Electron-hole Liquid Research Articles

Trion gas, electron-hole liquid, and metal-insulator transition in doped heterostructures based on transition metal dichalcogenides

Trion gas, electron-hole liquid, and metal-insulator transition in doped heterostructures based on transition metal dichalcogenides

Full‐Landscape Condensation Phases for Long‐Lived Excitons in 2D Tellurium: Crystal‐Field Splitting and Finite‐Momentum Excitons

AbstractThe realization of high‐temperature exciton macroscopic quantum phases in materials still remains challenging due to strict constraints in thermal stabilities and excitonic lifetimes. In this work, by using first‐principles calculations, the exciton dispersions and macroscopic quantum phase transitions of 2D α‐ and β‐Te are investigated. The excitons with lowest eigen energy for both α‐ and β‐Te are dark restricted by the crystal‐field symmetries. The Bose–Einstein condensation (BEC) transition for α‐ and β‐Te can be realized at 165.4 and 32.8 K with low excitation power densities of 0.42 × 1012 and 1.0 × 1012 cm−2, respectively. Furthermore, the phase transitions from insulating free exciton (FE) gas to conducting electron–hole plasma (EHP) and electron–hole liquid (EHL), as well as that from BEC to superfluidity phases are also predicted. Finally, the authors investigate the microscopic dynamics for bright excitons of 2D tellurium and find that they reach thermal equilibrium at 1–50 fs and excitonic lifetimes can reach 1–40 ns, beneficial for experimental observation of quantum condensate states. The findings in this work not only demonstrate the excellent optoelectronic properties of 2D tellurium allotropes, but also provide a promising platform for experimental realization of high‐temperature excitonic macroscopic quantum condensates.

Phase Diagram of High-Temperature Electron-Hole Quantum Droplet in Two-Dimensional Semiconductors.

Quantum liquids, systems exhibiting effects of quantum mechanics and quantum statistics at macroscopic levels, represent one of the most exciting research frontiers of modern physical science and engineering. Notable examples include Bose-Einstein condensation (BEC), superconductivity, quantum entanglement, and a quantum liquid. However, quantum liquids are usually only stable at cryogenic temperatures, significantly limiting fundamental studies and device development. Here we demonstrate the formation of stable electron-hole liquid (EHL) with the quantum statistic nature at temperatures as high as 700 K in monolayer MoS2 and elucidate that the high-temperature EHL exists as droplets in sizes of around 100-160 nm. We also develop a thermodynamic model of high-temperature EHL and, based on the model, compile an exciton phase diagram, revealing that the ionized photocarrier drives the gas-liquid transition, which is subsequently validated with experimental results. The high-temperature EHL provides a model system to enable opportunities for studies in the pursuit of other high-temperature quantum liquids. The results can also allow for the development of quantum liquid devices with practical applications in quantum information processing, optoelectronics, and optical interconnections.

Room temperature electron–hole liquid phase in monolayer MoSi2Z4 (Z = pinctogen)

Photo-excited electrons and holes in insulators, above a critical density and below a critical temperature, can condense to form an electron–hole liquid (EHL) phase. However, observing the EHL phase at room temperature is extremely challenging. Here, we introduce the monolayer (Z = N, As, P) series of compounds as a promising platform for observing the EHL phase at room temperature. The higher impact of the Coulomb interactions in two dimensions helps these monolayers support the EHL phase with an increased EHL binding energy and transition temperature, along with strongly bound excitons. Our findings motivate further exploration of the monolayers for realizing the EHL phase at high temperatures to harness collective phenomena for optoelectronic applications.

Emergence and Relaxation of an e–h Quantum Liquid Phase in Photoexcited MoS2 Nanoparticles at Room Temperature

AbstractLow‐dimensional transition metal dichalcogenide (TMDC) materials are heralding a new era in optoelectronics and valleytronics owing to their unique properties. Photo‐induced dynamics in these systems is mostly studied from the perspective of individual quasi‐particles—excitons, bi‐excitons, or, even, trions—their formation, evolution, and decay. The role of multi‐body and exciton dynamics, the associated collective behavior, condensation, and inter‐excitonic interactions remain intriguing and seek attention, especially in room‐temperature scenarios that are relevant for device applications. In this work, the formation and decay of an unexpected electron–hole quantum liquid phase at room‐temperature on ultrafast timescales in multi‐layer MoS2 nanoparticles is evidenced through femtosecond broadband transient absorption spectroscopy. The studies presented here reveal the complete dynamical picture: the initial electron–hole plasma (EHP) condenses into a quantum electron–hole liquid (EHL) phase that typically lasts as long as 10 ps, revealing its robustness, whereafter the system decays through phonons. The authors employ a successful physical model using a set of coupled nonlinear rate equations governing the individual populations of these constituent phases to extract their contributions to bandgap renormalization (BGR). Beyond the observation of the electron–hole liquid‐like state at room temperature, this work reveals the ultrafast dynamics of photo‐excited low‐dimensional systems arising out of collective many‐particle behavior and correlations.

Full-momentum exciton landscape and macroscopic quantum phase diagram in two-dimensional gallium oxides

High-temperature exciton macroscopic quantum phases have a wide application prospect in many fields such as ultrahigh power photonics and quantum information, and are extremely difficult to realize due to the strong thermal dissociation effect. In this study, the exciton dispersions and macroscopic quantum phase diagrams of two-dimensional (2D) ultrawide bandgap semiconductors I–Ga2O3 and II-Ga2O3 are investigated for the first time. Both I–Ga2O3 and II-Ga2O3 possess the complex excitonic composition and morphology, resulting from their highly degenerate and flat valence bands. For the exciton B1 (B1') with an ultra-large binding energy of 1.14 (1.03) eV in I–Ga2O3, the phase transition temperature from free exciton to Bose-Einstein condensation (TBEC) is as high as 356 (679) K, respectively. The critical carrier densities for the formation of electron-hole liquid at room temperature (NEHL) are 1.3 × 1013 cm−2 and 1.8 × 1013 cm−2, respectively. For the free exciton B1 with an ultra-large binding energy of 1.49 eV in II-Ga2O3, TBEC reaches 365 K and NEHL is 5.9 × 1013 cm−2. Our findings extend the material basis for the research of exciton macroscopic quantum phases and will boost their applications in novel optoelectronic devices.

Excitation of intracenter terahertz radiation by plasma oscillations in electron–hole liquid

A new mechanism for the excitation of impurity related terahertz radiation in semiconductors under the conditions of exciton condensation into an electron–hole liquid is reported. The interaction of impurity centers with plasmons localized on droplets of an electron–hole liquid produces ionization of the centers. The subsequent capture of nonequilibrium charge carriers by ionized impurities is followed by terahertz intracenter radiative transitions. In these processes, impurity centers play the role of antennas that convert the near electromagnetic field of plasmons on droplets of an electron–hole liquid into detected radiation. The main experiments were carried out on lithium-doped silicon crystals at helium temperatures under conditions of interband photoexcitation. A theoretical model of the excitation of impurity centers by localized plasmons is developed, which explains the main regularities observed in the experiment.

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.

Charge-separated electron-hole liquid in transition metal dichalcogenide heterostructures

The possibility of the formation of an electron-hole liquid in the type II heterostructures based on monolayers (bilayers) of transition metal dichalcogenides is considered. It is indicated that additional valleys in the conduction band, which are present in bilayers, are required for its observation. The binding energy of the interlayer exciton is found by the variation method. An analytical formula is found for the shape of the recombination line of the electron-hole liquid.

Biexciton-like quartet condensates in an electron-hole liquid

We theoretically study the ground-state properties and the condensations of exciton-like Cooper pairs and biexciton-like Cooper quartets in an electron-hole system. Applying the variational approach associated based on the quartet Bardeen-Cooper-Schrieffer (BCS) model to the four-component fermionic system consisting of spin-1/2 electrons and spin-1/2 holes, we show how Cooper pairs and quartet correlations appear in the equation of state at the thermodynamic limit. The biexciton-like four-body correlations survive even at the high-density regime as a many-body BCS-like state of Cooper quartets. Our results are useful for further understanding of exotic matter in the interdisciplinary context of quantum many-body physics with multiple degrees of freedom.

Towards high-temperature electron-hole condensate phases in monolayer tetrels metal halides: Ultra-long excitonic lifetimes, phase diagram and exciton dynamics

Excitons as composite bosons have been predicted to condense into Bose Einstein Condensation (BEC), Berezinskii-Kosterlitz-Thouless (BKT) superfluid or electron-hole liquid (EHL) states. However, short lifetime and small binding energy are the main obstacles that hinder the formation and observation of excitonic condensate at high temperature. Here we demonstrate excellent two-dimensional Tetrel Metal Halides (TMHs) platforms for excitonic quantum phase transition researches. We find that excitons in those monolayers possess effective masses similar to the free electron, promising large thermal de Broglie wavelengths. They can maintain stable bosonic characteristic at high temperature and concentration up to 1012 cm−2. The calculation on PbI2, PbBr2, PbCl2, SnI2, SnBr2, SnCl2 indicates BEC transition temperatures at 49 K, 103 K, 252 K, 36 K, 78 K, 152 K, comparable to the experimentally observed exciton BEC in MoSe2–WSe2 bilayer and 1 T-TiSe2 at 100 K and 190 K respectively. Besides, we confirm that the thermal equilibrium of excitonic subsystem can be established really fast, up to ∼10–100 fs. The excitons can live for ∼1–100 μs without direct radiation, beneficial for the formation and observation of condensate state. Our result paves the way not only for studies of quantum phase transition researches, but also for high-temperature excitonic devices.

Stability of electron-hole liquid in quantum wires

The energy and equilibrium density of electron-hole liquid in quantum wires is calculated using density functional theory . Nonlinear Schrödinger equations for electrons and holes are solved numerically. It is shown that electron-hole liquid in a quantum wire with a radius of a few exciton radii is stable in semiconductors with single-valley spectrum and isotropic masses of electrons and holes. • Density functional theory used to calculate the energy of electron-hole liquid in quantum wires. • The Schrödinger equations for electrons and holes are solved numerically. • Electron–hole liquid is stable in quantum wires with isotropic masses of electrons and holes. • Results of calculations are in satisfactory agreement with experimental data.

Phase Diagram of Electron–Hole Liquid in Monolayer Heterostructures Based on Transition Metal Dichalcogenides

In the last few years, interest in monomolecular layers of transition metal dichalcogenides (TMDs) has been driven by their unusual electronic and optical properties, which are very attractive for designing functional elements of new generation nanoelectronics. Recently, experimental evidence has appeared for the formation of a high-temperature strongly bound electron-hole liquid (EHL) in TMD monolayers. Strong binding of charge carriers is due to a significant decrease in the screening of the Coulomb interaction in monolayer heterostructures. In this work, the gas--liquid phase transition in a system of electrons and holes in quasi-two-dimensional heterostructures based on TMDs is considered and the critical parameters of such a transition are calculated. The metal-insulator transition is described and the phase diagram for such heterostructures is constructed.

Fermi liquid theory sheds light on hot electron-hole liquid in 1L−MoS2

Room-temperature electron-hole liquid has recently been experimentally identified in low-dimensional transition metal dichalcogenides. Here, the authors demonstrate that a first-principles Fermi liquid model effectively predicts the photoluminescence response of this phenomenon. Using density functional theory, in conjunction with previous Raman and photoluminescence spectroscopy results, they present a consistent quantitative picture of the electron-hole liquid phase transition in suspended, heat-strained 1$L$-MoS${}_{2}$ monolayers. They show a 23-fold increase in photoluminescence per unit of direct gap carrier density and 9:1 indirect-direct hole population ratio at high strain.

Stability of electron–hole liquid in quantum wells

Density functional theory is used to calculate the energy of electron–hole liquid and the equilibrium density of electron-hole pairs in quantum wells. Nonlinear Kohn–Sham equations for electrons and holes are solved numerically. The influence of the depth and width of the quantum well, the ratio of the hole and electron masses, and the spin splitting of the hole band on the properties of electron–hole liquid is studied. The critical temperature of electron–hole liquid in quantum wells is estimated. Good agreement between the calculations and experimental results is obtained.

Semimetallicity and electron-hole liquid in two-dimensional C and BN based compounds

Insulating-metallic transition mediated by substitutional atoms is predicted in a series of two-dimensional carbon-based structures. Introducing Si atoms in selected sites of tetrahexcarbon [Carbon 137 (2018) 266] according to rational chemical rules, metallicity by trivial band inversion without band gap opening is induced. Additional substitution of remaining C atoms by BN dimers introduces no changes in the metallic properties. A series of isomorphous two-dimensional materials with isoelectronic structures derived by exchanging group IV elements exhibiting various band gaps is obtained. Dynamical stability is verified with phonon analysis and beyond the harmonic approximation with molecular dynamics up to room temperature. The semi-metallic compounds have well-nested pockets of carriers and are good candidates for the formation of an excitonic insulator.

Collective states of excitons in semiconductors

A review of many-body effects in exciton ensembles in semiconductors is given with the emphasis on two-dimensional systems: structures with single and double quantum wells and with quantum microcavities. The Bose–Einstein condensation effect, an accumulation of a macroscopic number of excitons in the ground state of the system, is discussed. The known prohibition on condensation in low-dimensional systems can be lifted due to the disorder resulting from the chaotic potential. Manifestations of the finite exciton lifetime and, correspondingly, of the nonequilibrium of the excitonic system caused by processes of excitons entering and leaving the condensate state are analyzed. Other collective phases of excitons, namely, two-dimensional crystals of dipolar excitons and an electron–hole liquid, formed as a result of interparticle interactions, are discussed.

Thermal transport in compensated semimetals: Effect of electron-electron scattering on Lorenz ratio

It is well known that the electronic thermal conductivity of clean compensated semimetals can be greatly enhanced over the electric conductivity by the availability of an ambipolar mechanism of conduction, whereby electrons and holes flow in the same direction experiencing negligible Coulomb scattering as well as negligible impurity scattering. This enhancement -- resulting in a breakdown of the Wiedemann-Franz law with an anomalously large Lorenz ratio -- has been recently observed in two-dimensional monolayer and bilayer graphene near the charge neutrality point. In contrast to this, three-dimensional compensated semimetals such as WP$_2$ and Sb are typically found to show a reduced Lorenz ratio. This dramatic difference in behavior is generally attributed to different regimes of Fermi statistics in the two cases: degenerate electron-hole liquid in compensated semimetals versus non-degenerate electron-hole liquid in graphene. We show that this difference is not sufficient to explain the reduction of the Lorenz ratio in compensated semimetals. We argue that the solution of the puzzle lies in the ability of compensated semimetals to sustain sizeable regions of electron-hole accumulation near the contacts, which in turn is a consequence of the large separation of electron and hole pockets in momentum space. These accumulations suppress the ambipolar conduction mechanism and effectively split the system into two independent electron and hole conductors. We present a quantitative theory of the crossover from ambipolar to unipolar conduction as a function of the size of the electron-hole accumulation regions, and show that it naturally leads to a sample-size-dependent thermal conductivity.

Ground State of Quasi-Two-Dimensional Electron–Hole Liquid on Silicon Surface

The density functional theory is used for the determination of a ground state of a quasi-two-dimensional electron[Formula: see text]hole liquid (EHL) in the presence of an external electric field. The Kohn[Formula: see text]Sham equations for electrons and holes are numerically solved. The binding energies of electron[Formula: see text]hole pair are calculated for various silicon surfaces. It is shown that EHL can exist on the (111) Si.

P-type β-Ga2O3 metal-semiconductor-metal solar-blind photodetectors with extremely high responsivity and gain-bandwidth product

P-type β-Ga2O3 films deep-ultraviolet (DUV) solar-blind metal-semiconductor-metal (MSM) photodetectors (PDs) are fabricated with extremely high photoresponsivity (9.5 × 103 A/W), external quantum efficiency (4.7 × 106%), detectivity (1.5 × 1015 Jones), and gain-bandwidth product (106) at 5 V bias, very low noise equivalent power (4.9 × 10−16 W/Hz1/2) and high specific detectivity (1.9 × 1013 Jones) at 1 kHz and 3 V bias. The excellent performances of the p-type β-Ga2O3 DUV MSM PDs are attributed to the charge carrier multiplication via collective excitation of aggregated excitons and/or electron-hole liquid within the fabricated high-quality p-type β-Ga2O3 films, which possess the room-temperature Hall resistivity of 52.6 Ωcm, the hole mobility of 41.4 cm2/V⋅s, and the hole concentration of 2.86 × 1015 cm−3. The unprecedentedly high photoresponsivity and detectivity and the carrier multiplication mechanism in high-quality p-type β-Ga2O3 films pave a novel way to fabricate super sensitive DUV PDs based on p-type wide-bandgap oxide semiconductors.