The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in lattice potentials. For bosons, the Hubbard Hamiltonian has been deeply scrutinised for short-range on-site interactions. However, accessing longer-range couplings has remained elusive experimentally. This marks the frontier towards the extended Bose-Hubbard Hamiltonian that allows insulating ordered phases at fractional lattice fillings. Here we implement this Hamiltonian by confining semiconductor dipolar excitons in an artificial two-dimensional square lattice. Strong dipolar repulsions between nearest neighbouring lattice sites then stabilise an insulating state at half filling. This characteristic feature of the extended Bose-Hubbard model exhibits signatures theoretically expected for a checkerboard spatial order. Our work thus highlights that dipolar excitons enable controlled implementations of boson-like arrays with strong off-site interactions, in lattices with programmable geometries and over 100 sites.
The Bose condensation of 2D dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system. Their Bose condensation can experimentally be achieved much easily than for ideal or weakly correlated excitons.
By doing quantum Monte Carlo ab initio simulations we show that dipolar excitons, which are now under experimental study, actually are strongly correlated systems. Strong correlations manifest in significant deviations of excitation spectra from the Bogoliubov one, large Bose condensate depletion, short-range order in the pair correlation function, and peak(s) in the structure factor.
We apply the bosonization technique to derive the phase diagram of a balanced unit density two-component dipolar Fermi gas in a one dimensional lattice geometry. The considered interaction processes are of the usual contact and dipolar long-range density-density type together with peculiar correlated hopping terms which can be generated dynamically. Rigorous bounds for the transition lines are obtained in the weak coupling regime. In addition to the standard bosonization description, we derive the low energy phase diagram taking place when part of the interaction is embodied non-perturbatively…
Quadrupolar and dipolar phases of excitons in transition-metal dichalcogenide trilayer heterostructures
The Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；Department of Physics, Technion（理工学院物理系）；The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem（分子动力学弗里茨·哈伯研究中心，耶路撒冷希伯来大学）
We present compelling experimental evidence for a successful electrostatic trapping of two-dimensional dipolar excitons that results in stable formation of a well confined, high-density and spatially uniform dipolar exciton fluid. We show that, for at least half a microsecond, the exciton fluid sustains a density higher than the critical density for degeneracy if the exciton fluid temperature reaches the lattice temperature within that time. This method should allow for the study of strongly interacting bosons in two dimensions at low temperatures, and possibly lead towards the observation of …
Strongly correlated quantum particles in lattice potentials are the building blocks for a large variety of quantum insulators, for instance Mott phases and density waves breaking the lattice symmetry. Such collective states are accessible to bosonic and fermionic systems. To expand further the spectrum of accessible quantum matter phases, mixing both species is theoretically appealing, since density order then competes with phase separation. Here we manipulate such Bose-Fermi mixture by confining neutral (boson-like) and charged (fermion-like) dipolar excitons in an artificial square lattice o…
Trimer superfluidity of antiparallel dipolar excitons in a bilayer heterostructure
Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem（弗里茨·哈伯分子动力学研究中心，耶路撒冷希伯来大学）
We examine the free energy and the thermodynamic properties in the three-chain Hubbard model for Ta2NiSe5 to clarify the phase transitions between the uniform and the FFLO excitonic states which are expected to be observed in Ta2NiSe5 under high pressure.
We study a simple model of interacting bosons on a d-dimensional cubic lattice whose dynamics conserves both total boson number and total boson dipole moment. This model provides a simple framework in which several remarkable consequences of dipole conservation can be explored. As a function of chemical potential and hopping strength, the model can be tuned between gapped Mott insulating phases and various types of gapless condensates. The condensed phase realized at large hopping strengths, which we dub a Bose-Einstein insulator, is particularly interesting: despite having a Bose condensate, …
Two-dimensional (2D) moire materials provide a new solid-state platform with unprecedented controllability for studies of correlated quantum phenomena. To date, experimental studies have focused on the correlated electronic states; the correlated bosonic states in moire materials have remained practically unexplored. Here, we report a correlated dipolar excitonic insulator, a charge insulating state driven by the formation of excitons, in a Coulomb-coupled WSe2 monolayer and WSe2/WS2 moire bilayer at total hole doping density equal to the moire density. The system is a Mott insulator when all …
We investigate the emergence of a myriad of phases in the strong coupling regime of the dipolar Hubbard model in two dimensions. By using a combination of numerically unbiased methods in finite systems with analytical perturbative arguments, we show the versatility that trapped dipolar atoms possess in displaying a wide variety of many-body phases, which can be tuned simply by changing the collective orientation of the atomic dipoles. We further investigate the stability of these phases to thermal fluctuations in the strong coupling regime, highlighting that they can be accessed with current t…
By the example of the Hubbard model we analytically and numerically examine the formating and coexisting of localized electron--electron pairs (doublons) and localized electron--hole pairs (Frenkel--type excitons) . Here we demonstrate that at a variation of the on-site Coulomb repulsion U there occurs a quantum transition from the doublon to the exciton regime that is conditioned by the low-energy effective hybridization of the valence and conductivity subbands. We calculate momentum distribution functions and electronic spectrum functions for different U, which reveal topologically nontrivia…
We show that the charge transfer excitons in a Hubbard model system including nearest neighbor Coulomb interactions effectively attain some charge in doped systems and become visible in photoelectron and inverse photoelectron spectroscopies. This shows that the description of a doped system by an extended Hubbard model differs substantially from that of a simple Hubbard model. Longer range Coulomb interactions cause satellites in the one electron removal and addition spectra and the appearance of spectral weight if the gap of doped systems at energies corresponding to the excitons of the undop…
We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using Determinant Quantum Monte Carlo. To model both the onsite repulsion U and the interlayer interaction V we introduced a novel update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction V, which prohibits at this stage a unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest excit…
Photoinduced dynamics in an excitonic insulator is studied theoretically by using a two-orbital Hubbard model on the square lattice where the excitonic phase in the ground state is characterized by the BCS-BEC crossover as a function of the interorbital Coulomb interaction. We consider the case where the order has a wave vector $Q=(0,0)$ and photoexcitation is introduced by a dipole transition. Within the mean-field approximation, we show that the excitonic order can be enhanced by the photoexcitation when the system is initially in the BEC regime of the excitonic phase, whereas it is reduced …
We study the excitonic insulating (EI) phase in the two-band Hubbard models on the Penrose tiling. Performing the real-space mean-field calculations systematically, we obtain the ground state phase diagrams for the vertex and center models. We find that, in some regimes, the stable EI phase is induced by small interband interactions. We argue that this originates from the electron-hole pairing for the completely or nearly degenerate states, which are characteristic of the Penrose tiling. We also study spatial distribution of the order parameter, mapping it to the perpendicular space.
The competition of interactions implies the compensation of standard mechanisms which leads to the emergence of exotic phases between conventional phases. The extended Hubbard model (EHM) is a fundamental example for the competition of the local Hubbard interaction and the nearest-neighbor density-density interaction, which at half-filling and in one dimension leads to a bond order wave (BOW) between a charge density wave (CDW) and a quasi-long-range order Mott insulator (MI). We study the full momentum-resolved excitation spectrum of the one dimensional EHM in the CDW phase and clarify the re…
Using the dynamical mean-field approximation we investigate formation of excitonic condensate in the two-band Hubbard model in the vicinity of the spin-state transition. With temperature and band filling as the control parameters we realize all symmetry allowed spin-triplet excitonic phases, some exhibiting a ferromagnetic polarization. While the transitions are first-order at low temperatures, at elevated temperatures continuous transitions are found that give rise to a multi-critical point. Rapid but continuous transition between ferromagnetic and non-magnetic excitonic phases allows switchi…
Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space time evolution of an excitonic wave-packet using a two-orbital Hubbard model. The exciton is created by exciting an electron from a lower energy half-filled orbital to a higher energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave-packet, using the time-dependent density matrix renormalization group method. We find clear evidence of charge-spin and spin-orbit separation in real-space, by tracking the time evolution of local observables. We show th…
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q$=$π$ in $t_{2g}^4$ spin-orbit coupled three-orbital Hubbard models at electronic density $n=4$. In parallel, experiments involving iridates with non-integer valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of a novel excitonic condensate at $n=3.5$ in a one-dimensional Hubbard model with a degenerate $t_{2g}$ sector, when in the presence of spin-orbit coupli…
The three-chain Hubbard model for Ta$_2$NiSe$_5$ known as a candidate material for the excitonic insulator is investigated over the wide range of energy gap $D$ between the two-fold degenerate conduction bands and the nondegenerate valence band including both semiconducting ($D>0$) and semimetallic ($D<0$) cases. In the semimetallic case, the difference of the band degeneracy inevitably causes the imbalance of each Fermi wavenumber, resulting in a remarkable excitonic state characterized by the condensation of excitons with finite center-of-mass momentum $q$, the so-called Fulde-Ferrell-Larkin…
We use broadband ultra-fast pump-probe spectroscopy in the visible range to study the lowest excitations across the Mott-Hubbard gap in the orbitally ordered insulator YVO3. Separating thermal and non-thermal contributions to the optical transients, we show that the total spectral weight of the two lowest peaks is conserved, demonstrating that both excitations correspond to the same multiplet. The pump-induced transfer of spectral weight between the two peaks reveals that the low-energy one is a Hubbard exciton, i.e. a resonance or bound state between a doublon and a holon. Finally, we specula…
Layered bosonic dipolar fluids have been suggested to host a condensate of interlayer molecular bound states. However, its experimental observation has remained elusive. Motivated by two recent experimental works [Hubert et al., Phys. Rev. X 9, 021026 (2019) and D. J. Choksy et al., Phys. Rev. B 103 045126 (2021)], we theoretically study, using numerically exact quantum Monte Carlo calculations, the experimental signatures of collective interlayer pairing in vertically stacked indirect exciton (IX) layers. We find that IX energy shifts associated with each layer evolve non trivially as a funct…
Transition metal chalcogenide Ta$_2$NiSe$_5$, a promising material for the excitonic insulator, is investigated on the basis of the quasi-one-dimensional three-chain Hubbard model with two conduction ($c$) bands and one valence ($f$) band. In the semimetallic case where only one of two $c$ bands and the $f$ band cross the Fermi level, the transition from the $c$-$f$ compensated semimetal to the uniform excitonic insulator takes place at low temperature as the same as in the semiconducting case. On the other hand, when another $c$ band also crosses the Fermi level, the system shows three types …
Recent optical conductivity measurements reveal the presence of Hubbard excitons in certain Mott insulators. In light of these results, it is important to revisit the dynamics of these materials to account for excitonic correlations. We investigate time-resolved excitation and relaxation dynamics as a function of temperature in perovskite-type LaVO${}_{3}$ thin films using ultrafast optical pump-probe spectroscopy. LaVO${}_{3}$ undergoes a series of phase transitions at roughly the same critical temperature $T_C\cong 140\ K$, including a second-order magnetic phase transition (PM $\xrightarrow…
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-spi…
The possibility to form excitons in photoilluminated correlated materials is central from fundamental and application oriented perspectives. In this paper we show how the interplay of electron-electron interactions and a magnetic superstructure leads to the formation of a peculiar spinful dark exciton, which can be detected in ARPES-type experiments and optical measurements. We study this by using matrix product states (MPS) to compute the time evolution of single-particle spectral functions and of the optical conductivity following an electron-hole excitation in a class of one-dimensional cor…
Using the mean-field approximation, we study the $k$-space spin textures and local spin currents emerged in the spin-triplet excitonic insulator states of the two-band Hubbard model defined on the square and triangular lattices. We assume a noninteracting band structure with a direct band gap and introduce $s$-, $p$-, $d$-, and $f$-type cross-hopping integrals, i.e., the hopping of electrons between different orbitals on adjacent sites with four different symmetries. First, we calculate the ground-state phase diagrams in the parameter space of the band filling and interaction strengths, whereb…
To understand the essence of the exciton Mott transition in three-dimensional electron-hole systems, the metal-insulator transition is studied for a two-band Hubbard model in infinite dimensions with interactions of electron-electron (hole-hole) repulsion U and electron-hole attraction -U'. By using the dynamical mean-field theory, the phase diagram in the U-U' plane is obtained (which is exact in infinite dimensions) assuming that electron-hole pairs do not condense. When both electron and hole bands are half-filled, two types of insulating states appear: the Mott-Hubbard insulator for U > U'…
We determine the zero temeperature phase diagram of excitons in the symmetric transition-metal dichalcogenide tri-layer heterosctructure WSe2/MoSe2/WSe2. First principle calculations reveal two distinct types of interlayer excitonic states, a lower energy symmetric quadrupole and a higher energy asymmetric dipole. While interaction between quadrupolar excitons is always repulsive, anti-parallel dipolar excitons attract at large distances. We find quantum phase transitions between a repulsive quadrupole lattice phase and a staggered (anti-parallel) dipolar lattice phase, driven by the competiti…
For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the Density-Matrix Renormalization Group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the band width. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approac…
We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in picosecond range, can be explained even quantitatively with the multi-magnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the s-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor which can be traced back to strong correlations and conseq…
We study the real-time dynamics of a pair hole/doubly-occupied-site, namely a holon and a doublon, in a 1D Hubbard insulator with on-site and nearest-neighbor Coulomb repulsion. Our analysis shows that the pair is long-lived and the expected decay mechanism to underlying spin excitations is actually inefficient. For a nonzero inter-site Coulomb repulsion, we observe that part of the wave-function remains in a bound state. Our study also provides insight on the holon-doublon propagation in real space. Due to the one-dimensional nature of the problem, these particles move in opposite directions …
Spectroscopic ellipsometry was used to study the dielectric function of LiCuVO$_{4}$, a compound comprised of chains of edge-sharing CuO$_4$ plaquettes, in the spectral range (0.75 - 6.5) eV at temperatures (7-300) K. For photon polarization along the chains, the data reveal a weak but well-resolved two-peak structure centered at 2.15 and 2.95 eV whose spectral weight is strongly enhanced upon cooling near the magnetic ordering temperature. We identify these features as an exciton doublet in the Mott-Hubbard gap that emerges as a consequence of the Coulomb interaction between electrons on near…
We investigated temperature dependent optical spectra of the one-dimensional chain compound Sr$_{2}$CuO$_{3}$. The charge transfer transition polarized along the chain direction shows a strongly asymmetric line shape as expected in one-dimensional extended Hubbard model. At low temperature the charge transfer peak shows a large blue shift and reveals additional sharp peaks at the gap. Even though many spectroscopic studies suggest that this material can not have a bound exciton based on the one-dimensional extended Hubbard model, we attribute the additional sharp peaks to excitons, which come …
Harvard University（哈佛大学）；Institute of Science and Technology Austria（奥地利科学技术研究院）；University of Pennsylvania（宾夕法尼亚大学）；RWTH Aachen University（亚琛工业大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）
We predict that a new superfluid phase, the incompressible excitonic superfluid (IESF), in the phase diagram of ultracold Bose atoms in $d>1$ dimensional optical lattices, which is caused by the spontaneous breaking of the symmetry of translation of the lattice. Within mean field theory, the critical temperature of the phase transition from this IESF to the normal fluid (NF) is calculated and the triple-critical point of the three phases is determined. We also investigate both configuration and gauge field fluctuations and show the IESF state is stable against these fluctuations. We expect thi…
We present a dynamical mean-field study of two-particle dynamical response functions in two-band Hubbard model across several phase transitions. We observe that the transition between theexcitonic condensate and spin-state ordered state is continuous with a narrow strip of supersolidphase separating the two. Approaching transition from the excitonic condensate is announced bysoftening of the excitonic mode at theMpoint of the Brillouin zone. Inside the spin-state orderedphase there is a magnetically ordered state with 2x2 periodicity, which has no precursor in thenormal phase.
