We analyze the lineshape of the quasiparticle photoluminescence of monolayer and bilayer molybdenum ditelluride in temperature- and excitation intensity-dependent experiments. We confirm the existence of a negatively charged trion in the bilayer based on its emission characteristics and find hints for a coexistence of intra- and interlayer trions with a few meV splitting in energy. From the lineshape analysis of exciton and trion emission we extract values for exciton and trion deformation potentials as well as acoustical and optical phonon-limited mobilities in MoTe2, with the mobilities showing the highest values so far reported for transition metal dichalcogenides.
An ordered state of electrons in solids in which excitons condense was proposed many years ago as a theoretical possibility but has, until recently, never been observed. We review recent studies of semiconductor bilayer systems that provide clear evidence for this phenomenon and explain why exciton condensation in the quantum Hall regime, where these experiments were performed, is as likely to occur in electron-electron bilayers as in electron-hole bilayers. In current quantum Hall exciton condensates, disorder induces mobile vortices that flow in response to a supercurrent and limit the extre…
In ordinary semiconductor bilayers, exciton condensates appear at total Landau level filling factor $ν_{T}=1$. We predict that similar states will occur in Bernal stacked graphene bilayers at many non-zero integer filling factors. For $ν_{T} = -3,1$ we find that the superfluid density of the exciton condensate vanishes and that a finite-temperature fluctuation induced first order isotropic-smectic phase transition occurs when the layer densities are not balanced. These anomalous properties of bilayer graphene exciton condensates are due to the degeneracy of Landau levels with $n=0$ and $n=1$ o…
Exciton superfluid is a macroscopic quantum phenomenon in which large quantities of excitons undergo the Bose-Einstein condensation. Recently, exciton superfluid has been widely studied in various bilayer systems. However, experimental measurements only provide indirect evidence for the existence of exciton superfluid. In this article, by viewing the exciton in a bilayer system as an electric dipole, we provide a general theory for the electric dipole superconductivity, and derive the London-type and Ginzburg-Landau-type equations for the electric dipole superconductors. By using these equatio…
We report the direct observation of intervalley exciton between the Q conduction valley and $Γ$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Γ$ exciton lies at ~18 meV below the QK exciton and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton spectra at gate-tunable electric field, we reveal different interlayer electric dipole moments and Stark shifts between Q$Γ$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Γ$ and QK excitons. Both Q$Γ$ and QK excitons exhibit pronounced phonon re…
Bilayer quantum Hall systems at ν=1 support an excitonic ground state. In addition to the usual charged quasiparticles, this system possesses a condensate degree of freedom: exciton transport. Detection of this neutral transport mode is facilitated by the use of the Corbino multiply-connected geometry in which charge transport is suppressed. We here summarize our recent experiments on Corbino devices which directly demonstrate exciton transport across the bulk of the incompressible ν=1 quantum Hall state.
The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe$_2$ bilayers. In particular, we show that the strong hybridization of electrons at the $Λ$ point leads to a drastic reds…
We study the kinetics of 2D Bose gas cooling provided Bose particles interact with 3D phonons. At low temperatures phonon emission is prohibited by the energy and the momentum conservation. We show that both particle-particle scattering and impurity scattering assist the Bose gas cooling.
Bilayer electron-hole systems with unequal electron and hole densities are expected to have exciton condensate ground states with spontaneous spin-polarization in both conduction and valence bands. In the absence of spin-orbit and electron-hole exchange interactions there is no coupling between the spin-orientations in the two quantum wells. In this article we show that Rashba spin-orbit interactions lead to unconventional magnetic anisotropies, whose strength we estimate, and to ordered states with unusual quasiparticle spectra.
Spatially indirect excitons with displaced wavefunctions of electrons and holes play a pivotal role in a large portfolio of fascinating physical phenomena and emerging optoelectronic applications, such as valleytronics, exciton spin Hall effect, excitonic integrated circuit and high-temperature superfluidity. Here, we uncover three types of spatially indirect excitons (including their phonon replicas) and their quantum-confined Stark effects in hexagonal boron nitride encapsulated bilayer WSe2, by performing electric field-tunable photoluminescence measurements. Because of different out-of-pla…
We develop a theory of interlayer tunneling in the exciton condensate of bilayer quantum Hall systems, which predicts strongly enhanced, but finite, tunneling conductance peaks near zero bias even at zero temperature. It is emphasized that, though this strongly enhanced tunneling originates from spontaneous interlayer phase coherence, it is fundamentally not the Josephson effect. Because of strong interlayer correlation, the bilayer system behaves as a single system so that conventional tunneling theories treating two layers as independent systems are not applicable. Based on our theory, we co…
We investigate a bilayer system of critical HgTe quantum wells each featuring a spin-degenerate pair of massless Dirac fermions. In the presence of an electrostatic inter-layer Coulomb coupling, we determine the exciton condensate order parameter of the system self-consistently. Calculating the bulk topological $\mathbb Z_2$ invariant of the resulting mean field Hamiltonian, we discover a novel time reversal symmetric topological exciton condensate state coined the helical topological exciton condensate. We argue that this phase can exist for experimentally relevant parameters. Interestingly, …
Understanding the dynamics of excitons in two dimensional semiconductors requires a theory that incorporates the essential physics distinct from their three-dimensional counterparts. In addition to the modified dielectric environment, single-particle states with strongly non-parabolic dispersion appear in many two-dimensional band structures, so that "effective mass" is ill-defined. Focusing on electrostatically-biased bilayer graphene as an example where quartic (and higher) dispersion terms are necessary, we present a semi-analytic theory used to investigate the properties of ground and exci…
Realizing nonlinear optical response in the low photon density limit in solid-state systems has been a long-standing challenge. Semiconductor microcavities in the strong coupling regime hosting exciton-polaritons have emerged as attractive candidates in this context. However, the weak interaction between these quasiparticles has been a hurdle in this quest. Dipolar excitons provide an attractive strategy to overcome this limitation but are often hindered by their weak oscillator strength. The interlayer dipolar excitons in naturally occurring homobilayer MoS$_2$ alleviates this issue owing to …
The interaction of intralayer and interlayer excitons is studied in a two-dimensional semiconductor, homobilayer MoS$_2$. It is shown that the measured optical susceptibility reveals both the magnitude and the sign of the coupling constants. The interlayer exciton interacts capacitively with the intralayer B-exciton (positive coupling constant) consistent with hole tunnelling from one monolayer to the other. Conversely, the interlayer exciton interacts inductively with the intralayer A-exciton (negative coupling constant). First-principles many-body calculations show that this coupling arises …
We show how the excitonic features of biaxial MoS2 flakes are very sensitive to biaxial strain. We find a lower bound for the gauge factors of the A exciton and B exciton of (-41 +- 2) meV/% and (-45 +- 2) meV/% respectively, which are larger than those found for single-layer MoS2. Interestingly, the interlayer exciton feature also shifts upon biaxial strain but with a gauge factor that is systematically larger than that found for the A exciton, (-48 +- 4) meV/%. We attribute this larger gauge factor for the interlayer exciton to the strain tunable van der Waals interaction due to the Poisson …
The quantum Hall state at total filling factor $ν_T=1$ in bilayer systems realizes an exciton condensate and exhibits a zero-bias tunneling anomaly, similar to the Josephson effect in the presence of fluctuations. In contrast to conventional Josephson junctions, no Fraunhofer diffraction pattern has been observed, due to disorder induced topological defects, so-called merons. We consider interlayer tunneling in the presence of microwave radiation, and find Shapiro steps in the tunneling current-voltage characteristic despite the presence of merons. Moreover, the Josephson oscillations can also…
The condensation of excitons, bound electron-hole pairs in a solid, into a coherent collective electronic state was predicted over 50 years ago. Perhaps surprisingly, the phenomenon was first observed in a system consisting of two closely-spaced parallel two-dimensional electron gases in a semiconductor double quantum well. At an appropriate high magnetic field and low temperature, the bilayer electron system condenses into a state resembling a superconductor, only with the Cooper pairs replaced by excitons comprised of electrons in one layer bound to holes in the other. In spite of being char…
We study the exciton condensate in zero temperature limit in a special class of electron-hole bilayer systems adjacent to insulating ferromagnetic films. With the self-consistent mean-field approximation, we find that the Rashba spin-orbit interaction in the electron and hole layers can induce the p \pm ip or p pairing states depending on the different magnetization of the overlapped ferromagnetic films. Correspondingly, the topologically nontrivial or trivial phases emerge. Furthermore, in the topologically nontrivial phase, the quasiparticle excitations of the U(1) vortex are attached to fra…
Several recent experiments have reported an anomalous temperature dependence of the Coulomb drag effect in electron-hole bilayers. Motivated by these puzzling data, we study theoretically a low-density electron-hole bilayer, where electrons and holes avoid quantum degeneracy by forming excitonic molecules. We describe the ionization-recombination crossover between the electron-hole plasma and exciton gas and calculate both the intralayer and drag resistivity as a function of temperature. The latter exhibits a minimum followed by a sharp upturn at low temperatures in a qualitative agreement wit…
Excitons in bilayer transition metal dichalcogenides (2L-TMDs) are Coulomb-bound electron/hole pairs that can be viewed as broadly tunable analogs of atomic or molecular systems. Here, we study the properties of 2L-TMD excitons under strong electric field. To overcome the field limit, reached in previous experiments, we developed a new organic/inorganic molecular gating technique. Our approach allows reaching the field > 0.27 V nm-1, about twice higher than previously available. Under this field inter and intra-layer excitonic are brought into an energetic resonance, allowing us to discover ne…
We report an experimental study of temperature-dependent spectral lineshapes of phonon side-band emission stemming from dark excitons in monolayer and bilayer WSe$_{2}$. Using photoluminescence spectroscopy in the range from 4 to 100K, we observe a pronounced asymmetry in the phonon-assisted luminescence from momentum-indirect exciton reservoirs. We demonstrate that the corresponding spectral profiles are distinct from those of bright excitons with direct radiative decay pathways. The lineshape asymmetry reflects thermal distribution of exciton states with finite center-of-mass momenta, charac…
When two sheets of graphene stack in a twisted bilayer graphene (tBLG) configuration, the resulting constrained overlap between interplanar 2p orbitals produce angle-tunable electronic absorption resonances. Using a novel combination of multiphoton transient absorption (TA) microscopy and TEM, we resolve the resonant electronic structure, and ensuing electronic relaxation inside single tBLG domains. Strikingly, we find that the transient electronic population in resonantly excited tBLG domains is enhanced many fold, forming a major electronic relaxation bottleneck. 2-photon TA microscopy shows…
The ground state of two-dimensional (2D) electron systems with equal low densities of electrons and holes in nearby layers is an exciton fluid. We show that a reservoir for excitons can be established by contacting the two layers separately and maintaining the chemical potential difference at a value less than the spatially indirect band gap. Equilibration between the exciton fluid and the contacts proceeds via a process involving virtual intermediate states in which an unpaired electron or hole occupies a free carrier state in one of the 2D layers. We derive an approximate relationship betwee…
We introduce a design of electrically isolated floating bilayer GaAs quantum wells (QW) in which application of a large gating voltage controllably and highly reproducibly induces charges that remain trapped in the bilayer after removal of the gating voltage. At smaller gate voltages, the bilayer is fully electrically isolated from external electrodes by thick insulating barriers. This design permits full control of the total and differential densities of two coupled 2D electron systems. The floating bilayer design provides a unique approach for studying systems inaccessible by simple transpor…
Interlayer excitons are bound states of electrons and holes confined in separate two-dimensional layers. Due to their repulsive dipolar interaction, interlayer excitons can form a correlated liquid. If another electron-hole bilayer is present, excitons from different bilayers can exhibit mutual attraction. We study such a quadrilayer system by a hypernetted chain formalism. We compute ground state energies, pair correlation functions, and collective mode velocities as functions of the exciton densities. We estimate the critical density for the transition to a paired biexciton phase. For a stro…
Moiré superlattices formed in van der Waals bilayers have enabled the creation and manipulation of new quantum states, as is exemplified by the discovery of superconducting and correlated insulating states in twisted bilayer graphene near the magic angle. Twisted bilayer semiconductors may lead to tunable exciton lattices and topological states, yet signatures of moiré excitons have been reported only in closely angularly-aligned bilayers. Here we report tuning of moiré lattice in WS$_{2}$ /MoSe$_{2}$ bilayers over a wide range of twist angles, leading to the continuous tuning of moiré lattice…
We study the exciton condensate (EC) in a bilayer two-dimension-electron-gas (2DEG) adjacent to a type-II superconductor thin film with an array of pinned vortex lattices. By applying continuum low energy theory and carrying numerical simulations of lattice model within mean-field approximation, we find that if the order parameter of EC has a vortex profile, there are exact zero modes and associated \emph{rational} fractional charge for zero pseudospin potential ($μ$) and average chemical potential ($h$): $μ$=0 and $h$=0; while for $μ\mathtt{\neq}0$ and $h$=0, intervalley mixing splits the zer…
The band structure of bilayer graphene is tunable by introducing a relative twist angle between the two layers, unlocking exotic phases, such as superconductor and Mott insulator, and providing a fertile ground for new physics. At intermediate twist angles around 10°, highly degenerate electronic transitions hybridize to form excitonic states, a quite unusual phenomenon in a metallic system. We probe the bright exciton mode using resonant Raman scattering measurements to track the evolution of the intensity of the graphene Raman G peak, corresponding to the E2g phonon. By cryogenically cooling…
Interference between different possible paths lies at the heart of quantum physics. Such interference between coupled discrete and continuum states of a system can profoundly change its interaction with light as seen in Fano resonance. Here we present a unique many-body Fano system composed of a discrete phonon vibration and continuous electron-hole pair transitions in bilayer graphene. Mediated by the electron-phonon interactions, the excited state is described by new quanta of elementary excitations of hybrid phonon-exciton nature. Infrared absorption of the hybrid states exhibit characteris…
We discuss the diamagnetism induced in an isolated quantum Hall bilayer with total filling factor one by an in-plane magnetic field. This is a signature of counterflow superfluidity in these systems. We calculate magnetically induced currents in the presence of pinned vortices nucleated by charge disorder, and predict a history-dependent diamagnetism that could persist on laboratory timescales. For current samples we find that the maximum in-plane moment is small, but with stronger tunneling the moments would be measurable using torque magnetometry. Such experiments would allow the persistent …
Using resonant 2-photon excitation of interlayer electrons in twisted bilayer graphene (tBLG), we resolve photoluminescence (PL) that tunes spectrally with stacking angle, θ. This weak signal is 4- 5$\times$ larger than the non-resonant background and is emitted from the interlayer band anti-crossing regions traditionally associated with van Hove singularity resonances. However, our observation of resonant PL emission with delayed ~1 ps electronic thermalization suggests interlayer carriers may instead form bound-excitons. Using both the 2-photon PL and intraband transient absorption spectra, …
Recent advances in the field of vertically stacked 2D materials have revealed a rich exciton landscape. In particular, it has been demonstrated that out-of-plane electrical fields can be used to tune the spectral position of spatially separated interlayer excitons. Other studies have shown that there is a strong hybridization of exciton states, resulting from the mixing of electronic states in both layers. However, the connection between the twist-angle dependent hybridization and field-induced energy shifts has remained in the dark. Here, we investigate on a microscopic footing the interplay …
Monolayer (ML) transition metal dichalcogenides (TMDs) undergo substantial changes in the single-particle band structure and excitonic optical response upon the addition of just one layer. As opposed to the single-layer limit, the bandgap of bilayer (BL) TMD semiconductors is indirect which results in reduced photoluminescence with richly structured spectra that have eluded a detailed understanding to date. Here, we provide a closed interpretation of the elementary optical responses of BL WSe$_2$ as a representative material for the wider class of TMD semiconductors. By combining theoretical c…
Spatially indirect excitons can be created when an electron and a hole, confined to separate layers of a double quantum well system, bind to form a composite Boson. Because there is no recombination pathway such excitons are long lived making them accessible to transport studies. Moreover, the ability to independently tune both the intralayer charge density and interlayer electron-hole separation provides the capability to reach the low-density, strongly interacting regime where a BEC-like phase transition into a superfluid ground state is anticipated. To date, transport signatures of the supe…
Exciton condensation in an electron-hole bilayer system of monolayer transition metal dichalcogenides is analyzed at three different levels of theory to account for screening and quasiparticle renormalization. The large effective masses of the transition metal dichalcogenides place them in a strong coupling regime. In this regime, mean field (MF) theory with either an unscreened or screened interlayer interaction predicts a room temperature condensate. Interlayer and intralayer interactions renormalize the quasiparticle dispersion, and this effect is included in a GW approximation. The renorma…
We report electrical transport measurements on GaAs/AlGaAs based electron-hole bilayers. These systems are expected to make a transition from a pair of weakly coupled two-dimensional systems to a strongly coupled exciton system as the barrier between the layers is reduced. Once excitons form, phenomena such as Bose-Einstein condensation of excitons could be observed. In our devices, electrons and holes are confined in double quantum wells, and carriers in the devices are induced with top and bottom gates leading to variable density in each layer. Separate contact to each layer allows Coulomb d…
Exciton condensates (EC) are macroscopic coherent states arising from condensation of electron-hole pairs. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study EC. The tunnel barrier suppresses recombination yielding long-lived excitons. However, this separation also reduces interlayer Coulomb interactions, limiting the exciton binding strength. Here, we report the observation of EC in naturally occurring 2H-stacked bilayer WSe$_2$. In this system, the intrinsic spin-valley structure su…
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
The high-temperature superfluidity of two-dimensional dipolar excitons in two parallel TMDC layers is predicted. We study Bose-Einstein condensation in the two-component system of dipolar A and B excitons. The effective mass, energy spectrum of the collective excitations, the sound velocity and critical temperature are obtained for different TMDC materials. It is shown that in the Bogolubov approximation the sound velocity in the two-component dilute exciton Bose gas is always larger than in any one-component. The difference between the sound velocities for two-component and one-component dilu…
Experiments aimed at demonstrating Bose-Einstein condensation of excitons in two types of experiments with bilayer structures (coupled quantum wells) are reviewed, with an emphasis on the basic effects. Bose-Einstein condensation implies the existence of a macroscopic coherence, also known as off-diagonal long-range order, and proposed tests and past claims for coherence in these excitonic systems are discussed.
We study the phase diagram of the inverted InAs/GaSb bilayer quantum wells. For small tunneling amplitude between the layers, we find that the system is prone to formation of an s-wave exciton condensate phase, where the spin-structure of the order parameter is uniquely determined by the small spin-orbit coupling arising from the bulk inversion asymmetry. The phase is topologically trivial and does not support edge transport. On the contrary, for large tunneling amplitude, we obtain a topologically non-trivial quantum spin Hall insulator phase with a p-wave exciton order parameter, which enhan…
While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster time scale in MoSe$_2$ bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the $K$ va…
Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling $ν_T=1$. These correlations are manifested by a non-linear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly-coupled bilayers. The pseudogap suppression is strongest at $ν_T=1$ and grows rapidly as the critical layer separation for exciton condensation is approached from above.
This tutorial paper reviews some of the physics of quantum Hall bilayers with a focus on the case where there is low or zero tunnelling between the two layers. We describe the interlayer coherent states at filling factors nu=1 and nu=2 as exciton condensates and discuss some of the theory associated with these states.
The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. We present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe$_2$ monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton $g$-factors from first principles and tight-binding for all possible spin-va…
We demonstrate that counterflowing electrical currents can move through the bulk of the excitonic quantized Hall phase found in bilayer two-dimensional electron systems (2DES) even as charged excitations cannot. These counterflowing currents are transported by neutral excitons which are emitted and absorbed at the inner and outer boundaries of an annular 2DES sample via an Andreev reflection process.
We consider the excitonic effects on the thermal properties in the AB-stacked bilayer graphene. The calculations are based on the bilayer generalization of the usual Hubbard model at the half-filling. The full interaction bandwidth is used without any low-energy assumption. We obtain the unusually high values for the electronic figure of merit even at the room-temperatures which is very promising for the thermoelectric applications of the AB-bilayer structure. We discuss the effects of the interlayer Coulomb interaction and temperature on different thermal parameters in the bilayer graphene an…
We propose a state of excitonic solid for double layer two dimensional electron hole systems in transition metal dicalcogenides stacked on opposite sides of thin layers of BN. Properties of the exciton lattice such as its Lindemann ratio and possible supersolid behaviour are studied. We found that the solid can be stabilized relative to the fluid by the potential due to the BN.
