Polaron spectroscopy of a bilayer excitonic insulator Ivan Amelio1N. D. Drummond2Eugene Demler3Richard Schmidt4 5and Atac Imamoglu1 1Institute of Quantum Electronics ETH Zurich CH-8093 Zurich Switzerland

2025-05-02 0 0 634.15KB 8 页 10玖币
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Polaron spectroscopy of a bilayer excitonic insulator
Ivan Amelio,1N. D. Drummond,2Eugene Demler,3Richard Schmidt,4, 5 and Atac Imamoglu1
1Institute of Quantum Electronics ETH Zurich, CH-8093 Zurich, Switzerland
2Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
3Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
4Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
5Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
(Dated: October 21, 2022)
Recent advances in fabrication of two dimensional materials and their moiré heterostructures
have opened up new avenues for realization of ground-state excitonic insulators, where the structure
spontaneously develops a finite interlayer electronic polarization. We propose and analyze a scheme
where an optically generated intralayer exciton is screened by excitations out of the excitonic in-
sulator to form interlayer polarons. Using Quantum Monte-Carlo calculations we first determine
the binding energy of the biexciton state composed of inter- and intralayer excitons, which plays a
central role in understanding polaron formation. We describe the excitations out of the ground-state
condensate using BCS theory and use a single interacting-quasiparticle-pair excitation Ansatz to
describe dynamical screening of optical excitations. Our predictions carry the hallmarks of the ex-
citonic insulator excitation spectrum and show how changing the interlayer exciton binding energy
by increasing the layer separation modifies the optical spectra.
I. INTRODUCTION
An excitonic insulator (EXI) is a phase of matter where
the ground-state features bound electron-hole pairs [1, 2].
This is most easily realized in bilayer structures where the
lowest energy conduction band (CB) state of one layer
is tuned near resonance with the highest energy valence
band (VB) state of the other layer. Introduction of insu-
lating layers in between the layers suppresses tunnel cou-
pling, thereby ensuring separate charge conservation in
the two layers [3]. Exciton formation corresponds to the
binding of electron and hole pairs due to Coulomb attrac-
tion. Due to the aligned dipole moments, such ground-
state excitons are a promising candidate to mediate in-
teractions between itinerant electrons (holes) in the CB
(VB), providing a platform for the physics of Bose-Fermi
mixtures [4–6], potentially supporting superconductiv-
ity [7–9]. Recently, evidence for the formation of ground-
state excitons in bilayer transition metal dichalcogenides
(TMDs) in the absence of a magnetic field has been re-
ported using capacitance measurements [10].
In this Letter, we propose optical spectroscopy as a
probe of excitonic insulators. We particularly focus on an
electric field tunable MoS2/hBN/WSe2heterostructure
where the conduction band (CB) of MoS2can be tuned
into resonance with the valence band (VB) of WSe2[11].
We assume that an intralayer exciton (X) is injected by
resonant light absorption, which in turn acts as a quan-
tum impurity that can bind to interlayer excitons (IXs)
in the ground-state. Polaron spectroscopy has already
proved to be an invaluable tool to characterize many-
body states in TMD mono- and bilayers [12–15].
In the limit where the EXI is described by a dilute Bose
gas of IXs, the physics of the mobile impurity physics may
be regarded as a Bose polaron problem. Since the bind-
ing energy between the impurity and the bosons plays a
central role in understanding the polaron spectrum, we
compute the binding energy of this inter-intra layer biex-
citon X-IX by a 4-body Quantum Monte-Carlo (QMC)
calculation. For large interlayer distances, the biexciton
wavefunction and energy approach that of an intralayer
trion (T) loosely bound to a hole in the other layer.
However, the Bose polaron description does not gener-
ally apply to our system. In the first place, for increas-
ing interlayer distances the IX binding energy becomes
comparable to the trion binding energy and the inter-
nal structure of the IX plays a role. Moreover, at larger
chemical potentials, a description of the ground-state in
terms of tightly bound, point-like bosons is inadequate,
but rather pairing involves fermions close to the Fermi
surface.
To fully take into account the microscopic fermionic
nature of the system, we model the EXI using the mean-
field BCS formalism [2, 16, 17], while treating the in-
tralayer exciton as a rigid mobile impurity. The polaron
spectra are computed using a generalization of the Chevy
Ansatz, where two interacting fermionic quasiparticles
are excited and scatter off the mobile impurity. This
analysis recovers the expectation that the energy of the
attractive polaron at low IX densities is determined by
the X-IX binding energy. Moreover, we find that the
gap in the quasiparticle spectrum hampers the transfer
of the oscillator strength from the repulsive to the attrac-
tive branch. Interestingly, when the IX binding energy
is comparable to the quasiparticle gap, we predict the
emergence of a third peak, associated with an excited
state of the X-IX complex. Polaron spectroscopy of an
EXI carries clear signatures of interlayer pairing and may
provide a direct estimate of the quasiparticle pair excita-
tion gap. Moreover, potential valley polarization of the
EXI [11] could be easily assessed in polarization resolved
spectroscopy.
On a technical level, the generalized Ansatz we use has
been previously implemented in the context of 3D atomic
arXiv:2210.03658v2 [cond-mat.mes-hall] 20 Oct 2022
2
Fermi superfluids [18–20] and has allowed for interpola-
tion between different regimes, including the BEC-BCS
crossover for varying densities. To get a better under-
standing of the variational subspace, we analyze the el-
ementary neutral excitations of the EXI; we show that
even though the gapless Goldstone branch is not cap-
tured at the single-excitation level, all other collective
modes, including the ones referred to in the literature as
Higgs [21] or Bardasis-Schrieffer [22] modes, are well re-
produced. In computing the elementary excitations, we
extend the geometric approach of [23, 24] to BCS the-
ory, where the BCS state is treated as a Gaussian state
and the collective modes as fluctuations on the Gaussian
manifold. Moreover, we do not assume contact interac-
tions, but rather work with realistic bilayer Keldysh [25–
27] and exciton-electron [28] interactions, marking a key
difference with respect to atomic superfluids where in-
teractions are contact-like and the polaron behavior was
studied as a function of the 3D scattering length tuned
through a Feschbach resonance.
II. FEW-BODY BINDING ENERGIES
Experiments in charge-tunable TMD monolayers have
established that the dominant resonances in the optical
excitation spectra can be identified as attractive and re-
pulsive polarons (AP and RP). In the limit of vanish-
ing doping, the AP resonance energy approaches that
of a T [12]. Similarly, since the ground-state of the bi-
layer system in the small density BEC regime consists
effectively of tightly bound IXs, we expect that the X-IX
energy determines the position of the AP resonance. De-
termining the binding energies of X, IX, T and X-IX, is
therefore key to understand the optical excitation spectra
as a function of interlayer separation.
We compute the binding energies of different com-
plexes in a MoS2/hBN/WSe2heterostructure using the
diffusion QMC method as implemented in the casino
package [29]. prisedcomIn particular, as sketched in
Fig. 1a, we calculate the binding energies of the MoS2
X, the IX made of an electron in MoS2and a hole in
WSe2, the T in MoS2and the X-IX. Our calculation is
an extension of Refs. 30 and 31 to a bilayer system; im-
portantly, the trial wavefunctions decay exponentially at
large separations and satisfy the cusp conditions for the
Keldysh potential [31]. The Jastrow function includes
smoothly truncated polynomial expansions in interparti-
cle distances [32].
The QMC approach can only treat the intraband sec-
tors of the Coulomb operator. Even though the electron-
hole exchange terms do modify the binding energy of T,
and X-IX [31, 33], their contribution should be small as
compared to the actual binding energy. Based on that
we expect QMC calculation to provide a good estimate
of the binding energies.
We take me=mh= 0.55m0for the CB and VB masses
in MoS2, and mh= 0.40m0for the VB in WSe2. These
values match the reduced masses reported in the quan-
titative investigation by Goryca et al. [34]. We neglect
the less known mass ratio imbalance, having verified that
the binding energies are not very sensitive to it [33]. As
detailed in SI.A, we use the bilayer Keldysh potential [27]
for electron-hole and electron-electron interactions: We
take the relevant screening lengths from Ref. [34], and
use = 4.5for the dielectric constant of the hBN envi-
ronment. With these parameters, for a MoS2monolayer,
we obtain 217 meV for the X binding energy and 18 meV
for the trion, which are in good agreement with the ex-
perimental values in encapsulated samples [35].
Figure 1.b shows the calculated energy of the few-
body complexes as a function of the interlayer distance
d, having set as reference to zero the energies of the band
edges. We express din units of the thickness of a single
hBN layer (L1= 0.33 nm), and plot X, T, IX,X-IX for
d= 1,2,4,...,128 ×L1. We note that the MoS2exci-
ton and trion energies also depend on d, since the WSe2
monolayer contributes to screening. The binding energies
of T and X-IX, extracted from the energies depicted in
Fig. 1b are plotted in Fig. 1.c; here the binding energy Eb
for X-IX is given by Eb=EX+EIX EXIX. For large
interlayer distances yielding EXEIX , the X-IX state
can be described as a strongly bound negatively charged
intralayer trion T loosely bound to a hole in the WSe2
layer (see SI.B for the probability distribution functions).
III. MANY-BODY MODEL
To analyze optical excitation spectrum in the presence
of an EXI, we assume that the X can be treated as a
point-like quantum impurity with no internal degrees of
freedom. We also assume that IXs are spin-valley polar-
ized and a few-layer-thick hBN separates MoS2and WSe2
layers, ensuring that there is no electronic moiré poten-
tial. For simplicity, we consider the particle-hole sym-
metric case, with equal electron and hole masses (me=
mh=m) and set chemical potentials µe=µh=µ. In
practice, µe, µhcan be tuned either by connecting the
two layers to different reservoirs to form a biased junc-
tion or by applying a normal electric field Ez. In a recent
experiment [10] both mechanisms have been employed to
overcome the semiconductor band gap. Our theory can
be equally applied to both scenarios.
The total system Hamiltonian is given by
H=Hel +Himp +HW.(1)
Denoting CB and VB electrons respectively as a
ac, b av, the electronic Hamiltonian reads
Hel =X
k
εk(a
kak+bkb
k)+ 1
2AX
kpq
U(q)(a
k+qa
pqapak+
+bk+qbpqb
pb
k)1
AX
kpq
V(q)a
k+qbp+qb
pak(2)
摘要:

PolaronspectroscopyofabilayerexcitonicinsulatorIvanAmelio,1N.D.Drummond,2EugeneDemler,3RichardSchmidt,4,5andAtacImamoglu11InstituteofQuantumElectronicsETHZurich,CH-8093Zurich,Switzerland2DepartmentofPhysics,LancasterUniversity,LancasterLA14YB,UnitedKingdom3InstituteforTheoreticalPhysics,ETHZurich,80...

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