Spontaneous coherence in a cold exciton gas

High-Temperature Excitonic Condensation in 2D Lattice

Exploration of high-temperature bosonic condensation is of significant importance for the fundamental many-body physics and applications in nanodevices, which, however, remains a huge challenge. Here, in combination of many-body perturbation theory and first-principles calculations, a new-type spatially indirect exciton can be optically generated in two-dimensional (2D) Bi2S2Te because of its unique structure feature. In particular, the spin-singlet spatially indirect excitons in Bi2S2Te monolayer are dipole/parity allowed and reveal befitting characteristics for excitonic condensation, such as small effective mass and satisfied dilute limitation. Based on the layered Bi2S2Te, the possibility of the high-temperature excitonic Bose-Einstein condensation (BEC) and superfluid state in two dimensions, which goes beyond the current paradigms in both experiment and theory, are proved. It should be highlighted that record-high phase transition temperatures of 289.7 and 72.4 K can be theoretically predicted for the excitonic BEC and superfluidity in the atomic thin Bi2S2Te, respectively. It therefore can be confirmed that Bi2S2Te featuring bound bosonic states is a fascinating 2D platform for exploring the high-temperature excitonic condensation and applications in such as quantum computing and dissipationless nanodevices.

Giant hyperfine interaction between a dark exciton condensate and nuclei

We study the interaction of a dark exciton Bose-Einstein condensate with the nuclei in gallium arsenide/aluminum gallium arsenide coupled quantum wells and find clear evidence for nuclear polarization buildup that accompanies the appearance of the condensate. We show that the nuclei are polarized throughout the mesa area, extending to regions that are far away from the photoexcitation area and persisting for seconds after the excitation is switched off. Photoluminescence measurements in the presence of radio frequency radiation reveal that the hyperfine interaction between the nuclear and electron spins is enhanced by two orders of magnitude. We suggest that this large enhancement manifests the collective nature of the N-exciton condensate, which amplifies the interaction by a factor of [Formula: see text].

Controlled interlayer exciton ionization in an electrostatic trap in atomically thin heterostructures

Atomically thin semiconductor heterostructures provide a two-dimensional (2D) device platform for creating high densities of cold, controllable excitons. Interlayer excitons (IEs), bound electrons and holes localized to separate 2D quantum well layers, have permanent out-of-plane dipole moments and long lifetimes, allowing their spatial distribution to be tuned on demand. Here, we employ electrostatic gates to trap IEs and control their density. By electrically modulating the IE Stark shift, electron-hole pair concentrations above 2 × 1012 cm-2 can be achieved. At this high IE density, we observe an exponentially increasing linewidth broadening indicative of an IE ionization transition, independent of the trap depth. This runaway threshold remains constant at low temperatures, but increases above 20 K, consistent with the quantum dissociation of a degenerate IE gas. Our demonstration of the IE ionization in a tunable electrostatic trap represents an important step towards the realization of dipolar exciton condensates in solid-state optoelectronic devices.

Interfacial Charge-Transfer Excitonic Insulator in a Two-Dimensional Organic-Inorganic Superlattice

Excitonic insulators are long-sought-after quantum materials predicted to spontaneously open a gap by the Bose condensation of bound electron-hole pairs, namely, excitons, in their ground state. Since the theoretical conjecture, extensive efforts have been devoted to pursuing excitonic insulator platforms for exploring macroscopic quantum phenomena in real materials. Reliable evidence of excitonic character has been obtained in layered chalcogenides as promising candidates. However, owing to the interference of intrinsic lattice instabilities, it is still debatable whether those features, such as the charge density wave and gap opening, are primarily driven by the excitonic effect or by the lattice transition. Herein, we develop an intercalation chemistry strategy for obtaining a novel charge-transfer excitonic insulator in organic-inorganic superlattice interfaces that serves as an ideal platform to decouple the excitonic effect from the lattice effect. In this system, we observe a narrow excitonic gap, formation of a charge density wave without periodic lattice distortion, and metal-insulator transition, providing visualized evidence of exciton condensation occurring in thermal equilibrium. Our findings identify self-assembly intercalation chemistry as a new strategy for developing novel excitonic insulators.

Geometric Stiffness in Interlayer Exciton Condensates

Recent experiments have confirmed the presence of interlayer excitons in the ground state of transition metal dichalcogenide bilayers. The interlayer excitons are expected to show remarkable transport properties when they undergo Bose condensation. In this Letter, we demonstrate that quantum geometry of Bloch wave functions plays an important role in the phase stiffness of the interlayer exciton condensate. Notably, we identify a geometric contribution that amplifies the stiffness, leading to the formation of a robust condensate with an increased Berezinskii-Kosterlitz-Thouless temperature. Our results have direct implications for the ongoing experimental efforts on interlayer excitons in materials that have nontrivial quantum geometry. We provide estimates for the geometric contribution in transition metal dichalcogenide bilayers through a realistic continuum model with gated Coulomb interaction, and find that the substantially increased stiffness may allow an interlayer exciton condensate to be realized at amenable experimental conditions.

Electrical Control and Transport of Tightly Bound Interlayer Excitons in a MoSe_{2}/hBN/MoSe_{2} Heterostructure

Controlling interlayer excitons in Van der Waals heterostructures holds promise for exploring Bose-Einstein condensates and developing novel optoelectronic applications, such as excitonic integrated circuits. Despite intensive studies, several key fundamental properties of interlayer excitons, such as their binding energies and interactions with charges, remain not well understood. Here we report the formation of momentum-direct interlayer excitons in a high-quality MoSe_{2}/hBN/MoSe_{2} heterostructure under an electric field, characterized by bright photoluminescence (PL) emission with high quantum yield and a narrow linewidth of less than 4 meV. These interlayer excitons show electrically tunable emission energy spanning ∼180  meV through the Stark effect, and exhibit a sizable binding energy of ∼81  meV in the intrinsic regime, along with trion binding energies of a few millielectronvolts. Remarkably, we demonstrate the long-range transport of interlayer excitons with a characteristic diffusion length exceeding 10  μm, which can be attributed, in part, to their dipolar repulsive interactions. Spatially and polarization-resolved spectroscopic studies reveal rich exciton physics in the system, such as valley polarization, local trapping, and the possible existence of dark interlayer excitons. The formation and transport of tightly bound interlayer excitons with narrow linewidth, coupled with the ability to electrically manipulate their properties, open exciting new avenues for exploring quantum many-body physics, including excitonic condensate and superfluidity, and for developing novel optoelectronic devices, such as exciton and photon routers.

Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2

The fundamental properties of an exciton are determined by the spin, valley, energy, and spatial wavefunctions of the Coulomb-bound electron and hole. In van der Waals materials, these attributes can be widely engineered through layer stacking configuration to create highly tunable interlayer excitons with static out-of-plane electric dipoles, at the expense of the strength of the oscillating in-plane dipole responsible for light-matter coupling. Here we show that interlayer excitons in bi- and tri-layer 2H-MoSe2 crystals exhibit electric-field-driven coupling with the ground (1s) and excited states (2s) of the intralayer A excitons. We demonstrate that the hybrid states of these distinct exciton species provide strong oscillator strength, large permanent dipoles (up to 0.73 ± 0.01 enm), high energy tunability (up to ~200 meV), and full control of the spin and valley characteristics such that the exciton g-factor can be manipulated over a large range (from -4 to +14). Further, we observe the bi- and tri-layer excited state (2s) interlayer excitons and their coupling with the intralayer excitons states (1s and 2s). Our results, in good agreement with a coupled oscillator model with spin (layer)-selectivity and beyond standard density functional theory calculations, promote multilayer 2H-MoSe2 as a highly tunable platform to explore exciton-exciton interactions with strong light-matter interactions.

Direct Visualization of Dark Interlayer Exciton Transport in Moiré Superlattices

Moiré superlattices have emerged as an unprecedented manipulation tool for engineering correlated quantum phenomena in van der Waals heterostructures. With moiré potentials as a naturally configurable solid-state that sustains high exciton density, interlayer excitons in transition metal dichalcogenide heterostructures are expected to achieve high-temperature exciton condensation. However, the exciton degeneracy state is usually optically inactive due to the finite momentum of interlayer excitons. Experimental observation of dark interlayer excitons in moiré potentials remains challenging. Here we directly visualize the dark interlayer exciton transport in WS2/h-BN/WSe2 heterostructures using femtosecond transient absorption microscopy. We observe a transition from classical free exciton gas to quantum degeneracy by imaging temperature-dependent exciton transport. Below a critical degeneracy temperature, exciton diffusion rates exhibit an accelerating downward trend, which can be explained well by a nonlinear quantum diffusion model. These results open the door to quantum information processing and high-precision metrology in moiré superlattices.

Recent progress of exciton transport in two-dimensional semiconductors

Spatial manipulation of excitonic quasiparticles, such as neutral excitons, charged excitons, and interlayer excitons, in two-dimensional semiconductors offers unique capabilities for a broad range of optoelectronic applications, encompassing photovoltaics, exciton-integrated circuits, and quantum light-emitting systems. Nonetheless, their practical implementation is significantly restricted by the absence of electrical controllability for neutral excitons, short lifetime of charged excitons, and low exciton funneling efficiency at room temperature, which remain a challenge in exciton transport. In this comprehensive review, we present the latest advancements in controlling exciton currents by harnessing the advanced techniques and the unique properties of various excitonic quasiparticles. We primarily focus on four distinct control parameters inducing the exciton current: electric fields, strain gradients, surface plasmon polaritons, and photonic cavities. For each approach, the underlying principles are introduced in conjunction with its progression through recent studies, gradually expanding their accessibility, efficiency, and functionality. Finally, we outline the prevailing challenges to fully harness the potential of excitonic quasiparticles and implement practical exciton-based optoelectronic devices.

Ultrafast exciton fluid flow in an atomically thin MoS2 semiconductor

Excitons (coupled electron-hole pairs) in semiconductors can form collective states that sometimes exhibit spectacular nonlinear properties. Here, we show experimental evidence of a collective state of short-lived excitons in a direct-bandgap, atomically thin MoS2 semiconductor whose propagation resembles that of a classical liquid as suggested by the nearly uniform photoluminescence through the MoS2 monolayer regardless of crystallographic defects and geometric constraints. The exciton fluid flows over ultralong distances (at least 60 μm) at a speed of ~1.8 × 107 m s-1 (~6% the speed of light). The collective phase emerges above a critical laser power, in the absence of free charges and below a critical temperature (usually Tc ≈ 150 K) approaching room temperature in hexagonal-boron-nitride-encapsulated devices. Our theoretical simulations suggest that momentum is conserved and local equilibrium is achieved among excitons; both these features are compatible with a fluid dynamics description of the exciton transport.

Thickness- and Twist-Angle-Dependent Interlayer Excitons in Metal Monochalcogenide Heterostructures

Interlayer excitons, or bound electron-hole pairs whose constituent quasiparticles are located in distinct stacked semiconducting layers, are being intensively studied in heterobilayers of two-dimensional semiconductors. They owe their existence to an intrinsic type-II band alignment between both layers that convert these into p-n junctions. Here, we unveil a pronounced interlayer exciton (IX) in heterobilayers of metal monochalcogenides, namely, γ-InSe on ε-GaSe, whose pronounced emission is adjustable just by varying their thicknesses given their number of layers dependent direct band gaps. Time-dependent photoluminescense spectroscopy unveils considerably longer interlayer exciton lifetimes with respect to intralayer ones, thus confirming their nature. The linear Stark effect yields a bound electron-hole pair whose separation d is just (3.6 ± 0.1) Å with d being very close to d_Se = 3.4 Å which is the calculated interfacial Se separation. The envelope of IX is twist-angle-dependent and describable by superimposed emissions that are nearly equally spaced in energy, as if quantized due to localization induced by the small moiré periodicity. These heterostacks are characterized by extremely flat interfacial valence bands making them prime candidates for the observation of magnetism or other correlated electronic phases upon carrier doping.

A Pair of 2D Quantum Liquids: Investigating the Phase Behavior of Indirect Excitons

Long-lived indirect excitons (IXs) exhibit a rich phase diagram, including a Bose-Einstein condensate (BEC), a Wigner crystal, and other exotic phases. Recent experiments have hinted at a "classical" liquid of IXs above the BEC transition. To uncover the nature of this phase, we use a broad range of theoretical tools and find no evidence of a driving force toward classical condensation. Instead, we attribute the condensed phase to a quantum electron-hole liquid (EHL), first proposed by Keldysh for direct excitons. Taking into account the association of free carriers into bound excitons, we study the phase equilibrium between a gas of excitons, a gas of free carriers, and an EHL for a wide range of electron-hole separations, temperatures, densities, and mass ratios. Our results agree reasonably well with recent measurements of GaAs/AlGaAs coupled quantum wells.

The Role of Spin-Flip Collisions in a Dark-Exciton Condensate

We show that a Bose-Einstein condensate consisting of dark excitons forms in GaAs coupled quantum wells at low temperatures. We find that the condensate extends over hundreds of micrometers, well beyond the optical excitation region, and is limited only by the boundaries of the mesa. We show that the condensate density is determined by spin-flipping collisions among the excitons, which convert dark excitons into bright ones. The suppression of this process at low temperature yields a density buildup, manifested as a temperature-dependent blueshift of the exciton emission line. Measurements under an in-plane magnetic field allow us to preferentially modify the bright exciton density and determine their role in the system dynamics. We find that their interaction with the condensate leads to its depletion. We present a simple rate-equations model, which well reproduces the observed temperature, power, and magnetic-field dependence of the exciton density.

Unconventional excitonic states with phonon sidebands in layered silicon diphosphide

Complex correlated states emerging from many-body interactions between quasiparticles (electrons, excitons and phonons) are at the core of condensed matter physics and material science. In low-dimensional materials, quantum confinement affects the electronic, and subsequently, optical properties for these correlated states. Here, by combining photoluminescence, optical reflection measurements and ab initio theoretical calculations, we demonstrate an unconventional excitonic state and its bound phonon sideband in layered silicon diphosphide (SiP2), where the bound electron-hole pair is composed of electrons confined within one-dimensional phosphorus-phosphorus chains and holes extended in two-dimensional SiP2 layers. The excitonic state and emergent phonon sideband show linear dichroism and large energy redshifts with increasing temperature. Our ab initio many-body calculations confirm that the observed phonon sideband results from the correlated interaction between excitons and optical phonons. With these results, we propose layered SiP2 as a platform for the study of excitonic physics and many-particle effects.

Probing dark exciton navigation through a local strain landscape in a WSe2 monolayer

In WSe₂ monolayers, strain has been used to control the energy of excitons, induce funneling, and realize single-photon sources. Here, we developed a technique for probing the dynamics of free excitons in nanoscale strain landscapes in such monolayers. A nanosculpted tapered optical fiber is used to simultaneously generate strain and probe the near-field optical response of WSe₂ monolayers at 5 K. When the monolayer is pushed by the fiber, its lowest energy states shift by as much as 390 meV (>20% of the bandgap of a WSe₂ monolayer). Polarization and lifetime measurements of these red-shifting peaks indicate they originate from dark excitons. We conclude free dark excitons are funneled to high-strain regions during their long lifetime and are the principal participants in drift and diffusion at cryogenic temperatures. This insight supports proposals on the origin of single-photon sources in WSe₂ and demonstrates a route towards exciton traps for exciton condensation.

Here, the authors use a tapered optical fibre to create a dynamic, reversible strain in a suspended WSe₂ monolayer, and observe that dark excitons are funnelled to high-strain regions and are the principal participants in drift and diffusion at cryogenic temperatures.

Indirect momentum excitation of graphene using high transversal modes of light in hyperbolic media

Electrons in indirect semiconductors can optically transit between the valance and conduction band edges only when the momentum conservation is satisfied with help of a third quasi-particle, such as a phonon. In this report, we theoretically demonstrate that indirect interband transition of graphene electrons can be optically enabled only by light with highly enhanced transversal modes, which can be generated by scattering of point dipole radiation with periodic metal slits fabricated in a natural hyperbolic material. The light-matter interaction for graphene electrons is reformulated by using indirect transition matrix elements, and interband polarizations of graphene are obtained by solving quantum kinetic equations of motion in the semi-classical regime. The interband optical current density of graphene as a function of the polarization angle of the incident field shows clear hexagonal response to the high transversal modes of light, which results from the low dependence on dephasing rate and dominance of the indirect polarizations over the direct interband contributions.

Excitons and emergent quantum phenomena in stacked 2D semiconductors

The design and control of material interfaces is a foundational approach to realize technologically useful effects and engineer material properties. This is especially true for two-dimensional (2D) materials, where van der Waals stacking allows disparate materials to be freely stacked together to form highly customizable interfaces. This has underpinned a recent wave of discoveries based on excitons in stacked double layers of transition metal dichalcogenides (TMDs), the archetypal family of 2D semiconductors. In such double-layer structures, the elegant interplay of charge, spin and moiré superlattice structure with many-body effects gives rise to diverse excitonic phenomena and correlated physics. Here we review some of the recent discoveries that highlight the versatility of TMD double layers to explore quantum optics and many-body effects. We identify outstanding challenges in the field and present a roadmap for unlocking the full potential of excitonic physics in TMD double layers and beyond, such as incorporating newly discovered ferroelectric and magnetic materials to engineer symmetries and add a new level of control to these remarkable engineered materials.

Transport Modeling of Locally Photogenerated Excitons in Halide Perovskites

Excitons have fundamental impacts on optoelectronic properties of semiconductors. Halide perovskites, with long carrier lifetimes and ionic crystal structures, may support highly mobile excitons because the dipolar nature of excitons suppresses phonon scattering. Inspired by recent experimental progress, we perform device modeling to rigorously analyze exciton formation and transport in methylammonium lead triiodide under local photoexcitation by using a finite element method. Mobile excitons, coexisting with free carriers, can dominate photocurrent generation at low temperatures. The simulation results are in excellent agreement with the experimentally observed strong temperature and gate dependence of carrier diffusion. This work signifies that efficient exciton transport can substantially influence charge transport in the family of perovskite materials.

Evidence of ideal excitonic insulator in bulk MoS2 under pressure

Spontaneous condensation of excitons is a long-sought phenomenon analogous to the condensation of Cooper pairs in a superconductor. It is expected to occur in a semiconductor at thermodynamic equilibrium if the binding energy of the excitons-electron (e) and hole (h) pairs interacting by Coulomb force-overcomes the band gap, giving rise to a new phase: the "excitonic insulator" (EI). Transition metal dichalcogenides are excellent candidates for the EI realization because of reduced Coulomb screening, and indeed a structural phase transition was observed in few-layer systems. However, previous work could not disentangle to which extent the origin of the transition was in the formation of bound excitons or in the softening of a phonon. Here we focus on bulk [Formula: see text] and demonstrate theoretically that at high pressure it is prone to the condensation of genuine excitons of finite momentum, whereas the phonon dispersion remains regular. Starting from first-principles many-body perturbation theory, we also predict that the self-consistent electronic charge density of the EI sustains an out-of-plane permanent electric dipole moment with an antiferroelectric texture in the layer plane: At the onset of the EI phase, those optical phonons that share the exciton momentum provide a unique Raman fingerprint for the EI formation. Finally, we identify such fingerprint in a Raman feature that was previously observed experimentally, thus providing direct spectroscopic confirmation of an ideal excitonic insulator phase in bulk [Formula: see text] above 30 GPa.

Moiré pattern of interference dislocations in condensate of indirect excitons

Interference patterns provide direct measurement of coherent propagation of matter waves in quantum systems. Superfluidity in Bose-Einstein condensates of excitons can enable long-range ballistic exciton propagation and can lead to emerging long-scale interference patterns. Indirect excitons (IXs) are formed by electrons and holes in separated layers. The theory predicts that the reduced IX recombination enables IX superfluid propagation over macroscopic distances. Here, we present dislocation-like phase singularities in interference patterns produced by condensate of IXs. We analyze how exciton vortices and skyrmions should appear in the interference experiments and show that the observed interference dislocations are not associated with these phase defects. We show that the observed interference dislocations originate from the moiré effect in combined interference patterns of propagating condensate matter waves. The interference dislocations are formed by the IX matter waves ballistically propagating over macroscopic distances. The long-range ballistic IX propagation is the evidence for IX condensate superfluidity.

Crescent States in Charge-Imbalanced Polariton Condensates

We study two-dimensional charge-imbalanced electron-hole systems embedded in an optical microcavity. We find that strong coupling to photons favors states with pairing at zero or small center-of-mass momentum, leading to a condensed state with spontaneously broken time-reversal and rotational symmetry and unpaired carriers that occupy an anisotropic crescent-shaped sliver of momentum space. The crescent state is favored at moderate charge imbalance, while a Fulde-Ferrel-Larkin-Ovchinnikov-like state-with pairing at large center-of-mass momentum-occurs instead at strong imbalance. The crescent state stability results from long-range Coulomb interactions in combination with extremely long-range photon-mediated interactions.

Polariton Electric-Field Sensor

We experimentally demonstrate a dipolar polariton based electric-field sensor. We tune and optimize the sensitivity of the sensor by varying the dipole moment of polaritons. We show polariton interactions play an important role in determining the conditions for optimal electric-field sensing, and achieve a sensitivity of 0.12   V m^{-1} Hz^{-0.5}. Finally, we apply the sensor to illustrate that excitation of polaritons modifies the electric field in a spatial region much larger than the optical excitation spot.

Homotopy Phases of FQHE with Long-Range Quantum Entanglement in Monolayer and Bilayer Hall Systems

Correlated phases in Hall systems have topological character. Multilayer configurations of planar electron systems create the opportunity to change topological phases on demand using macroscopic factors, such as vertical voltage. We present an analysis of such phenomena in close relation to recent experiments with multilayer Hall setups including GaAs and graphene multi-layers. The consequences of the blocking or not of the inter-layer electron tunneling in stacked Hall configurations are analyzed and presented in detail. Multilayer Hall systems are thus tunable topological composite nanomaterials, in the case of graphene-stacked systems by both intra- and inter-layer voltage.

Heterogeneous deformation of two-dimensional materials for emerging functionalities

Atomically thin 2D materials exhibit strong intralayer covalent bonding and weak interlayer van der Waals interactions, offering unique high in-plane strength and out-of-plane flexibility. While atom-thick nature of 2D materials may cause uncontrolled intrinsic/extrinsic deformation in multiple length scales, it also provides new opportunities for exploring coupling between heterogeneous deformations and emerging functionalities in controllable and scalable ways for electronic, optical, and optoelectronic applications. In this review, we discuss (i) the mechanical characteristics of 2D materials, (ii) uncontrolled inherent deformation and extrinsic heterogeneity present in 2D materials, (iii) experimental strategies for controlled heterogeneous deformation of 2D materials, (iv) 3D structure-induced novel functionalities via crumple/wrinkle structure or kirigami structures, and (v) heterogeneous strain-induced emerging functionalities in exciton and phase engineering. Overall, heterogeneous deformation offers unique advantages for 2D materials research by enabling spatial tunability of 2D materials' interactions with photons, electrons, and molecules in a programmable and controlled manner.

Room-Temperature Macroscopic Coherence of Two Electron-Hole Plasmas in a Microcavity

Macroscopic coherence of Bose condensates is a fundamental and practical phenomenon in many-body systems, such as the long-range correlation of exciton-polariton condensates with a dipole density typically below the exciton Mott-transition limit. Here we extend the macroscopic coherence of electron-hole-photon interacting systems to a new region in the phase diagram-the high-density plasma region, where long-range correlation is generally assumed to be broken due to the rapid dephasing. Nonetheless, a cooperative state of electron-hole plasma does emerge through the sharing of the superfluorescence field in an optical microcavity. In addition to the in situ coherence of e-h plasma, a long-range correlation is formed between two 8-μm-spaced plasma ensembles even at room temperature. Quantized and self-modulated correlation modes are generated for e-h ensembles in the plasma region. By controlling the distance between the two ensembles, multiple coupling regimes are revealed, from strong correlation to perturbative phase correlation and finally to an incoherent classical case, which has potential implications for tunable and high-temperature-compatible quantum devices.

Indirect Excitons and Trions in MoSe2/WSe2 van der Waals Heterostructures

Indirect excitons (IX) in semiconductor heterostructures are bosons, which can cool below the temperature of quantum degeneracy and can be effectively controlled by voltage and light. IX quantum Bose gases and IX devices were explored in GaAs heterostructures where an IX range of existence is limited to low temperatures due to low IX binding energies. IXs in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by large binding energies giving the opportunity for exploring excitonic quantum gases and for creating excitonic devices at high temperatures. TMD heterostructures also offer a new platform for studying single-exciton phenomena and few-particle complexes. In this work, we present studies of IXs in MoSe₂/WSe₂ heterostructures and report on two IX luminescence lines whose energy splitting and temperature dependence identify them as neutral and charged IXs. The experimentally found binding energy of the indirect charged excitons, that is, indirect trions, is close to the calculated binding energy of 28 meV for negative indirect trions in TMD heterostructures [Deilmann, T.; Thygesen, K. S. Nano Lett. 2018, 18, 1460]. We also report on the realization of IXs with a luminescence line width reaching 4 meV at low temperatures. An enhancement of IX luminescence intensity and the narrow line width are observed in localized spots.

Valley-Layer Coupling: A New Design Principle for Valleytronics

The current valleytronics research is based on the paradigm of time-reversal-connected valleys in two-dimensional (2D) hexagonal materials, which forbids the fully electric generation of valley polarization by a gate field. Here, we go beyond the existing paradigm to explore 2D systems with a novel valley-layer coupling (VLC) mechanism, where the electronic states in the emergent valleys have a valley-contrasted layer polarization. The VLC enables a direct coupling between a valley and a gate electric field. We analyze the symmetry requirements for a system to host VLC, demonstrate our idea via first-principles calculations and model analysis of a concrete 2D material example, and show that an electric, continuous, wide-range, and switchable control of valley polarization can be achieved by VLC. Furthermore, we find that systems with VLC can exhibit other interesting physics, such as valley-contrasting linear dichroism and optical selection of the valley and the electric polarization of interlayer excitons. Our finding opens a new direction for valleytronics and 2D materials research.

Electrical control of interlayer exciton dynamics in atomically thin heterostructures

A van der Waals heterostructure built from atomically thin semiconducting transition metal dichalcogenides (TMDs) enables the formation of excitons from electrons and holes in distinct layers, producing interlayer excitons with large binding energy and a long lifetime. By employing heterostructures of monolayer TMDs, we realize optical and electrical generation of long-lived neutral and charged interlayer excitons. We demonstrate that neutral interlayer excitons can propagate across the entire sample and that their propagation can be controlled by excitation power and gate electrodes. We also use devices with ohmic contacts to facilitate the drift motion of charged interlayer excitons. The electrical generation and control of excitons provide a route for achieving quantum manipulation of bosonic composite particles with complete electrical tunability.

Evidence of high-temperature exciton condensation in two-dimensional atomic double layers

A Bose-Einstein condensate is the ground state of a dilute gas of bosons, such as atoms cooled to temperatures close to absolute zero¹. With much smaller mass, excitons (bound electron-hole pairs) are expected to condense at considerably higher temperatures^2-7. Two-dimensional van der Waals semiconductors with very strong exciton binding are ideal systems for the study of high-temperature exciton condensation. Here we study electrically generated interlayer excitons in MoSe₂-WSe₂ atomic double layers with a density of up to 10¹² excitons per square centimetre. The interlayer tunnelling current depends only on the exciton density, which is indicative of correlated electron-hole pair tunnelling⁸. Strong electroluminescence arises when a hole tunnels from WSe₂ to recombine with an electron in MoSe₂. We observe a critical threshold dependence of the electroluminescence intensity on exciton density, accompanied by super-Poissonian photon statistics near the threshold, and a large electroluminescence enhancement with a narrow peak at equal electron and hole densities. The phenomenon persists above 100 kelvin, which is consistent with the predicted critical condensation temperature^9-12. Our study provides evidence for interlayer exciton condensation in two-dimensional atomic double layers and opens up opportunities for exploring condensate-based optoelectronics and exciton-mediated high-temperature superconductivity¹³.

Charge-Accumulation Effect in Transition Metal Dichalcogenide Heterobilayers

Charge transfer in transition-metal-dichalcogenides (TMDs) heterostructures is a prerequisite for the formation of interlayer excitons, which hold great promise for optoelectronics and valleytronics. Charge accumulation accompanied by a charge-transfer process can introduce considerable effect on interlayer exciton-based applications; nevertheless, this aspect has been rarely studied up to date. This work demonstrates how the charge accumulation affects the light emission of interlayer excitons in van der Waals heterobilayers (HBs) consisting of monolayer WSe₂ and WS₂ . As excitation power increases, the photoluminescence intensity of interlayer excitons increases more rapidly than that of intralayer excitons. The phenomenon can be explained by charge-accumulation effect, which not only increases the recombination probability of interlayer excitons but also saturates the charge-transfer process. This scenario is further confirmed by a careful examination of trion binding energy of WS₂ , which nonlinearly increases with the increase of the excitation power before reaching a maximum of about 75 meV. These investigations provide a better understanding of interlayer excitons and trions in HBs, which may provoke further explorations of excitonic physics as well as TMDs-based devices.

Dynamical formation of a strongly correlated dark condensate of dipolar excitons

Strongly interacting bosons display a rich variety of quantum phases, the study of which has so far been focused in the dilute regime, at a fixed number of particles. Here we demonstrate the formation of a dense Bose-Einstein condensate in a long-lived dark spin state of 2D dipolar excitons. A dark condensate of weakly interacting excitons is very fragile, being unstable against a coherent coupling of dark and bright spin states. Remarkably, we find that strong dipole-dipole interactions stabilize the dark condensate. As a result, the dark phase persists up to densities high enough for a dark quantum liquid to form. The striking experimental observation of a step-like dependence of the exciton density on the pump power is reproduced quantitatively by a model describing the nonequilibrium dynamics of driven coupled dark and bright condensates. This unique behavior marks a dynamical condensation to dark states with lifetimes as long as a millisecond, followed by a brightening transition at high densities.

Optical Signature of Quantum Coherence in Fully Dark Exciton Condensates

We predict that the collision of two fully dark exciton condensates produces bright interference fringes. So, quite surprisingly, the collision of coherent dark states makes light. This remarkable effect, which is many body in essence, comes from the composite boson nature of excitons, through the fermion exchanges they can have which transform dark states into bright states. The possibility of optically detecting quantum coherence in a regime where the system is hidden by its total darkness was up to now considered as hopeless.

Exciton Gas Transport through Nanoconstrictions

An indirect exciton is a bound state of an electron and a hole in spatially separated layers. Two-dimensional indirect excitons can be created optically in heterostructures containing double quantum wells or atomically thin semiconductors. We study theoretically the transmission of such bosonic quasiparticles through nanoconstrictions. We show that the quantum transport phenomena, for example, conductance quantization, single-slit diffraction, two-slit interference, and the Talbot effect, are experimentally realizable in systems of indirect excitons. We discuss similarities and differences between these phenomena and their counterparts in electronic devices.

Trapping Dipolar Exciton Fluids in GaN/(AlGa)N Nanostructures

Dipolar excitons offer a rich playground for both design of novel optoelectronic devices and fundamental many-body physics. Wide GaN/(AlGa)N quantum wells host a new and promising realization of dipolar excitons. We demonstrate the in-plane confinement and cooling of these excitons, when trapped in the electrostatic potential created by semitransparent electrodes of various shapes deposited on the sample surface. This result is a prerequisite for the electrical control of the exciton densities and fluxes, as well for studies of the complex phase diagram of these dipolar bosons at low temperature.

Defect Proliferation at the Quasicondensate Crossover of Two-Dimensional Dipolar Excitons Trapped in Coupled GaAs Quantum Wells

We study ultracold dipolar excitons confined in a 10  μm trap of a double GaAs quantum well. Based on the local density approximation, we unveil for the first time the equation of state of excitons. Specifically, in this regime and below a critical temperature of about 1 K, we show that for a local density n∼(2-3)×10^{10}  cm^{-2} a coherent quasicondensate phase forms in the inner region of the trap, encircled by a more dilute and normal component in the outer rim. Remarkably, this spatial arrangement correlates directly with the concentration of defects in the exciton density, which is strongly decreased in the quasicondensed region, consistent with a superfluid phase. Thus, our observations point towards a Berezinskii-Kosterlitz-Thouless crossover for two-dimensional excitons.

Slave rotor approach to exciton condensation in a two-band system

We have studied exciton formation and condensation in an extended Falicov-Kimball model, going beyond the weak coupling approach, employing a semi-analytical technique: the slave-rotor mean-field theory (SRMF). In this essentially strong coupling theory, charge and spin (or orbital/pseudospin) degrees are treated as independent degrees of freedom, coupled by a local constraint. Using a two-site-extension of SRMF, we capture the effective many body scale beyond conventional mean-field theory. While the formation of excitons is favoured by the interband hybridization [Formula: see text], it is strongly influenced by the on-site Coulomb interaction [Formula: see text]. Beyond a critical hybridization, there is condensation of excitons, leading to a transition from a metal to an excitonic insulator phase. Moreover, the behaviour of excitonic averages differs from the usual Hartree-Fock mean-field theory. Low-[Formula: see text] results show that excitonic order parameter (Δ) is continuous across the transition both for single as well as two-site approximation, changing to weakly first order one at intermediate [Formula: see text] for the later. The large-[Formula: see text] limit shows a continuous transition for two-site analysis but remains first order in the single-site approximation. The slave rotor theory gives a mixed state of excitons and metal in both the analyses. We have also checked the effect of intersite correlation and localized band hopping on the exciton condensation.

Bose Condensation of Long-Living Direct Excitons in an Off-Resonant Cavity

We propose a way to increase the lifetime of two-dimensional direct excitons and show the possibility to observe their macroscopically coherent state at temperatures much higher than that of indirect exciton condensation. For a single GaAs quantum well embedded in photonic layered heterostructures with subwavelength period, we predict the exciton radiative decay to be strongly suppressed. Quantum hydrodynamics joined with the Bogoliubov approach are used to study the Berezinskii-Kosterlitz-Thouless crossover in a finite exciton system with intermediate densities. Below the estimated critical temperatures, drastic growth of the correlation length is shown to be accompanied by a manyfold increase of the photoluminescence intensity.

Electrical Reservoirs for Bilayer Excitons

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, thereby avoiding the presence of free carriers in either layer. Equilibration between the exciton fluid and the contacts proceeds via a process involving virtual intermediate states in which an unpaired electron or hole virtually occupies a free carrier state in one of the 2D layers. We derive an approximate relationship between the exciton-contact equilibration rate and the electrical conductances between the contacts and individual 2D layers when the contact chemical potentials align with the free-carrier bands, and explain how electrical measurements can be used to measure thermodynamic properties of the exciton fluids.

Slow wave contraction frequency plateaux in the small intestine are composed of discrete waves of interval increase associated with dislocations

NEW FINDINGS

What is the central question of this study? What is the nature of slow wave-driven contraction frequency gradients in the small intestine? What is the main finding and its importance? Frequency plateaux are composed of discrete waves of increased interval, each wave associated with a contraction dislocation. Smooth frequency gradients are generated by localized neural modulation of wave frequency, leading to functionally important wave turbulence. Both patterns are emergent properties of a network of coupled oscillators, the interstitial cells of Cajal.

ABSTRACT

A gut-wide network of interstitial cells of Cajal generates electrical oscillations (slow waves) that orchestrate waves of muscle contraction. In the small intestine there is a gradient in slow wave frequency from high at the duodenum to low at the terminal ileum. Time-averaged measurements of frequency have suggested either a smooth or a stepped (plateaued) gradient. We measured individual contraction intervals from diameter maps of the mouse small intestine to create interval maps (IMaps). The IMaps showed that each frequency plateau was composed of discrete waves of increased interval. Each interval wave originated at a terminating contraction wave, a 'dislocation', at the proximal boundary of the plateau. In a model chain of coupled phase oscillators, interval wave frequency increased as coupling decreased or as the natural frequency gradient or noise increased. Injuring the intestine at a proximal point, to destroy coupling, suppressed distal steps, which then reappeared with gap junction block by carbenoxolone. This lent further support to our previous hypothesis that lines of dislocations were fixed by points of low coupling strength. Dislocations, induced by electrical field pulses in the intestine and by equivalent phase shift in the model, were associated with interval waves. When the enteric nervous system was active, IMaps showed a chaotic, turbulent pattern of interval change, with no frequency steps or plateaux. This probably resulted from local, stochastic release of neurotransmitters. Plateaux, dislocations, interval waves and wave turbulence arise from a dynamic interplay between natural frequency and coupling in the network of interstitial cells of Cajal.

Pancharatnam-Berry phase in condensate of indirect excitons

The Pancharatnam-Berry phase is a geometric phase acquired over a cycle of parameters in the Hamiltonian governing the evolution of the system. Here, we report on the observation of the Pancharatnam-Berry phase in a condensate of indirect excitons (IXs) in a GaAs-coupled quantum well structure. The Pancharatnam-Berry phase is directly measured by detecting phase shifts of interference fringes in IX interference patterns. Correlations are found between the phase shifts, polarization pattern of IX emission, and onset of IX spontaneous coherence. The evolving Pancharatnam-Berry phase is acquired due to coherent spin precession in IX condensate and is observed with no decay over lengths exceeding 10 μm indicating long-range coherent spin transport.

Indirect excitons in van der Waals heterostructures at room temperature

Indirect excitons (IXs) are explored both for studying quantum Bose gases in semiconductor materials and for the development of excitonic devices. IXs were extensively studied in III-V and II-VI semiconductor heterostructures where IX range of existence has been limited to low temperatures. Here, we present the observation of IXs at room temperature in van der Waals transition metal dichalcogenide (TMD) heterostructures. This is achieved in TMD heterostructures based on monolayers of MoS₂ separated by atomically thin hexagonal boron nitride. The IXs we realize in the TMD heterostructure have lifetimes orders of magnitude longer than lifetimes of direct excitons in single-layer TMD and their energy is gate controlled. The realization of IXs at room temperature establishes the TMD heterostructures as a material platform both for a field of high-temperature quantum Bose gases of IXs and for a field of high-temperature excitonic devices.

Time-Reversal Symmetry-Breaking Nematic Insulators near Quantum Spin Hall Phase Transitions

We study the phase diagram of a model quantum spin Hall system as a function of band inversion and band-coupling strength, demonstrating that when band hybridization is weak, an interaction-induced nematic insulator state emerges over a wide range of band inversion. This property is a consequence of the long-range Coulomb interaction, which favors interband phase coherence that is weakly dependent on momentum and therefore frustrated by the single-particle Hamiltonian at the band inversion point. For weak band hybridization, interactions convert the continuous gap closing topological phase transition at inversion into a pair of continuous phase transitions bounding a state with broken time-reversal and rotational symmetries. At intermediate band hybridization, the topological phase transition proceeds instead via a quantum anomalous Hall insulator state, whereas at strong hybridization interactions play no role. We comment on the implications of our findings for InAs/GaSb and HgTe/CdTe quantum spin Hall systems.

Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures

Transition metal dichalcogenides have valley degree of freedom, which features optical selection rule and spin-valley locking, making them promising for valleytronics devices and quantum computation. For either application, a long valley polarization lifetime is crucial. Previous results showed that it is around picosecond in monolayer excitons, nanosecond for local excitons and tens of nanosecond for interlayer excitons. Here we show that the dark excitons in two-dimensional heterostructures provide a microsecond valley polarization memory thanks to the magnetic field induced suppression of valley mixing. The lifetime of the dark excitons shows magnetic field and temperature dependence. The long lifetime and valley polarization lifetime of the dark exciton in two-dimensional heterostructures make them promising for long-distance exciton transport and macroscopic quantum state generations.

Experimental Study of the Exciton Gas-Liquid Transition in Coupled Quantum Wells

We study the exciton gas-liquid transition in GaAs/AlGaAs coupled quantum wells. Below a critical temperature, T_{C}=4.8  K, and above a threshold laser power density the system undergoes a phase transition into a liquid state. We determine the density-temperature phase diagram over the temperature range 0.1-4.8 K. We find that the latent heat increases linearly with temperature at T≲1.1  K, similarly to a Bose-Einstein condensate transition, and becomes constant at 1.1≲T<4.8  K. Resonant Rayleigh scattering measurements reveal that the disorder in the sample is strongly suppressed and the diffusion coefficient sharply increases with decreasing temperature at T<T_{C}, allowing the liquid to spread over large distances away from the excitation region. We suggest that our findings are manifestations of a quantum liquid behavior.

Long-Lived Direct and Indirect Interlayer Excitons in van der Waals Heterostructures

We report the observation of a doublet structure in the low-temperature photoluminescence of interlayer excitons in heterostructures consisting of monolayer MoSe₂ and WSe₂. Both peaks exhibit long photoluminescence lifetimes of several tens of nanoseconds up to 100 ns verifying the interlayer nature of the excitons. The energy and line width of both peaks show unusual temperature and power dependences. While the low-energy peak dominates the spectra at low power and low temperatures, the high-energy peak dominates for high power and temperature. We explain the findings by two kinds of interlayer excitons being either indirect or quasi-direct in reciprocal space. Our results provide fundamental insights into long-lived interlayer states in van der Waals heterostructures with possible bosonic many-body interactions.

Floquet control of dipolaritons in quantum wells

We developed the theory of dipolaritons in semiconductor quantum wells irradiated by an off-resonant electromagnetic wave (dressing field). Solving the Floquet problem for the dressed dipolaritons, we demonstrated that the field drastically modifies all dipolaritonic properties. In particular, the dressing field strongly affects the terahertz emission from the considered system. The described effect paves the way for optical control of prospective dipolariton-based terahertz devices.

Bose-Einstein condensation and indirect excitons: a review

We review recent progress on Bose-Einstein condensation (BEC) of semiconductor excitons. The first part deals with theory, the second part with experiments. This Review is written at a time where the problem of exciton Bose-Einstein condensation has just been revived by the understanding that the exciton condensate must be dark because the exciton ground state is not coupled to light. Here, we theoretically discuss this missed understanding before providing its experimental support through experiments that scrutinize indirect excitons made of spatially separated electrons and holes. The theoretical part first discusses condensation of elementary bosons. In particular, the necessary inhibition of condensate fragmentation by exchange interaction is stressed, before extending the discussion to interacting bosons with spin degrees of freedom. The theoretical part then considers composite bosons made of two fermions like semiconductor excitons. The spin structure of the excitons is detailed, with emphasis on the crucial fact that ground-state excitons are dark: indeed, this imposes the exciton Bose-Einstein condensate to be not coupled to light in the dilute regime. Condensate fragmentations are then reconsidered. In particular, it is shown that while at low density, the exciton condensate is fully dark, it acquires a bright component, coherent with the dark one, beyond a density threshold: in this regime, the exciton condensate is 'gray'. The experimental part first discusses optical creation of indirect excitons in quantum wells, and the detection of their photoluminescence. Exciton thermalisation is also addressed, as well as available approaches to estimate the exciton density. We then switch to specific experiments where indirect excitons form a macroscopic fragmented ring. We show that such ring provides efficient electrostatic trapping in the region of the fragments where an essentially-dark exciton Bose-Einstein condensate is formed at sub-Kelvin bath temperatures. The macroscopic spatial coherence of the photoluminescence observed in this essentially dark region confirms this conclusion.

Enabling valley selective exciton scattering in monolayer WSe2 through upconversion

Excitons, Coulomb bound electron–hole pairs, are composite bosons and their interactions in traditional semiconductors lead to condensation and light amplification. The much stronger Coulomb interaction in transition metal dichalcogenides such as WSe₂ monolayers combined with the presence of the valley degree of freedom is expected to provide new opportunities for controlling excitonic effects. But so far the bosonic character of exciton scattering processes remains largely unexplored in these two-dimensional materials. Here we show that scattering between B-excitons and A-excitons preferably happens within the same valley in momentum space. This leads to power dependent, negative polarization of the hot B-exciton emission. We use a selective upconversion technique for efficient generation of B-excitons in the presence of resonantly excited A-excitons at lower energy; we also observe the excited A-excitons state 2s. Detuning of the continuous wave, low-power laser excitation outside the A-exciton resonance (with a full width at half maximum of 4 meV) results in vanishing upconversion signal.

Monolayer transition metal dichalcogenides host excitons, bound electron-hole pairs that play a pivotal role in optoelectronic applications relying on strong light-matter interaction. Here, the authors unveil the spectroscopic signature of boson scattering of two-dimensional excitons in monolayer WSe₂.

Nanoscale electrodynamics of strongly correlated quantum materials

Electronic, magnetic, and structural phase inhomogeneities are ubiquitous in strongly correlated quantum materials. The characteristic length scales of the phase inhomogeneities can range from atomic to mesoscopic, depending on their microscopic origins as well as various sample dependent factors. Therefore, progress with the understanding of correlated phenomena critically depends on the experimental techniques suitable to provide appropriate spatial resolution. This requirement is difficult to meet for some of the most informative methods in condensed matter physics, including infrared and optical spectroscopy. Yet, recent developments in near-field optics and imaging enabled a detailed characterization of the electromagnetic response with a spatial resolution down to 10 nm. Thus it is now feasible to exploit at the nanoscale well-established capabilities of optical methods for characterization of electronic processes and lattice dynamics in diverse classes of correlated quantum systems. This review offers a concise description of the state-of-the-art near-field techniques applied to prototypical correlated quantum materials. We also discuss complementary microscopic and spectroscopic methods which reveal important mesoscopic dynamics of quantum materials at different energy scales.