The quantum Hall physics of bilayer graphene is extremely rich due to the interplay between a layer degree of freedom and delicate fractional states. Recent experiments show that when an electric field perpendicular to the bilayer causes Landau levels of opposing layers to cross in energy, a even-denominator Hall plateau can coexist with a finite density of inter-layer excitons. We present theoretical and numerical evidence that this observation is due to a new phase of matter -- a Fermi sea of topological excitons.
Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling $ν_T=1$. These correlations are manifested by a non-linear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly-coupled bilayers. The pseudogap suppression is strongest at $ν_T=1$ and grows rapidly as the critical layer separation for exciton condensation is approached from above.
This tutorial paper reviews some of the physics of quantum Hall bilayers with a focus on the case where there is low or zero tunnelling between the two layers. We describe the interlayer coherent states at filling factors nu=1 and nu=2 as exciton condensates and discuss some of the theory associated with these states.
We demonstrate that counterflowing electrical currents can move through the bulk of the excitonic quantized Hall phase found in bilayer two-dimensional electron systems (2DES) even as charged excitations cannot. These counterflowing currents are transported by neutral excitons which are emitted and absorbed at the inner and outer boundaries of an annular 2DES sample via an Andreev reflection process.
Bilayer electron-hole systems, where carriers in one layer are electrons and carriers in the other are holes, have been actively investigated in recent years with the focus on Bose-Einstein condensation of excitons. This condensation is expected to occur when the layer separation d is much smaller than the interparticle distance r_sa_B within each layer. In this Brief Report, we argue for the existence of a state, Wigner supersolid, in which excitons are phase-coherent but form a Wigner crystal due to dipolar repulsion. We present the qualitative phase diagram of a bilayer system, and discuss …
We have considered the AB-stacked bilayer graphene Josephson junction. The bilayers are supposed to be in the charge equilibrium states and at the half-filling in each of the electronic layers of the construction and at each value of the external gate. By considering the interacting bilayers in both sides of the junction and by taking into account both intralayer and interlayer Coulomb interaction effects, we have calculated the normal and excitonic tunnel currents through the junction. The electronic band renormalizations have been taken into account, due to the excitonic pairing effects and …
Double-layer electron systems in the quantum Hall regime have excitonic condensate ground states when the layers are close together and the total Landau level filling factor is close to an odd integer. In this paper we discuss the microscopic physics of these states and recent progress toward building a theory of the anomalous collective transport effects that occur in separately contacted bilayers when the condensate is present.
We study the electronic properties of AA-stacked bilayer graphene in a transverse electric field. The strong on-site Coulomb repulsion stabilizes the antiferromagnetic order in such a system. The antiferromagnetic order is suppressed by the transverse bias voltage, at least partially. The inter-plane Coulomb repulsion and non-zero voltage stabilize an exciton order parameter. The exciton order parameter coexists with the antiferromagnetism and can be as large as several tens of meV for realistic values of the bias voltage and interaction constants. The application of a transverse bias voltage …
In this paper, we consider the spectral properties of the bilayer graphene with the local excitonic pairing interaction between the electrons and holes. We consider the generalized Hubbard model, which includes both intralayer and interlayer Coulomb interaction parameters. The solution of the excitonic gap parameter is used to calculate the electronic band structure, single-particle spectral functions, the hybridization gap, and the excitonic coherence length in the bilayer graphene. We show that the local interlayer Coulomb interaction is responsible for the semimetal-semiconductor transition…
We show that the "dark condensates" that arise when excitons form a Bose-Einstein condensate in a material with an indirect bandgap are not completely dark to optical emission. Rather, such states are "leaky condensates" in which optical emission is facilitated by many-body interactions. We analyze the properties of these leaky condensates in the context of twisted bilayers of transition metal dichalcogenides, which host strongly interacting excitons and an indirect bandgap. We show that this interaction-driven "leaky" emission dominates photoluminescence at low temperatures, with distinctive …
We investigate the quasiparticle excitation of the bilayer quantum Hall (QH) system at total filling factor $ν_{\mathrm{T}} = 1$ in the limit of negligible interlayer tunneling under tilted magnetic field. We show that the intrinsic quasiparticle excitation is of purely pseudospin origin and solely governed by the inter- and intra-layer electron interactions. A model based on exciton formation successfully explains the quantitative behavior of the quasiparticle excitation gap, demonstrating the existence of a link between the excitonic QH state and the composite fermion liquid. Our results pro…
Magneto-transport and drag measurements on a quasi-Corbino 2D electron bilayer at the systems total filling factor 1 (v_tot=1) reveal a drag voltage that is equal in magnitude to the drive voltage as soon as the two layers begin to form the expected v_tot=1 exciton condensate. The identity of both voltages remains present even at elevated temperatures of 0.25 K. The conductance in the current carrying layer vanishes only in the limit of strong coupling between the two layers and at T->0 K which suggests the presence of an excitonic circular current.
Bilayer electron-hole systems undergo excitonic condensation when the distance d between the layers is smaller than the typical distance between particles within a layer. All excitons in this condensate have a fixed dipole moment which points perpendicular to the layers, and therefore this condensate of dipoles couples to external electromagnetic fields. We study the transport properties of this dipolar condensate system based on a phenomenological model which takes into account contributions from the condensate and quasiparticles. We discuss, in particular, the drag and counterflow transport,…
The competing ground states of bilayer graphene are studied by applying renormalization group techniques to a bilayer honeycomb lattice with nearest neighbor hopping. In the absence of interactions, the Fermi surface of this model at half-filling consists of two nodal points with momenta $\mathbf{K}$, $\mathbf{K}'$, where the conduction band and valence band touch each other, yielding a semi-metal. Since near these two points the energy dispersion is quadratic with perfect particle-hole symmetry, excitonic instabilities are inevitable if inter-band interactions are present. Using a perturbativ…
Using Diffusion Monte Carlo simulations we have investigated the ground state of a symmetric electron-hole bilayer and determined its phase diagram at T=0. We find clear evidence of an excitonic condensate, whose stability however is affected by in-layer electronic correlation. This stabilizes the electron-hole plasma at large values of the density or inter-layer distance, and the Wigner crystal at low density and large distance. We have also estimated pair correlation functions and low order density matrices, to give a microscopic characterization of correlations, as well as to try and estima…
We have investigated the tunneling properties of an electron double quantum well system where the lowest Landau level of each quantum well is half filled. This system is expected to be a Bose condensate of excitons. Our four-terminal dc measurements reveal a nearly vanishing interlayer voltage and the existence of critical tunneling currents which depend on the strength of the condensate state.
We study the texture of the exciton condensate at low temperatures in an independently gated electron-hole bilayer system. A model Hamiltonian is solved in real space within a mean-field approximation. It is found that, with increased electron-hole density polarization, the system experiences phase transformations from the zero center-of-mass momentum superfluid state, through one- and two-dimensional exciton pair modulated states, into the normal state. At weak density polarization, the modulating state resembles the Larkin-Ovchinikov state in superconductors in the presence of an exchange fi…
The physics of vortices, instantons and deconfinement is studied for layered superfluids in connection to bilayer quantum Hall systems at filling fraction nu=1. We develop an effective gauge theory taking into account both vortices and instantons induced by interlayer tunneling. The renormalization group flow of the gauge charge and the instanton fugacity shows that the coupling of the gauge field to vortex matter produces a continuous transition between the confining phase of free instantons and condensed vortices and a deconfined gapless superfluid where magnetic charges are bound into dipol…
In the present work, we consider the excitonic effects in the twisted bilayer graphene (tBLG) within the rotated bilayer Hubbard model. Both, intralayer and interlayer Coulomb interactions have been considered and the half-filling condition is imposed for the electronic densities is both layers of the bilayer. We calculate the excitonic pairing gap parameter and the chemical potential for different twist angles and different values of the interlayer Coulomb interaction parameter. Furthermore, we show the appearance of the electronic flat bands in the electronic band structure, mediated by the …
We will discuss the relevant conditions to observe a critical tunneling current [New J. Phys. 10, 045018 (2008)] in electron double-layer systems at a total filling factor of 1 and find they are related to the effective layer separation and the temperature. Our studies suggest that the intensity of the critical tunneling behavior is also directly linked to the area of the sample.
We study the bilayer quantum Hall system at total filling factor ν_T = 1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation firstly assuming that only one momentum Q0 is macroscopically occupied and later we consider t…
We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently-reported broken-symmetry spontane…
Graphene, a single sheet of graphite with honeycomb lattice structure, has massless carriers with tunable density and polarity. We investigate the ground state phase diagram of two graphene sheets (embedded in a dielectric) separated by distance $d$ where the top layer has electrons and the bottom layer has holes, using mean-field theory. We find that a uniform excitonic condensate occurs over a large range of carrier densities and is weakly dependent on the relative orientation of the two sheets. We obtain the excitonic gap, quasiparticle energy and the density of states. We show that both, t…
We report quantum Monte Carlo calculations of biexciton binding energies in ideal two-dimensional bilayer systems with isotropic electron and hole masses. We have also calculated exciton-exciton interaction potentials, and pair distribution functions for electrons and holes in bound biexcitons. Comparing our data with results obtained in a recent study using a model exciton-exciton potential [C. Schindler and R. Zimmermann, Phys. Rev. B \textbf{78}, 045313 (2008)], we find a somewhat larger range of layer separations at which biexcitons are stable. We find that individual excitons retain their…
We construct a quantum Ginsburg-Landau theory to study the quantum phase transition from the excitonic superfluid (ESF) to a possible pseudo-spin density wave (PSDW) at some intermediate distances driven by the magneto-roton minimum collapsing at a finite wavevector. We analyze the properties of the PSDW and explicitly show that a square lattice is the favorite lattice. We suggest that correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature dependent drag consistent with the experimental data. Comparisons with previous microscopic …
We studied a vertical ``quantum dot molecule'', where one of the dots is occupied with electrons and the other with holes. We find that different phases occur in the ground state, depending on the carrier density and the interdot distance. When the system is dominated by shell structure, orbital degeneracies can be removed either by Hund's rule, or by Jahn-Teller deformation. Both mechanisms can lead to a maximum of the addition energy at mid-shell. At low densities and large interdot distances, bound electron-hole pairs are formed.
Using the self-consistent Born approximation we study the delocalization of interlayer excitons in the bilayer Heisenberg quantum antiferromagnet. Under realistic conditions we find that the coupling between the exciton motion and the spin system is strongly enhanced as compared to the case of a single carrier, to a degree that it mimics the confinement physics of carriers in Ising spin systems. We predict that the "ladder spectrum" associated with this confinement physics should be visible in the c-axis exciton spectra of insulating bilayer cuprates such as YBa2Cu3O6. Our discovery indicates …
We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit that the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling α=J_{\perp}/Jz. In the disordered phase at large α, a coherent quasiparticle peak appears representing free motion of the exciton in a spin singlet background. In the Néel phase, which applies to more r…
A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.
We consider suspened bilayer graphene under applied perpendicular electric bias field that is known to generate a single particle gap $2Δ$ and a related electric polarization ${\cal P}$. We argue that the bias also drives a quantum phase transition from band insulator to superfluid exciton condensate. The transition occurs when the exciton binding energy exceeds the band gap $2Δ$. We predict the critical bias (converted to band gap), $Δ_c\approx 60$ meV, below which the excitons condense. The critical temperature, $T_c(Δ)$, is maximum at $Δ\approx 25$ meV, $T_c^\text{max}\approx 115$ K, decrea…
We report on small-cluster exact-diagonalization calculations which prove the formation of electron-hole pairs (excitons) as prerequisite for spontaneous interlayer phase coherence in bilayer systems described by the extended Falicov-Kimball model. Evaluating the anomalous Green's function and momentum distribution function of the pairs, and thereby analyzing the dependence of the exciton binding energy, condensation amplitude, and coherence length on the Coulomb interaction strength, we demonstrate a crossover between a BCS-like electron-hole pairing transition and a Bose-Einstein condensatio…
Exciton instability in graphene bilayer systems is studied in the case of a short-ranged Coulomb interaction and a finite voltage difference between the layers. Self-consistent exciton gap equations are derived and solved numerically and analytically under controlled approximation. We obtain that a critical strength of the Coulomb interaction exists for the formation of excitons. The critical strength depends on the amount of voltage difference between the layers and on the inter-layer hopping parameter.
The effect of impurities which induce local interlayer tunneling in bilayer exciton condensates is discussed. We show that a localized single fermion bound state emerges inside the gap for any strength of impurity scattering and calculate the dependence of the impurity state energy and wave function on the potential strength. We show that such an impurity induced single fermion state enhances the interlayer coherence around it, and is similar to the superconducting proximity effect. As a direct consequence of these single impurity states, we predict that a finite concentration of such impuriti…
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…
We study Andreev reflection and Josephson currents in topological bilayer exciton condensates (TEC). These systems can create 100% spin entangled nonlocal currents with high amplitudes due to perfect nonlocal Andreev reflection. This Andreev reflection process can be gate tuned from a regime of purely retro reflection to purely specular reflection. We have studied the bound states in TEC-TI-TEC Josephson junctions and find a gapless dispersion for perpendicular incidence. The presence of a sharp transition in the supercurrent-phase relationship when the system is in equilibrium is a signature …
The ground state of a bilayer quantum Hall system at $ν_{\rm T}=1$ with model pseudopotential is investigated by the DMRG method. Firstly, pseudopotential parameters appropriate for the system with finite layer thickness are derived, and it is found that the finite thickness makes the excitonic phase more stable. Secondly, a model, where only a few pseudopotentials with small relative angular momentum have finite values, is studied, and it is clarified how the excitonic phase is destroyed as intra-layer pseudopotential becomes larger. The importance of the intra-layer repulsive interaction at …
Using a weak-coupling renormalization group formalism, we study competing ordered phases for repulsively interacting fermions on the bilayer honeycomb lattice away from half-filling, which is realized experimentally as doped bilayer graphene. As electrons are added to the system, excitonic order is suppressed, and unconventional superconductivity appears generically in its place. In general it is found that the maximum critical temperature for superconductivity appears directly adjacent to the dome of particle-hole order, illustrating the importance of fluctuations in these channels for the fo…
In the present paper, we consider the excitonic effects on the single particle normal density of states (DOS) in the bilayer graphene (BLG). The local interlayer Coulomb interaction is considered between the particles on the non-equivalent sublattice sites in different layers of the BLG. We show the presence of the excitonic shift of the neutrality point, even for the noninteracting layers. Furthermore, for the interacting layers, a very large asymmetry in the DOS structure is shown between the particle and hole channels. At the large values of the interlayer hopping amplitude, a large number …
University of Maryland, College Park（马里兰大学帕克分校）；Universität Heidelberg（海德堡大学）；Laboratory for Physical Sciences（物理科学实验室）；Brookhaven National Laboratory（布鲁海文国家实验室）；National Institute for Materials Science（物质材料研究机构）
Symmetric electron-hole bilayer systems have been studied at zero temperature using the diffusion quantum Monte Carlo method. A flexible trial wave function is used that can describe fluid, excitonic and biexcitonic phases. We calculate condensate fractions and pair correlation functions for a large number of densities rs and layer separations d. At small d we find a one-component fluid phase, an excitonic fluid phase, and a biexcitonic fluid phase, and the transitions among them appear to be continuous. At d = 0, excitons appear to survive down to about rs = 0.5 a.u., and biexcitons form at r…
We investigate the nature of the magnetic excitations of a bilayer single-orbital Hubbard model in the intermediate-coupling regime. This model exhibits a quantum phase transition (QPT) between a paramagnetic (PM) and an insulating antiferromagnetic (AFM) phase at a critical value of the coupling strength. By using the random phase approximation, we show that the QPT is continuous when the PM state is a band insulator and that the corresponding quantum critical point (QCP) arises from the condensation of preformed excitons. These low-energy excitons reemerge on the other side of the QCP as the…
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…
We study the coupled quantum Hall bilayers each at half-filled first excited Landau levels with varying the layer distance. Based on numerical exact diagonalization on torus, we identify two distinct phases separated by a critical layer distance $d_c$. From $d_c$ to infinite layer distance, the topological phase is smoothly connected to a direct tensor product of two Moore-Read states, while the interlayer coherence emerges at $d<d_c$ characterized by the $xy$ easy-plane ferromagnetic energy spectra, gapless pseudospin excitations and the finite exciton superfluid stiffness, corresponding to t…
We propose moiré bilayer as a platform where exotic quantum phases can be stabilized and electrically detected. Moiré bilayer consists of two separate moiré superlattice layers coupled through the inter-layer Coulomb repulsion. In the small distance limit, an SU(4) spin can be formed by combining layer pseudospin and the real spin. As a concrete example, we study an SU(4) spin model on triangular lattice in the fundamental representation. By tuning a three-site ring exchange term $K\sim \frac{t^3}{U^2}$, we find SU(4) symmetric crystallized phase and an SU(4)$_1$ chiral spin liquid (CSL) at th…
We construct a quantum Ginsburg-Landau theory to study the quantum phases and transitions in electron hole bilayer system. We propose that in the dilute limit as distance is increased, there is a first order transition from the excitonic superfluid (ESF) to the excitonic supersolid (ESS) driven by the collapsing of a roton minimum, then a 2nd order transition from the ESS to excitonic normal solid. We show the latter transition is in the same universality class of superfluid to Mott transition in a rigid lattice. We then study novel elementary low energy excitations inside the ESS. We find tha…
We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems an exciton is the bound state of a double occupied and empty site. In the strong coupling limit the exciton acts as a hard-core boson. Its physics are captured by the exciton t-J model, containing an effective XXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean field theory we constructed the ground state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal and the exciton …
