Exciton Condensation Research Articles

Quantum criticality of excitonic Mott metal-insulator transitions in black phosphorus

Quantum phase transition refers to the abrupt change of ground states of many-body systems driven by quantum fluctuations. It hosts various intriguing exotic states around its quantum critical points approaching zero temperature. Here we report the spectroscopic and transport evidences of quantum critical phenomena of an exciton Mott metal-insulator-transition in black phosphorus. Continuously tuning the interplay of electron-hole pairs by photo-excitation and using Fourier-transform photo-current spectroscopy as a probe, we measure a comprehensive phase diagram of electron-hole states in temperature and electron-hole pair density parameter space. We characterize an evolution from optical insulator with sharp excitonic transition to metallic electron-hole plasma phases featured by broad absorption and population inversion. We also observe strange metal behavior that resistivity is linear in temperature near the Mott transition boundaries. Our results exemplify an ideal platform to investigating strongly-correlated physics in semiconductors, such as crossover between superconductivity and superfluity of exciton condensation.

Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.

Excitonic ordering in strongly correlated spin crossover systems: Induced magnetism and excitonic excitation spectrum

The effects associated with interatomic hoppings of excitons and the excitonic Bose condensate formation in strongly correlated spin crossover systems are considered in the framework of the effective Hamiltonian for the two-band Kanamori model. The appearance of antiferromagnetic ordering due to the exciton order is found even in the absence of interatomic exchange interaction. The spectrum of excitonic excitations is calculated at various points of the temperature vs crystal field phase diagram. Outside the region of exciton ordering, the spectrum has a gap, which vanishes at the boundary of the exciton condensate phase. The nonuniform spectral weight distribution over the Brillouin zone is found. The role of electron-phonon interaction is discussed as well.

Quantum anomalous Hall effect and electric-field-induced topological phase transition in AB-stacked MoTe2/WSe2 moiré heterobilayers

We propose a mechanism to explain the quantum anomalous Hall (QAH) effect and the electric-field-induced topological phase transition in AB-stacked $\mathrm{MoTe}{}_{2}/\mathrm{WSe}{}_{2}$ moir\'e heterobilayers at $\ensuremath{\nu}=1$ hole filling. We suggest that the Chern band of the QAH state is generated from an intrinsic band inversion composed of the highest two moir\'e hole bands with opposite valley numbers and a gap opening induced by two Coulomb-interaction-driven magnetic orders. These magnetic orders, including an in-plane ${120}^{\ensuremath{\circ}}$-N\'eel order and an in-plane ferromagnetic order, interact with moir\'e bands via corresponding in-plane exchange fields. The N\'eel order ensures the insulating gap, the ferromagnetic order induces the nonzero Chern number, and both orders contribute to time-reversal symmetry breaking. The N\'eel order is acquired from the Hartree-Fock exchange interaction and the formation of ferromagnetic order is attributed to interlayer-exciton condensation and exciton ferromagnetism. The exciton ferromagnetism can be demonstrated by excitonic Bose-Hubbard physics and Berezinskii-Kosterlitz-Thouless transition. In low electric fields, the equilibrium state is a Mott-insulator state. At a certain electric field, a correlated insulating state composed of the hole-occupied band and the exciton condensate becomes the thermodynamically stable phase and the topological phase transition occurs as the ferromagnetic order emerges. The consistency between the present theory and experimental observations is discussed. Experimental observations, including the spin-polarized/valley-coherent nature of the QAH state, the absence of charge gap closure at the topological phase transition, the canted spin texture, and the insulator-to-metal transition are interpreted by the mechanism.

Charge Transfer Dynamics in MoSe2/hBN/WSe2 Heterostructures

Ultrafast charge transfer processes provide a facile way to create interlayer excitons in directly contacted transition metal dichalcogenide (TMD) layers. More sophisticated heterostructures composed of TMD/hBN/TMD enable new ways to control interlayer exciton properties and achieve novel exciton phenomena, such as exciton insulators and condensates, where longer lifetimes are desired. In this work, we experimentally study the charge transfer dynamics in a heterostructure composed of a 1 nm thick hBN spacer between MoSe2 and WSe2 monolayers. We observe the hole transfer from MoSe2 to WSe2 through the hBN barrier with a time constant of 500 ps, which is over 3 orders of magnitude slower than that between TMD layers without a spacer. Furthermore, we observe strong competition between the interlayer charge transfer and intralayer exciton-exciton annihilation processes at high excitation densities. Our work opens possibilities to understand charge transfer pathways in TMD/hBN/TMD heterostructures for the efficient generation and control of interlayer excitons.

Signature of Cascade Transitions between Interlayer Excitons in a Moiré Superlattice.

A moiré superlattice in transition metal dichalcogenides heterostructure provides an exciting platform for studying strongly correlated electronics and excitonic physics, such as multiple interlayer exciton (IX) energy bands. However, the correlations between these IXs remain elusive. Here, we demonstrate the cascade transitions between IXs in a moiré superlattice by performing energy- and time-resolved photoluminescence measurements in the MoS_{2}/WSe_{2} heterostructure. Furthermore, we show that the lower-energy IX can be excited to higher-energy ones, facilitating IX population inversion. Our finding of cascade transitions between IXs contributes to the fundamental understanding of the IX dynamics in moiré superlattices and may have important applications, such as in exciton condensate, quantum information protocols, and quantum cascade lasers.

Directional growth of quasi-2D Cu2O monocrystals on rGO membranes in aqueous environments.

The preparation technology of unconventional low-dimensional Cu2O monocrystals, which exhibit specific crystal planes and present significantly unique interfacial and physicochemical properties, is attracting increasing attention and interest. Herein, by integrating a high-temperature oxidation process under vacuum and a pure-water incubation process under ambient conditions, we propose the self-assembled growth and synthesis of quasi-two-dimensional Cu2O monocrystals on reduced graphene oxide (rGO) membranes. The prepared Cu2O crystals have a single (110) crystal plane, regular rectangular morphology, and potentially well conductivity. Experimental and theoretical results suggest that this assembly is attributed to the pre-nucleation clusters aggregation and directional attachment of Cu and O on the rGO membranes in aqueous environment and cation-π interactions between the (110) crystal plane of Cu2O and rGO surface. Our findings offer a potential avenue for the discovery and design of advanced low-dimensional single-crystal materials with specific interfacial properties in a pure aqueous environment.

Hot exciton effect in photoluminescence of monolayer transition metal dichalcogenide

AbstractHot excitons are usually neglected in optical spectroscopy in two‐dimensional semiconductors for the sake of momentum conservation, as the majority of hot excitons are out of light cones. In this letter, we elaborate on the contribution of hot excitons to optical properties of monolayer Molybdenum diselenide (MoSe2) with photoluminescence (PL) and PL excitation (PLE) spectroscopy. With the excitation‐intensity‐dependent PL, temperature‐dependent PL and PLE experiments combined with the simulations, we experimentally distinguish the influences of the exciton temperature and the lattice temperature in the PL spectrum. It is concluded that the acoustic phonon‐assisted PL accounts for the non‐Lorentzian high energy tail in the PL spectrum, and the hot exciton effect is significant to linear optical properties of transition metal dichalcogenides. Besides, the effective exciton temperature is found to be several tens of Kelvin higher than the lattice temperature at non‐resonant optical excitation. It indicates that the exciton temperature needs to be carefully taken into account when considering the exciton‐related quantum phase phenomena such as exciton condensation. It is experimentally demonstrated that the effective exciton temperature can be tuned by excitation energy.Key points The acoustic phonon‐assisted photoluminescence (PL) accounts for the non‐Lorentzian high‐energy tail in the PL spectrum. “Hot” excitons play a significant role in optical properties of two‐dimensional transition metal dichalcogenides. The effective exciton temperature could be tuned by excitation energy.

Doping a Mott insulator with excitons in a moiré bilayer: Fractional superfluid, neutral Fermi surface, and Mott transition

In this paper we explore possible phases arising from doping neutral excitons into a Mott insulator in the context of moir\'e bilayers. We consider two moir\'e layers coupled together only through inter-layer repulsion and there is a U(2)$\times$ U(2) symmetry. The densities of the two layers can be tuned to be $n_t=x,n_b=1-x$ with $n_t+n_b=1$. $x=0$ limit is a layer polarized Mott insulator and small $x$ regime can be reached by doping inter-layer excitons at density $x$. Charge gap can remain finite at small $x$, as is demonstrated experimentally in the WSe$_2$-hBN-WSe$_2$/WS$_2$ system. To capture the intertwinement of the spin and exciton degree of freedom, we propose a four-flavor spin model. In addition to the obvious possibility of single exciton condensation phase, we also identified more exotic physics with fractionalization: (I) We define spin gap $\Delta_t, \Delta_b$ for the two layers respectively. As long as the spin gap at either layer is finite, single exciton condensation is impossible and we can only have paired exciton condensation. If both spin gaps are finite, it can be a fractional exciton superfluid with paired exciton condensation coexisting with $Z_2$ spin liquid. Numerical evidences for such a phase will be provided. (II) If the layer polarized Mott insulator at $x=0$ is in a U(1) spin liquid with spinon Fermi surface, the natural phase at $x>0$ hosts neutral Fermi surface formed by fermionic excitons. There are metallic counter-flow transport and also Friedel oscillations in layer polarization in this exotic phase. Our numerical simulation in one dimension observes an analog of this neutral Fermi surface phase. (III) There could be a metal-insulator transition (MIT) by tuning $x$ in the universality class of a bandwidth tuned MIT. We provide one theory for such a continuous Mott transition and predicted a universal drag resistivity.

Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in 1T-TiSe_{2}.

1T-TiSe_{2} is one of the most studied charge density wave (CDW) systems, not only because of its peculiar properties related to the CDW transition, but also due to its status as a promising candidate of exciton insulator signaled by the proposed plasmon softening at the CDW wave vector. Using high-resolution electron energy loss spectroscopy, we report a systematic study of the temperature-dependent plasmon behaviors of 1T-TiSe_{2}. We unambiguously resolve the plasmon from phonon modes, revealing the existence of Landau damping to the plasmon at finite momentums, which does not support the plasmon softening picture for exciton condensation. Moreover, we discover that the plasmon lifetime at zero momentum responds dramatically to the band gap evolution associated with the CDW transition. The interband transitions near the Fermi energy in the normal phase are demonstrated to serve as a strong damping channel of plasmons, while such a channel in the CDW phase is suppressed due to the CDW gap opening, which results in the dramatic tunability of the plasmon in semimetals or small-gap semiconductors.

Excitonic Correlations, Spin-State Ordering, and Magnetic-Field Effects in One-Dimensional Two-Orbital Hubbard Model for Spin-Crossover Region

The electronic properties of excitonic insulators have been examined precisely in recent years. Pictures of exciton condensation may be applied to the spin-state transition observed in perovskite cobalt oxides. We examine the crystal-field and magnetic-field dependences of spatial spin structures on the basis of the density matrix renormalization group method using an effective model for the one-dimensional two-orbital Hubbard model in strong-coupling limit. We find an excitonic insulating (EI) phase and a spin-state ordering (SSO) phase in the intermediate region between low-spin and high-spin phases. In the EI phase, spin-triplet excitons are spatially fluctuating due to quantum effects, and an incommensurate spin correlation realizes. The analyses of a spin gap and degeneracy of entanglement spectra suggest the realization of the Haldane-like edge state in the EI phase. In the SSO phase, 3-fold or incommensurate SSO structures realize depending on the crystal-field splitting. These structures are stabilized as a result of the competition of exchange interactions between spin states.

Moiré exciton condensate: Nonlinear Dirac point, broken-symmetry Bloch waves, and unusual optical selection rules

Moir\'e exciton features tunable Dirac dispersion and spatially dependent optical selection rules. With the long lifetime due to its interlayer nature, it is promising to realize a Bose-Einstein condensation of moir\'e excitons. Here we study the properties of moir\'e exciton condensate within the mean-field theory, with special focus on exciton-exciton interaction effect on the nonlinear Bloch band and Bloch waves of exciton condensate in moir\'e potential. We find the nonlinear dispersion of the moir\'e exciton condensate exhibits complex loop structure induced by exciton-exciton interaction. A nonlinear Dirac cone emerges at $\boldsymbol{\Gamma}$ point of the Bloch band, with a three-fold degenerate nonlinear Dirac point. Each degenerate Bloch wave at nonlinear Dirac point spontaneously breaks $C3$ rotational symmetry of the moir\'e potential, and themselves differ by $C3$ rotations. Since they reside in the light cone, these nontrivial Bloch band structure and broken-symmetry Bloch waves can be experimentally detected by examining light emission from those states. Symmetry breaking of Bloch states implies unusual optical selection rules compared with single exciton case: moir\'e exciton condensate at $\boldsymbol{\Gamma}$ point emits light with all three components of polarization instead of only left or right circular polarization. We further propose that, by applying in-plane electric field on one layer to drive an initially optically dark exciton condensate towards light cone, the light polarization of final states as well as their dependence on field direction serves as the smoking gun for experimental observation.

Tuning moiré excitons in Janus heterobilayers for high-temperature Bose-Einstein condensation.

Using first-principles calculations, we predict that moiré excitons in twisted Janus heterobilayers could realize tunable and high-temperature Bose-Einstein condensation (BEC). The electric dipole in the Janus heterobilayers leads to charge-transfer interlayer and intralayer moiré excitons with exceptionally long lifetimes, in the absence of spacer layers. The electric dipole is also expected to enhance exciton-exciton repulsions at high exciton densities and can modulate moiré potentials that trap excitons for their condensation. The key parameters for exciton condensation, including exciton Bohr radius, binding energy, effective mass, and critical Mott density, are examined as a function of the twist angle. Last, exciton phase diagrams for the Janus heterobilayers are constructed from which one can estimate the BEC (>100 K) and superfluid (~30 K) transition temperatures. In addition to indirect interlayer excitons, we find that direct intralayer excitons can also condense at high temperatures, consistent with experiments.

Quantum phase transitions in a model Hamiltonian exhibiting entangled simultaneous fermion-pair and exciton condensations

Quantum states of a novel Bose-Einstein condensate, in which both fermion-pair and exciton condensations are simultaneously present, have recently been realized theoretically in a model Hamiltonian system. Here we identify quantum phase transitions in that model between fermion-pair and exciton condensations based on a geometric analysis of the convex set of ground-state two-particle reduced density matrices (2-RDMs). The 2-RDM set provides a finite representation of the infinite parameter space of Hamiltonians that readily reveals a fermion-pair condensate phase and two distinct exciton condensate phases, as well as the emergence of first- and second-order phase transitions as the particle number of the system is increased. The set, furthermore, shows that the fermion-exciton condensate (FEC) lies along the second-order phase transition between the exciton and fermion-pair condensate phases. The detailed information about the exciton and fermion-pair phases, the forces behind these phases, as well as their associated transitions provides additional insight into the formation of the FEC condensate, which we anticipate will prove useful in its experimental realization.

Quasimolecular electronic structure of the spin-liquid candidate Ba3InIr2O9

The mixed-valent iridate Ba3InIr2O9 has been discussed as a promising candidate for quantum spin-liquid behavior. The compound exhibits Ir$^{4.5+}$ ions in face-sharing IrO6 octahedra forming Ir2O9 dimers with three t2g holes per dimer. Our results establish Ba3InIr2O9 as a cluster Mott insulator. Strong intra-dimer hopping delocalizes the three t2g holes in quasi-molecular dimer states while inter-dimer charge fluctuations are suppressed by Coulomb repulsion. The magnetism of Ba3InIr2O9 emerges from spin-orbit entangled quasi-molecular moments with yet unexplored interactions, opening up a new route to unconventional magnetic properties of 5d compounds. Using single-crystal x-ray diffraction we find the monoclinic space group C2/c already at room temperature. Dielectric spectroscopy shows insulating behavior. Resonant inelastic x-ray scattering (RIXS) reveals a rich excitation spectrum below 1.5 eV with a sinusoidal dynamical structure factor that unambiguously demonstrates the quasi-molecular character of the electronic states. Below 0.3 eV, we observe a series of excitations. According to exact diagonalization calculations, such low-energy excitations reflect the proximity of Ba3InIr2O9 to a hopping-induced phase transition based on the condensation of a quasi-molecular spin-orbit exciton. The dimer ground state roughly hosts two holes in a bonding j=1/2 orbital and the third hole in a bonding j=3/2 orbital.

Excitonic magnetic polarons in II-VI diluted magnetic semiconductor nanostructures

Exciton is the elementary excitation in semiconductors with energy close to Eg, bound by electron and hole. Spin is an intrinsic form of angular momentum carried by elementary particles, especially for electron, transition metal(TM) ion and photon. Here we discuss the excitonic magnetic polaron-----coupling of exciton or electron with coupled spins of doped Transition metal(TM) ions in the micrometer sized diluted magnetic semiconductor(DMS) nanostructures, and their formation, dynamic spectral responses, collective behaviors have been discussed in this review, because they have important influences on their optical properties, reflected by the profound spin-related emission behaviors and the collective magnetic excitonic polaron condensation processes in such micrometer sized DMS space, which may have valuable applications in the quantum modulation and lighting technology.

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.

Excitonic properties in a double-layer graphene

This paper investigates theoretically the excitonic condensation state at zero temperature in a double-layer graphene structure. In the framework of the unrestricted Hartree–Fock approximation, the electron-hole system in the structure described in the two-band electronic model is analyzed and one finds a set of self-consistent equations determining the excitonic order parameter. The optical properties of the excitonic condensation state then are examined in the Kubo linear optical response theory. Our results indicate that in the case of sufficiently large Coulomb interaction, the BEC excitonic condensation state might occur at low electronic excitation density. By turning the external electric field, the superfluid state stabilizes in the BCS-type excitonic condensate. The optical conductivity spectrum also provides us more insight into the excitonic condensation states.

Observation of Bose-Einstein condensates of excitons in a bulk semiconductor

An unambiguous observation of the Bose-Einstein condensation (BEC) of excitons in a photoexcited bulk semiconductor and elucidation of its inherent nature have been longstanding problems in condensed matter physics. Here, we observe the quantum phase transition and a Bose-Einstein condensate appearing in a trapped gas of 1s paraexcitons in bulk Cu2O below 400 mK, by directly visualizing the exciton cloud in real space using mid-infrared induced absorption imaging that we realized in a dilution refrigerator. Our study shows that the paraexciton condensate is undetectable by conventional luminescence spectroscopy. We find an unconventionally small condensate fraction of 0.016 with the spatial profile of the condensate well described by mean-field theory. Our discovery of this new type of BEC in the purely matter-like exciton system interacting with a cold phonon bath could pave the way for the classification of its long-range order, and for essential understanding of quantum statistical mechanics of non-equilibrium open systems.

Self-trapped excitons in diamond: A Δ-SCF approach.

This paper reports the first variationally based predictions of the lowest excited state in diamond (Γ25' → Γ15) in the unrelaxed (optical) and structurally relaxed (thermal) configurations, from direct Δ-self-consistent-field (SCF) calculations based on B3LYP, PBE0, HSE06, and GGA functionals. For the B3LYP functional, which has the best overall performance, the energy of the optical state, 7.27eV, is within the observed range of (7.2-7.4) eV and is predicted to be insulating, with indirect bandgaps of (5.6-5.8) eV. Mulliken analyses of the excited state wavefunction indicate extensive redistributions of charge and spin resulting in a strongly excitonic state with a central charge of -0.8ǀeǀ surrounded by charges of +0.12ǀeǀ at the four nearest neighbor sites. The thermally relaxed state is predicted to be similarly excitonic, with comparable bandgaps and atomic charges. Calculations of the ground and excited state relaxations lead to a Stokes shift of 0.47eV and predicted Γ-point luminescence energy of 6.89eV. Assuming a similar shift at the band edge (X1), an estimate of 5.29eV is predicted for the luminescence energy, which compares with the observed value of 5.27eV. Excited state vibrational spectra show marked differences from the ground state, with the introduction of an infrared peak at 1150cm-1 and a modest shift of 2cm-1 in the TO(X) Raman mode at 1340cm-1. Similar calculations of the lowest energy bi- and triexcitons predict these to be bound states in both optical and thermal configurations and plausible precursors to exciton condensation. Estimates of bi- and triexciton luminescence energies predict red shifts with respect to the single exciton line, which are compared to the recently reported values.