We study correlated phases occurring in the flat lowest band of the dice lattice model at flux density one half. We discuss how to realize the dice lattice model, also referred to as the T_3 lattice, in cold atomic gases. We construct the projection of the model to the lowest dice band, which yields a Hubbard-Hamiltonian with interaction-assisted hopping processes. We solve this model for bosons in two limits. In the limit of large density, we use Gross-Pitaevskii mean-field theory to reveal time-reversal symmetry breaking vortex lattice phases. At low density, we use exact diagonalization to identify three stable phases at fractional filling factors νof the lowest band, including a classical crystal at ν=1/3, a supersolid state at ν=1/2 and a Mott insulator at ν=1.
We study ribbons of the dice two-dimensional lattice (that we call ``dice ladders'') known to have nontrivial topological properties, such as Chern numbers 2 [Wang and Y. Ran, Phys. Rev. B {\bf 84}, 241103 (2011)]. Our main results are two folded: (1) Analyzing the tight-binding model in the presence of Rashba spin-orbit coupling and an external magnetic field, we observed that dice ladders qualitatively display properties similar to their two-dimensional counterpart all the way to the limit of only two legs in the short direction. This includes flat bands near the Fermi level, edge currents a…
A longstanding puzzle for the lowest Landau level crystal phase has been an order of magnitude discrepancy between the theoretically calculated energy of the defects and the measured activation gap. We perform an extensive study of various kinds of defects in the correlated composite fermion crystal and find that the lowest energy defect is a six-fold symmetric "hyper-correlated bubble interstitial," in which an interstitial particle forms a strongly correlated bound state with a particle of the crystal. The energy of the bubble defect is a factor of $\sim$3 smaller than that of the lowest ene…
Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically electron localization in the lowest Landau level in the presence of a power-law correlated disorder potential. Careful comparisons between classical and quantum dynamics suggest that the extended Harris criterion is applicable in the quantum case. This leads to a prediction of new localization quantum critical points in integer quantum Hall systems with power-law c…
Many-body calculations of the total energy of interacting Dirac electrons in finite graphene samples exhibit joint occurrence of cusps at angular momenta corresponding to fractional fillings characteristic of formation of incompressible (gapped) correlated states (nu=1/3 in particular) and opening of an insulating energy gap (that increases with the magnetic field) at the Dirac point, in correspondence with experiments. Single-particle basis functions obeying the zigzag boundary condition at the sample edge are employed in exact diagonalization of the interelectron Coulomb interaction, showing…
In two-dimensional hole systems confined to wide GaAs quantum wells, where the heavy- and light- hole states are close in energy, we observe a very unusual crossing of the lowest two Landau levels as the sample is tilted in magnetic field. At a magic tilt angle $θ\simeq 34^{\circ}$, which surprisingly is independent of the well-width or hole density, in a large filling factor range near $ν=1$ the lowest two levels are nearly degenerate as evinced by the presence of two-component quantum Hall states. Remarkably, a quantum Hall state is seen at $ν=1$, consistent with a \textit{correlated} $Ψ_{11…
We study the density of states and localization properties of the lowest Landau levels of graphene at high magnetic fields. We focus on the effects caused by correlated long-range hopping disorder, which, in exfoliated graphene, is induced by static ripples. We find that the broadening of the lowest Landau level shrinks exponentially with increasing disorder correlation length. At the same time, the broadening grows linearly with magnetic field and with disorder amplitudes. The lowest Landau level peak shows a robust splitting, whose origin we identify as the breaking of the sublattice (valley…
We introduce the notion of the strongly correlated band insulator (SCI), where the lowest energy excitations are collective modes (excitons) rather than the single particles. We construct controllable 1/N expansion for SCI to describe their observables properties. A remarkable example of the SCI is bilayer graphene which is shown to be tunable between the SCI and usual weak coupling regime.
We show that the solid phase between the 1/5 and 2/9 fractional quantum Hall states arises from an extremely delicate interplay between type-1 and type-2 composite fermion crystals, clearly demonstrating its nontrivial, strongly correlated character. We also compute the phase diagram of various crystals occurring over a wide range of filling factors, and demonstrate that the elastic constants exhibit non-monotonic behavior as a function of the filling factor, possibly leading to distinctive experimental signatures that can help mark the phase boundaries separating different kinds of crystals.
Coulomb drag resulting from interlayer electron-electron scattering in double layer 2D electron systems at high magnetic field has been measured. Within the lowest Landau level the observed drag resistance exceeds its zero magnetic value by factors of typically 1000. At half-filling of the lowest Landau level in each layer (nu = 1/2) the data suggest that our bilayer systems are much more strongly correlated than recent theoretical models based on perturbatively coupled composite fermion metals.
An unconventional insulating phase and a superconducting phase were recently discovered in the twisted bilayer graphene [Y. Cao et al, Nature {\bf 556}, 80; {\bf 556}, 43 (2018)], but the relevant low-energy electronic states have not been clearly identified yet. In this work, I show that the interlayer hopping induces a spatially modulated Dirac mass term in the continuum Hamiltonian, and leads to a low-energy band formed by Dirac zero modes in the moiré superlattice. This moiré band becomes extremely flat and thus strongly correlated as the Dirac velocity vanishes at the magic angle, and ent…
We study spectra for a 2D electron in the lowest Landau level with randomly distributed, repulsively correlated electric impurities. The lowest energy band reflects an effective magnetic field downshifted by an integer multiple of the impurity density. The downshift is precisely half that for the corresponding electron density in the composite-fermion picture of the fractional quantum Hall regime.
Semiconductor moiré heterostructures exhibit rich correlation-induced many-body phenomena with signatures of emergent magnetism, Mott insulating states or generalized Wigner crystals observed in optical spectroscopy by probing intralayer excitons. However, as the staggered band alignment in the underlying WSe$_2$/WS$_2$ heterobilayer system separates photoexcited electrons and holes to form lowest-energy interlayer excitons, direct access to interactions between correlated charge states and ground state moiré excitons remained elusive. Here, we use MoSe$_2$/WS$_2$ heterostacks with type-I band…
In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Green's function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results we…
This paper has its motivation in the study of the Fractional Quantum Hall Effect. We consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level. When repulsive interactions are strong enough in this model, highly correlated states emerge, built on Laughlin's famous wave function. We investigate a model for the response of such strongly correlated ground states to variations of an external potential. This leads to a family of variational problems of a new type. Our main results are rigorous energy esti…
We consider 2D Dirac fermions in the presence of three types of disorder: random scalar potential, random gauge potential and random mass with long-range correlations decaying as a power law. Using various methods such as the self-consistent Born approximation (SCBA), renormalization group (RG), the matrix Green function formalism and bosonisation we calculate the density of states and study the full counting statistics of fermionic transport at lower energy. The SCBA and RG show that the random correlated scalar potentials generate an algebraically small energy scale below which the density o…
We compute the phase diagram of twisted bilayer graphene near the magic angle where the occurrence of flat bands enhances the effects of electron-electron interactions and thus unleashes strongly-correlated phenomena. Most importantly, we find a crossover between d+id superconductivity and Mott insulating behavior near half-filling of the lowest electron band when the temperature is increased. This is consistent with recent experiments. Our results are obtained using unbiased many-body renormalization group techniques combined with a mean-field analysis of the effective couplings.
We investigate the fate of the quantum Hall extended states within a continuum model with spatially correlated disorder potentials. The model can be projected onto a couple of the lowest Landau bands. Levitation of the $n=0$ critical states is observed if at least the two lowest Landau bands are considered. The dependence on the magnetic length $l_B=(\hbar/(eB))^{1/2}$ and on the correlation length of the disorder potential $η$ is combined into a single dimensionless parameter $\hatη=η/l_B$. This enables us to study the behavior of the critical states for vanishing magnetic field. In the two L…
We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux $ϕ$, using an Anderson tight-binding model. In our model, the system of $N=2M$ atomic sites of the ring is assumed to be partitioned into $M$ pairs of identical nearest-neighbour sites (dimers). The site energies for different dimers are taken to be uncorrelated gaussian variables. For this system we obtain the exact flux-dependent energy levels to second order in the random site energies, using an earlier exact transfer matrix perturbation theory. T…
Study of the ground-state electronic spin-polarization can permit discovery and identification of novel correlated phases in the quantum Hall (QH) system. It can thus determine the potential usefulness of QH states for quantum computing. However, prior measurements involving optical and NMR techniques may perturb the system away from delicate ground-states. Here, we present spin-resolved pulsed tunneling (SRPT) that precisely determines the complete phase diagram of the ground-state spin-polarization as a function of magnetic field (B) and filling factor (ν). We observe fully-polarized ν = 5/2…
