Collapse of integer Hall gaps in a double-quantum-well system

Chern-Simons Modified RPA-Eliashberg Theory of the ν=1/2+1/2 Quantum Hall Bilayer

The ν=1/2+1/2 quantum Hall bilayer has been previsously modeled using Chern-Simons-RPA-Eliashberg (CSRPAE) theory to describe pairing between the two layers. However, these approaches are troubled by a number of divergences and ambiguities. By using a "modified" RPA approximation to account for mass renormalization, we can work in a limit where the cyclotron frequency is taken to infinity, effectively projecting to a single Landau level. This, surprisingly, controls the important divergences and removes ambiguities found in prior attempts at CSRPAE. Examining BCS pairing of composite fermions we find that the angular momentum channel l=+1 dominates for all distances d between layers and at all frequency scales. Examining BCS pairing of composite fermion electrons in one layer with composite fermion holes in the opposite layer, we find the l=0 pairing channel dominates for all d and all frequencies. The strength of the pairing in these two different descriptions of the same phase of matter is found to be almost identical. This agrees well with our understanding that these are two different but dual descriptions of the same phase of matter.

s-Wave Paired Electron and Hole Composite Fermion Trial State for Quantum Hall Bilayers with ν=1

We introduce a new variational wave function for a quantum Hall bilayer at total filling ν_{T}=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The s-wave trial wave function naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover.

Electrically tunable Feshbach resonances in twisted bilayer semiconductors

[Figure: see text].

Numerical Study of Quantum Hall Bilayers at Total Filling ν_{T}=1: A New Phase at Intermediate Layer Distances

We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.

Fractional Solitons in Excitonic Josephson Junctions

The Josephson effect is especially appealing to physicists because it reveals macroscopically the quantum order and phase. In excitonic bilayers the effect is even subtler due to the counterflow of supercurrent as well as the tunneling between layers (interlayer tunneling). Here we study, in a quantum Hall bilayer, the excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. The system is mapped into a pseudospin ferromagnet then described numerically by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, we identify a family of fractional sine-Gordon solitons which resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Each fractional soliton carries a topological charge Q that is not necessarily a half/full integer but can vary continuously. The calculated current-phase relation (CPR) shows that solitons with Q = ϕ0/2π is the lowest energy state starting from zero ϕ0 - until ϕ0 > π - then the alternative group of solitons with Q = ϕ0/2π - 1 takes place and switches the polarity of CPR.

Magnetic field driven interminiband charge transfer in InGaAs/InP superlattices

The characteristic energies, occupancies and polarizations of the minibands formed by the Γ-Γ and Γ-Xz interlayer electon tunnelings in the InGaAs/InP superlattices are studied in the regime of the integer quantum Hall effect by polarization resolved photoluminescence. Accordingly, the magnetic field induced shrinkage of the interminiband gap, predicted by the theory, and as a consequence, the redistribution of charge over the superlattice minibands and the depolarization of the quantum Hall electron states are observed at odd filling factors. The response of the electrons residing in the InGaAs/InP superlattice minibands to the magnetic field is found very similar to the corresponding response of the electrons confined in the symmetric and anti-symmetric two-dimensional minibands of GaAs/AlGaAs double quantum wells. The presented results are evidence of the formation of the correlated states in multi-component electron systems formed in semiconductor multiple layers at odd filling factors.

Wave turbulence in quantum fluids

Wave turbulence (WT) occurs in systems of strongly interacting nonlinear waves and can lead to energy flows across length and frequency scales much like those that are well known in vortex turbulence. Typically, the energy passes although a nondissipative inertial range until it reaches a small enough scale that viscosity becomes important and terminates the cascade by dissipating the energy as heat. Wave turbulence in quantum fluids is of particular interest, partly because revealing experiments can be performed on a laboratory scale, and partly because WT among the Kelvin waves on quantized vortices is believed to play a crucial role in the final stages of the decay of (vortex) quantum turbulence. In this short review, we provide a perspective on recent work on WT in quantum fluids, setting it in context and discussing the outlook for the next few years. We outline the theory, review briefly the experiments carried out to date using liquid H2 and liquid (4)He, and discuss some nonequilibrium excitonic superfluids in which WT has been predicted but not yet observed experimentally. By way of conclusion, we consider the medium- and longer-term outlook for the field.

Quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene

ABC-stacked trilayer graphene's chiral band structure results in three (n=0, 1, 2) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction-driven states of the 12-fold degenerate (including spin and valley) N=0 Landau level. In particular, at many filling factors ν(T) = ±5, ±4, ±2, ±1 a quantum phase transition from a quantum Hall liquid state to a triangular charge-density wave occurs as a function of the single particle-induced Landau level orbital splitting Δ(LL). Experimental signatures of this phase transition are also discussed.

Circularly polarized photoluminescence as a probe of density of states in GaAs/AlGaAs quantum Hall bilayers

Polarized magnetophotoluminescence is employed to study the energies and occupancies of four lowest Landau levels in a couple quantum Hall GaAs/AlGaAs double quantum well. As a result, a magnetic field-induced redistribution of charge over the Landau levels manifesting to the continuous formation of the charge density wave and direct evidence for the symmetric-antisymmetric gap shrinkage at ν=3 are found. The observed interlayer charge exchange causes depolarization of the ferromagnetic ground state.

Nanotransformation and current fluctuations in exciton condensate junctions

We analyze the nonlinear transport properties of a bilayer exciton condensate that is contacted by four metallic leads by calculating the full counting statistics of electron transport for arbitrary system parameters. Despite its formal similarity to a superconductor the transport properties of the exciton condensate turn out to be completely different. We recover the generic features of exciton condensates such as counterpropagating currents driven by excitonic Andreev reflections and make predictions for nonlinear transconductance between the layers as well as for the current (cross)correlations and generalized Johnson-Nyquist relationships. Finally, we explore the possibility of connecting another mesoscopic system (in our case a quantum point contact) to the bottom layer of the exciton condensate and show how the excitonic Andreev reflections can be used for transforming voltage at the nanoscale.

Quantum Hall effects in graphene-based two-dimensional electron systems

In this article we review the quantum Hall physics of graphene-based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J D 1 and 2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including the role of disorder in current experiments. Special attention is given to the interesting low magnetic field limit, and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.

Tuning the effects of Landau level mixing on anisotropic transport in quantum Hall systems

Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resistance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction-induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We consider numerically a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau level mixing plays an important role.

Quantum Hall superfluids in topological insulator thin films

Three-dimensional topological insulators have protected Dirac-cone surface states. In this Letter we argue that gapped excitonic superfluids with spontaneous coherence between top and bottom surfaces can occur in the topological insulator (TI)-thin-film quantum Hall regime. We find that the large dielectric constants of TI materials increase the layer separation range over which coherence survives and decrease the superfluid sound velocity, but have little influence on the superfluid density or on the charge gap. The coherent state at total Landau-level filling factor νT=0 is predicted to be free of edge modes, qualitatively altering its transport phenomenology compared to the widely studied case of νT=1 in GaAs double-quantum wells.

Anomalous exciton condensation in graphene bilayers

In ordinary semiconductor bilayers, exciton condensates appear at total Landau-level filling factor nu{T}=1. We predict that similar states will occur in Bernal stacked graphene bilayers at many nonzero integer filling factors. For nu{T}=-3, 1 we find that the superfluid density of the exciton condensate vanishes and that a finite-temperature fluctuation-induced first order isotropic-smectic phase transition occurs when the layer densities are not balanced. These anomalous properties of bilayer graphene exciton condensates are due to the degeneracy of Landau levels with n=0 and n=1 orbital character.

Intrinsic gap and exciton condensation in the nu{T}=1 bilayer system

We investigate the quasiparticle excitation of the bilayer quantum Hall (QH) system at a total filling factor nu{T}=1 in the limit of negligible interlayer tunneling under a tilted magnetic field. We show that the intrinsic quasiparticle excitation is of purely pseudospin origin and solely governed by the inter- and intralayer 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 provide a new insight into the nature of the phase transition between the two states.

Phase diagram of a quantum Hall pseudospin ferromagnet in a two-subband electron system

We employ the self-consistent local density approximation and the microscopic Hartree-Fock theory to investigate the quantum Hall pseudospin ferromagnets at the Landau levels degenerate regime of a single quantum well with two-subbands filled. We carry out a detailed calculation of the pseudospin anisotropy energy using real experimental parameters and obtain the phase diagrams that would be accessed experimentally by changing the electron density and the bias voltage. We find that an easy-plane and easy-axis quantum Hall pseudospin ferromagnet can form at total filling factors ν = 3 and ν = 4, respectively, which are consistent with experimental observation. Our study provides some insight into the symmetry of the ground state and may help in understanding the underlying mechanism.

First-order quantum phase transition of excitons in quantum Hall bilayers

We show that the quantum phase transformation between compressible metallic and incompressible excitonic states in the coupled bilayers at total Landau level filling factor nuT=1 becomes discontinuous (first order) by impacts of different terms of the electron-electron interactions that prevail on weak residual disorder. The evidence is based on precise determinations of the excitonic order parameter by inelastic light scattering measurements close to the phase boundary. While there is marked softening of low-lying excitations, our experiments underpin the roles of competing order parameters linked to quasiparticle correlations in removing the divergence of quantum fluctuations.

Intra-Landau-level cyclotron resonance in bilayer graphene

Interaction driven integer quantum-Hall effects are anticipated in graphene bilayers because of the near degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate k3/2 dispersion. We speculate on the possibility of unusual localization physics associated with these modes.

Electronic transport properties of the Ising quantum Hall ferromagnet in a Si quantum well

Magnetotransport properties are investigated for a high mobility Si two-dimensional electron system in the vicinity of a Landau level crossing point. At low temperatures, the resistance peak having a strong anisotropy shows large hysteresis which is attributed to Ising quantum Hall ferromagnetism. The peak is split into two peaks in the paramagnetic regime. A mean field calculation for the peak positions indicates that electron scattering is strong when the pseudospin is partially polarized. We also study the current-voltage characteristics which exhibit a wide voltage plateau.

Spin-dependent phase diagram of the nuT=1 bilayer electron system

We show that the spin degree of freedom plays a decisive role in the phase diagram of the nu(T)=1 bilayer electron system using an in-plane field B( parallel) in the regime of negligible tunneling. We observe that the phase boundary separating the quantum Hall and compressible states at d/l(B) = 1.90 for B(parallel) = 0 (d: interlayer distance, l(B): magnetic length) steadily shifts with B(parallel) before saturating at d/l(B) = 2.33 when the compressible state becomes fully polarized. Using a simple model for the energies of the competing phases, we can quantitatively describe our results. A new phase diagram as a function of d/l(B) and the Zeeman energy is established and its implications as to the nature of the phase transition are discussed.

Theory of the pseudospin resonance in semiconductor bilayers

The pseudospin degree of freedom in a semiconductor bilayer gives rise to a collective mode analogous to the ferromagnetic-resonance mode of a ferromagnet. We present a many-body theory of the dependence of the energy and the damping of this mode on layer separation d. Based on these results, we discuss the possibilities of realizing transport-current driven pseudospin-transfer oscillators in semiconductors, and of using the pseudospin-transfer effect as an experimental probe of intersubband plasmons.

Bosonization approach for bilayer quantum Hall systems at nu(T)=1

We develop a nonperturbative bosonization approach for bilayer quantum Hall systems at nu(T)=1, which allows us to systematically study the existence of an exciton condensate in these systems. An effective boson model is derived and the excitation spectrum is calculated in both the Bogoliubov and the Popov approximations. In the latter case, we show that the ground state of the system is an exciton condensate only when the distance between the layers is very small compared to the magnetic length, indicating that the system possibly undergoes another phase transition before the incompressible-compressible one. The effect of a finite electron interlayer tunneling is included and a quantitative phase diagram is proposed.

Observation of collapse of pseudospin order in bilayer quantum Hall ferromagnets

The Hartree-Fock paradigm of bilayer quantum Hall states with finite tunneling at filling factor nu=1 has full pseudospin ferromagnetic order with all the electrons in the lowest symmetric Landau level. Inelastic light scattering measurements of low energy spin excitations reveal major departures from the paradigm at relatively large tunneling gaps. The results indicate the emergence of a novel correlated quantum Hall state at nu=1 characterized by reduced pseudospin order. Marked anomalies occur in spin excitations when pseudospin polarization collapses by application of in-plane magnetic fields.

Spin degree of freedom in the nu=1 bilayer electron system investigated by nuclear spin relaxation

The nuclear-spin-relaxation rate 1/T(1) has been measured in a bilayer electron system at and around total Landau level filling factor nu=1. The measured 1/T(1), which probes electron spin fluctuations, is found to increase gradually from the quantum Hall (QH) state at low fields through a phase transition to the compressible state at high fields. Furthermore, 1/T(1) in the QH state shows a noticeable increase away from nu=1. These results demonstrate that, as opposed to common assumption, the electron spin degree of freedom is not completely frozen either in the QH or the compressible states.

Noise spectroscopy and interlayer phase coherence in bilayer quantum Hall systems

Bilayer quantum Hall systems develop strong interlayer phase coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current noise is that of the zero wave vector collective mode, which is sensitive to the degree of order in the system. Local electric potential noise measured in a plane above the bilayer system, on the other hand, is sensitive to finite-wave-vector collective modes and, hence, to the soft-magnetoroton picture of the order-disorder phase transition.

Observation of soft magnetorotons in bilayer quantum Hall ferromagnets

Inelastic light-scattering measurements of low-lying collective excitations of electron double layers in the quantum Hall state at total filling nu(T)=1 reveal a deep magnetoroton in the dispersion of charge-density excitations across the tunneling gap. The roton softens and sharpens markedly when the phase boundary for transitions to highly correlated compressible states is approached. The findings are interpreted with Hartree-Fock evaluations that link soft magnetorotons to enhanced excitonic Coulomb interactions and to quantum phase transitions in the ferromagnetic bilayers.

Phase diagram of interacting composite fermions in the bilayer nu=2/3 quantum hall effect

We study the phase diagram of composite fermions (CFs) in the presence of spin and pseudospin degrees of freedom in the bilayer nu=2/3 quantum Hall (QH) state. Activation studies elucidate the existence of three different QH states with two different types of hysteresis in the magnetotransport. While a noninteracting CF model provides a qualitative account of the phase diagram, the observed renormalization of tunneling gap and a non-QH state at high densities are not explained in the noninteracting CF model, and are suggested to be manifestations of interactions between CFs.

Pseudospin canting transition and stripes in bilayer quantum Hall ferromagnets: a self-charging capacitor

We predict that in nu(T) = 1 bilayer quantum Hall (QH) pseudoferromagnets, an in-plane magnetic field can induce a reentrant pseudospin "canting" transition between interlayer charge balanced (planar) to imbalanced (canted) QH states. At T = 0 ( T>0) this quantum (classical) transition is in a new, anisotropic, compressible (2+1)D (2D) Ising universality class. The striking experimental signatures are the universal nonlinear charge-voltage and in-plane field relations, and the divergence of the differential bilayer capacitance at the transition, resulting in a bilayer capacitor that spontaneously charges itself, even in the absence of an applied interlayer voltage.

Is there a dc Josephson effect in bilayer quantum Hall systems?

We argue on the basis of phenomenological and microscopic considerations that there is no dc Josephson effect in ordered bilayer quantum Hall systems, even at T = 0. Instead the tunnel conductance is strongly enhanced, approaching a finite value proportional to the square of the order parameter as the interlayer tunneling amplitude vanishes.

Dipolar excitons, spontaneous phase coherence, and superfluid-insulator transition in bilayer quantum Hall systems at nu = 1

The spontaneous interlayer phase coherent (111) state of a bilayer quantum Hall system at filling factor nu = 1 may be viewed as a condensate of interlayer particle-hole pairs or excitons. We show that when the layers are biased in such a way that these excitons are very dilute, they may be viewed as pointlike bosons. We calculate the exciton dispersion relation and show that the exciton-exciton interaction is dominated by the dipole moment they carry. In addition to the phase coherent state, we also find a Wigner crystal/glass phase in the presence/absence of disorder which is an insulating state for the excitons. The position of the phase boundary is estimated and the transition between these two phases is discussed.

Theory of interlayer tunneling in bilayer quantum Hall ferromagnets

Spielman et al. [Phys. Rev. Lett. 84, 5808 (2000] recently observed a large and sharp Josephson-like zero-bias peak in the tunnel conductance of a bilayer system in a quantum Hall ferromagnet state. We argue that disorder-induced topological defects in the pseudospin order parameter limit the peak size and destroy the predicted Josephson effect. We predict that the peak would be split and shifted by an in-plane magnetic field in a way that maps the dispersion relation of the ferromagnet's Goldstone mode. We also predict resonant structures in the dc I-V characteristic under bias by an ac electric field.

Strong correlation to weak correlation phase transition in bilayer quantum Hall systems

At small layer separations, the ground state of a nu = 1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence. The evolution of this state with increasing layer separation d has been a matter of controversy. We report on small system exact diagonalization calculations which suggest that a single-phase transition, likely of first order, separates incompressible states with strong interlayer correlations from compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.

Half-polarized quantum hall states

We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall nu = 2 / 3 and nu = 2 / 5 states versus spin polarization has a downward cusp at half the maximal spin polarization. We map the two-component fermion system onto a system of excitons and describe the ground state as a liquid state of excitons with nonzero values of exciton angular momentum.

Resonantly enhanced tunneling in a double layer quantum hall ferromagnet

The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling nuT=1 the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed.

Canted antiferromagnetic phase in a double quantum well in a tilted quantizing magnetic field

We investigate the double-layer electron system in a parabolic quantum well at filling factor nu=2 in a tilted magnetic field using capacitance spectroscopy. The competition between two ground states is found at the Zeeman splitting appreciably smaller than the symmetric-antisymmetric splitting. Although at the transition point the system breaks up into domains of the two competing states, the activation energy turns out to be finite, signaling the occurrence of a new insulator-insulator quantum phase transition. We interpret the obtained results in terms of a predicted canted antiferromagnetic phase.

Evidence of soft-mode quantum phase transitions in electron double layers

Inelastic light scattering by low-energy spin-excitations reveals three distinct configurations of spin of electron double layers in gallium arsenide quantum wells at even-integer quantum Hall states. The transformations among these spin states appear as quantum phase transitions driven by the interplay between Coulomb interactions and Zeeman splittings. One of the transformations correlates with the emergence of a spin-flip intersubband excitation at vanishingly low energy and provides direct evidence of a link between quantum phase transitions and soft collective excitations in a two-dimensional electron system.