et al._ (2009).

The high Tc superconductors so far are all rather bad metals in the normal
state, have low densities of state at EF, are ionic metals containing
transition metal ions, and are quasi-two-dimensional and highly anisotropic,
so it seems any competitive theory should explain why. Spin fluctuations may
play a major role, but it seems that is not enough to explain all of these
common features. The fact that they are anisotropic bad metals with low
densities of states may be because this decreases the screening of the
attractive interaction, partly from poorly screened Coulomb fluctuations from
phonons or polarons. Correlations may enhance the EPI as we found here, and in
addition lead to lower entropy from fluctuations among multiplets in the
normal state leading to higher Tc’s.

We thank I. I. Mazin, I. I. Naumov, M. Ahart, P, Zhang, X. Chen and V.
Struzhkin for helpful discussions. This research was supported as part of
EFree, an Energy Frontier Research Center funded by the US Department of
Energy Office of Science, Office of Basic Energy Sciences under Award DE-
SC0001057. K. H acknowledges the supports from NSF DMR 0746395. Computations
were performed at NERSC supercomputing facility.

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