Bose-Einstein condensation and indirect excitons: a review

Diverse Excitonic Phenomena in Asymmetric Trilayer Transition Metal Dichalcogenide Heterostructures

Interlayer excitons formed in two-dimensional transition metal dichalcogenide (TMD) heterostructures can be easily tuned due to the large spatial separation. In this work, we discuss the electronic and excitonic optical properties of trilayer heterostructures MoS2/MoSSe/WSe2 and MoS2/MoSSe/MoSe2 using state-of-the-art GW+BSE calculations. In both trilayer geometries, we discover a variety of exciton states, including interlayer excitons, every-other-layer excitons, and their hybridized states, h-IX. Importantly, the h-IXs are optically bright through hybridizing with the intralayer excitons, and the radiative lifetimes of h-IXs range from subnanoseconds to tens of microseconds at 77 K, depending on their compositions. We also reveal that the diversity of the low-lying IXs in MoS2/MoSSe/MoSe2 is higher than that of MoS2/MoSSe/WSe2, because more energy levels participate in transitions in MoS2/MoSSe/MoSe2. Our findings demonstrate that the appropriate energy alignment via manipulating the Janus layer is crucial for realizing rich excitonic states in trilayer TMD heterostructures.

Quantum tunneling high-speed nano-excitonic modulator

High-speed electrical control of nano-optoelectronic properties in two-dimensional semiconductors is a building block for the development of excitonic devices, allowing the seamless integration of nano-electronics and -photonics. Here, we demonstrate a high-speed electrical modulation of nanoscale exciton behaviors in a MoS2 monolayer at room temperature through a quantum tunneling nanoplasmonic cavity. Electrical control of tunneling electrons between Au tip and MoS2 monolayer facilitates the dynamic switching of neutral exciton- and trion-dominant states at the nanoscale. Through tip-induced spectroscopic analysis, we locally characterize the modified recombination dynamics, resulting in a significant change in the photoluminescence quantum yield. Furthermore, by obtaining a time-resolved second-order correlation function, we demonstrate that this electrically-driven nanoscale exciton-trion interconversion achieves a modulation frequency of up to 8 MHz. Our approach provides a versatile platform for dynamically manipulating nano-optoelectronic properties in the form of transformable excitonic quasiparticles, including valley polarization, recombination, and transport dynamics.

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].

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.

Sound, Superfluidity, and Layer Compressibility in a Ring Dipolar Supersolid

We propose a protocol to excite the Goldstone modes of a supersolid dipolar Bose-Einstein condensed gas confined in a ring geometry. By abruptly removing an applied periodic modulation proportional to cos(φ), where φ is the azimuthal angle, we explore the resulting oscillations of the gas by solving the extended Gross-Pitaevskii equation. The value of the two longitudinal sound velocities exhibited in the supersolid phase are analyzed using the hydrodynamic theory of supersolids at zero temperature, which explicitly takes into account both the superfluid and the crystal nature of the system. This approach allows for the determination of the layer compressibility modulus as well as of the superfluid fraction, f_{S}, in agreement with the Leggett estimate of the nonclassical moment of inertia.

van der Waals 2D transition metal dichalcogenide/organic hybridized heterostructures: recent breakthroughs and emerging prospects of the device

The near-atomic thickness and organic molecular systems, including organic semiconductors and polymer-enabled hybrid heterostructures, of two-dimensional transition metal dichalcogenides (2D-TMDs) can modulate their optoelectronic and transport properties outstandingly. In this review, the current understanding and mechanism of the most recent and significant breakthrough of novel interlayer exciton emission and its modulation by harnessing the band energy alignment between TMDs and organic semiconductors in a TMD/organic (TMDO) hybrid heterostructure are demonstrated. The review encompasses up-to-date device demonstrations, including field-effect transistors, detectors, phototransistors, and photo-switchable superlattices. An exploration of distinct traits in 2D-TMDs and organic semiconductors delves into the applications of TMDO hybrid heterostructures. This review provides insights into the synthesis of 2D-TMDs and organic layers, covering fabrication techniques and challenges. Band bending and charge transfer via band energy alignment are explored from both structural and molecular orbital perspectives. The progress in emission modulation, including charge transfer, energy transfer, doping, defect healing, and phase engineering, is presented. The recent advancements in 2D-TMDO-based optoelectronic synaptic devices, including various 2D-TMDs and organic materials for neuromorphic applications are discussed. The section assesses their compatibility for synaptic devices, revisits the operating principles, and highlights the recent device demonstrations. Existing challenges and potential solutions are discussed. Finally, the review concludes by outlining the current challenges that span from synthesis intricacies to device applications, and by offering an outlook on the evolving field of emerging TMDO heterostructures.

The Key Role of Non-Local Screening in the Environment-Insensitive Exciton Fine Structures of Transition-Metal Dichalcogenide Monolayers

In this work, we present a comprehensive theoretical and computational investigation of exciton fine structures of WSe2-monolayers, one of the best-known two-dimensional (2D) transition-metal dichalcogenides (TMDs), in various dielectric-layered environments by solving the first-principles-based Bethe-Salpeter equation. While the physical and electronic properties of atomically thin nanomaterials are normally sensitive to the variation of the surrounding environment, our studies reveal that the influence of the dielectric environment on the exciton fine structures of TMD-MLs is surprisingly limited. We point out that the non-locality of Coulomb screening plays a key role in suppressing the dielectric environment factor and drastically shrinking the fine structure splittings between bright exciton (BX) states and various dark-exciton (DX) states of TMD-MLs. The intriguing non-locality of screening in 2D materials can be manifested by the measurable non-linear correlation between the BX-DX splittings and exciton-binding energies by varying the surrounding dielectric environments. The revealed environment-insensitive exciton fine structures of TMD-ML suggest the robustness of prospective dark-exciton-based optoelectronics against the inevitable variation of the inhomogeneous dielectric environment.

Excitonic Condensate in Flat Valence and Conduction Bands of Opposite Chirality

Excitonic Bose-Einstein condensation (EBEC) has drawn increasing attention recently with the emergence of 2D materials. A general criterion for EBEC, as expected in an excitonic insulator (EI) state, is to have negative exciton formation energies in a semiconductor. Here, using exact diagonalization of a multiexciton Hamiltonian modeled in a diatomic kagome lattice, we demonstrate that the negative exciton formation energies are only a prerequisite but insufficient condition for realizing an EI. By a comparative study between the cases of both conduction and valence flat bands (FBs) versus that of a parabolic conduction band, we further show that the presence and increased FB contribution to exciton formation provide an attractive avenue to stabilize the excitonic condensate, as confirmed by calculations and analyses of multiexciton energies, wave functions, and reduced density matrices. Our results warrant a similar many-exciton analysis for other known and/or new candidates of EIs and demonstrate the FBs of opposite parity as a unique platform for studying exciton physics, paving the way to material realization of spinor BEC and spin superfluidity.

Dual-density waves with neutral and charged dipolar excitons of GaAs bilayers

Strongly correlated quantum particles in lattice potentials are the building blocks for a wide variety of quantum insulators-for instance, Mott phases and density waves breaking lattice symmetry^1-3. Such collective states are accessible to bosonic and fermionic systems^2,4-10,11,12. To expand further the spectrum of accessible quantum matter phases, mixing both species is theoretically appealing because density order then competes with phase separation^13-16. Here we manipulate such a Bose-Fermi mixture by confining neutral (boson-like) and charged (fermion-like) dipolar excitons in an artificial square lattice of a GaAs bilayer. At unitary lattice filling, strong inter- and intraspecies interactions stabilize insulating phases when the fraction of charged excitons is around (1/3, 1/2, 2/3). We evidence that dual Bose-Fermi density waves are then realized, with species ordered in alternating stripes. Our observations highlight that dipolar excitons allow for controlled implementations of Bose-Fermi Hubbard models extended by off-site interactions.

Graphene and Beyond: Recent Advances in Two-Dimensional Materials Synthesis, Properties, and Devices

Since the isolation of graphene in 2004, two-dimensional (2D) materials research has rapidly evolved into an entire subdiscipline in the physical sciences with a wide range of emergent applications. The unique 2D structure offers an open canvas to tailor and functionalize 2D materials through layer number, defects, morphology, moiré pattern, strain, and other control knobs. Through this review, we aim to highlight the most recent discoveries in the following topics: theory-guided synthesis for enhanced control of 2D morphologies, quality, yield, as well as insights toward novel 2D materials; defect engineering to control and understand the role of various defects, including in situ and ex situ methods; and properties and applications that are related to moiré engineering, strain engineering, and artificial intelligence. Finally, we also provide our perspective on the challenges and opportunities in this fascinating field.

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.

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.

Interlayer Excitons in Transition Metal Dichalcogenide Semiconductors for 2D Optoelectronics

Optoelectronic materials that allow on-chip integrated light signal emitting, routing, modulation, and detection are crucial for the development of high-speed and high-throughput optical communication and computing technologies. Interlayer excitons in 2D van der Waals heterostructures, where electrons and holes are bounded by Coulomb interaction but spatially localized in different 2D layers, have recently attracted intense attention for their enticing properties and huge potential in device applications. Here, a general view of these 2D-confined hydrogen-like bosonic particles and the state-of-the-art developments with respect to the frontier concepts and prototypes is presented. Staggered type-II band alignment enables expansion of the interlayer direct bandgap from the intrinsic visible in monolayers up to the near- or even mid-infrared spectrum. Owing to large exciton binding energy, together with ultralong lifetime, room-temperature exciton devices and observation of quantum behaviors are demonstrated. With the rapid advances, it can be anticipated that future studies of interlayer excitons will not only allow the construction of all-exciton information processing circuits but will also continue to enrich the panoply of ideas on quantum phenomena.

Properties of Spatially Indirect Excitons in Nanowire Arrays

This paper deals with the excitons formed by electrons and holes located in different, closely placed semiconducting nanowires (spatially indirect excitons). We calculated the charge densities and the binding energies of the excitons for different nanowire diameters D and distances h between the nanowires. Together with the estimated exciton lifetimes, these results suggest that at certain h and D, the spatially indirect excitons in the nanowire arrays may have the potential to serve as information-processing units. Possible ways of exciton generation in the nanowire arrays are discussed.

Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure

Dipolar bosonic gases are currently the focus of intensive research due to their interesting many-body physics in the quantum regime. Their experimental embodiments range from Rydberg atoms to GaAs double quantum wells and van der Waals heterostructures built from transition metal dichalcogenides. Although quantum gases are very dilute, mutual interactions between particles could lead to exotic many-body phenomena such as Bose-Einstein condensation and high-temperature superfluidity. Here, we report the effect of repulsive dipolar interactions on the dynamics of interlayer excitons in the dilute regime. By using spatial and time-resolved photoluminescence imaging, we observe the dynamics of exciton transport, enabling a direct estimation of the exciton mobility. The presence of interactions significantly modifies the diffusive transport of excitons, effectively acting as a source of drift force and enhancing the diffusion coefficient by one order of magnitude. The repulsive dipolar interactions combined with the electrical control of interlayer excitons opens up appealing new perspectives for excitonic devices.

Charged Bosons Made of Fermions in Bilayer Structures with Strong Metallic Screening

Two-dimensional monolayer structures of transition metal dichalogenides (TMDs) have been shown to allow many higher-order excitonic bound states, including trions (charged excitons), biexcitons (excitonic molecules), and charged biexcitons. We report here experimental evidence and the theoretical basis for a new bound excitonic complex, consisting two free carriers bound to an exciton in a bilayer structure. Our experimental measurements on structures made using two different materials show a new spectral line at the predicted energy with two different TMD materials (MoSe₂ and WSe₂) with both n- and p-doping if and only if all the required theoretical conditions for this complex are fulfilled, in particular, only in the presence of a parallel metal layer that significantly screens the repulsive interaction between the like-charge carriers. Because these four-carrier bound states are charged bosons, they could eventually be the basis for a new path to superconductivity without Cooper pairing.

Moiré superlattices and related moiré excitons in twisted van der Waals heterostructures

Recent advances in moiré superlattices and moiré excitons, such as quantum emission arrays, low-energy flat bands, and Mott insulators, have rapidly attracted attention in the fields of optoelectronics, materials, and energy research. The interlayer twist turns into a degree of freedom that alters the properties of the systems of materials, and the realization of moiré excitons also offers the feasibility of making artificial exciton crystals. Moreover, moiré excitons exhibit many exciting properties under the regulation of various external conditions, including spatial polarisation, alternating dipolar to alternating dipolar moments and gate-dependence to gate voltage dependence; all are pertinent to their applications in nano-photonics and quantum information. But the lag in theoretical development and the low-efficiency of processing technologies significantly limit the potential of moiré superlattice applications. In this review, we systematically summarise and discuss the recent progress in moiré superlattices and moiré excitons, and analyze the current challenges, and put forward relevant recommendations. There is no doubt that further research will lead to breakthroughs in their application and promote reforms and innovations in traditional solid-state physics and materials science.

A roadmap for interlayer excitons

Interlayer excitons in van der Waals heterostructures have tunable electron-hole separation in both real space and momentum space, enabling unprecedented control over excitonic properties to be exploited in a wide array of future applications ranging from exciton condensation to valleytronic and optoelectronic devices.

Quasicondensation of Bilayer Excitons in a Periodic Potential

We study two-dimensional excitons confined in a lattice potential, for high fillings of the lattice sites. We show that a quasicondensate is possibly formed for small values of the lattice depth, but for larger ones the critical phase-space density for quasicondensation rapidly exceeds our experimental reach, due to an increase of the exciton effective mass. On the other hand, in the regime of a deep lattice potential where excitons are strongly localized at the lattice sites, we show that an array of phase-independent quasicondensates, different from a Mott insulator, is realized.

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.

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.

Upconverted electroluminescence via Auger scattering of interlayer excitons in van der Waals heterostructures

The intriguing physics of carrier-carrier interactions, which likewise affect the operation of light emitting devices, stimulate the research on semiconductor structures at high densities of excited carriers, a limit reachable at large pumping rates or in systems with long-lived electron-hole pairs. By electrically injecting carriers into WSe₂/MoS₂ type-II heterostructures which are indirect in real and k-space, we establish a large population of typical optically silent interlayer excitons. Here, we reveal their emission spectra and show that the emission energy is tunable by an applied electric field. When the population is further increased by suppressing the radiative recombination rate with the introduction of an hBN spacer between WSe₂ and MoS₂, Auger-type and exciton-exciton annihilation processes become important. These processes are traced by the observation of an up-converted emission demonstrating that excitons gaining energy in non-radiative Auger processes can be recovered and recombine radiatively.

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.

Interlayer valley excitons in heterobilayers of transition metal dichalcogenides

Stacking different two-dimensional crystals into van der Waals heterostructures provides an exciting approach to designing quantum materials that can harness and extend the already fascinating properties of the constituents. Heterobilayers of transition metal dichalcogenides are particularly attractive for low-dimensional semiconductor optics because they host interlayer excitons-with electrons and holes localized in different layers-which inherit valley-contrasting physics from the monolayers and thereby possess various novel and appealing properties compared to other solid-state nanostructures. This Review presents the contemporary experimental and theoretical understanding of these interlayer excitons. We discuss their unique optical properties arising from the underlying valley physics, the strong many-body interactions and electrical control resulting from the electric dipole moment, and the unique effects of a moiré superlattice on the interlayer exciton potential landscape and optical properties.

Hot electron relaxation dynamics in semiconductors: assessing the strength of the electron-phonon coupling from the theoretical and experimental viewpoints

The rapid development of the computational methods based on density functional theory, on the one hand, and of time-, energy-, and momentum-resolved spectroscopy, on the other hand, allows today an unprecedently detailed insight into the processes governing hot-electron relaxation dynamics, and, in particular, into the role of the electron-phonon coupling. Instead of focusing on the development of a particular method, theoretical or experimental, this review aims to treat the progress in the understanding of the electron-phonon coupling which can be gained from both, on the basis of recently obtained results. We start by defining several regimes of hot electron relaxation via electron-phonon coupling, with respect to the electron excitation energy. We distinguish between energy and momentum relaxation of hot electrons, and summarize, for several semiconductors of the IV and III-V groups, the orders of magnitude of different relaxation times in different regimes, on the basis of known experimental and numerical data. Momentum relaxation times of hot electrons become very short around 1 eV above the bottom of the conduction band, and such ultrafast relaxation mechanisms are measurable only in the most recent pump-probe experiments. Then, we give an overview of the recent progress in the experimental techniques allowing to obtain detailed information on the hot-electron relaxation dynamics, with the main focus on time-, energy-, and momentum-resolved photoemission experiments. The particularities of the experimental approach developed by one of us, which allows to capture time-, energy-, and momentum-resolved hot-electron distributions, as well as to measure momentum relaxation times of the order of 10 fs, are discussed. We further discuss the main advances in the calculation of the electron-phonon scattering times from first principles over the past ten years, in semiconducting materials. Ab initio techniques and efficient interpolation methods provide the possibility to calculate electron-phonon scattering times with high precision at reasonable numerical cost. We highlight the methods of analysis of the obtained numerical results, which allow to give insight into the details of the electron-phonon scattering mechanisms. Finally, we discuss the concept of hot electron ensemble which has been proposed recently to describe the hot-electron relaxation dynamics in GaAs, the applicability of this concept to other materials, and its limitations. We also mention some open problems.

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.

van der Waals Layered Materials: Opportunities and Challenges

Since graphene became available by a scotch tape technique, a vast class of two-dimensional (2D) van der Waals (vdW) layered materials has been researched intensively. What is more intriguing is that the well-known physics and chemistry of three-dimensional (3D) bulk materials are often irrelevant, revealing exotic phenomena in 2D vdW materials. By further constructing heterostructures of these materials in the planar and vertical directions, which can be easily achieved via simple exfoliation techniques, numerous quantum mechanical devices have been demonstrated for fundamental research and technological applications. It is, therefore, necessary to review the special features in 2D vdW materials and to discuss the remaining issues and challenges. Here, we review the vdW materials library, technology relevance, and specialties of vdW materials covering the vdW interaction, strong Coulomb interaction, layer dependence, dielectric screening engineering, work function modulation, phase engineering, heterostructures, stability, growth issues, and the remaining challenges.