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Register a new userNonequilibrium phenomena in high Landau levels
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Developments in the physics of 2D electron systems during the last decade have revealed a new class of nonequilibrium phenomena in the presence of a moderately strong magnetic field. The hallmark of these phenomena is magnetoresistance oscillations generated by the external forces that drive the electron system out of equilibrium. The rich set of dramatic phenomena of this kind, discovered in high mobility semiconductor nanostructures, includes, in particular, microwave radiation-induced resistance oscillations and zero-resistance states, as well as Hall field-induced resistance oscillations and associated zero-differential resistance states. We review the experimental manifestations of these phenomena and the unified theoretical framework for describing them in terms of a quantum kinetic equation. The survey contains also a thorough discussion of the magnetotransport properties of 2D electrons in the linear response regime, as well as an outlook on future directions, including related nonequilibrium phenomena in other 2D electron systems.
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Effects of disorder and valley polarization in graphene are investigated in the quantum Hall regime. We find anomalous localization properties for the lowest Landau level (LL), where disorder can induce wavefunction delocalization (instead of localization), both for white-noise and gaussian-correlated disorder. We quantitatively identify the contribution of each sublattice to wavefunction amplitudes. Following the valley (sublattice) polarization of states within LLs for increasing disorder we show: (i) valley mixing in the lowest LL is the main effect behind the observed anomalous localization properties, (ii) the polarization suppression with increasing disorder depends on the localization for the white-noise model, while, (iii) the disorder induces a partial polarization in the higher Landau levels for both disorder models.
Recent experiments on Coulomb drag in the quantum Hall regime have yielded a number of surprises. The most striking observations are that the Coulomb drag can become negative in high Landau levels and that its temperature dependence is non-monotonous. We develop a systematic diagrammatic theory of Coulomb drag in strong magnetic fields explaining these puzzling experiments. The theory is applicable both in the diffusive and the ballistic regimes; we focus on the experimentally relevant ballistic regime (interlayer distance $a$ smaller than the cyclotron radius $R_c$). It is shown that the drag at strong magnetic fields is an interplay of two contributions arising from different sources of particle-hole asymmetry, namely the curvature of the zero-field electron dispersion and the particle-hole asymmetry associated with Landau quantization. The former contribution is positive and governs the high-temperature increase in the drag resistivity. On the other hand, the latter one, which is dominant at low $T$, has an oscillatory sign (depending on the difference in filling factors of the two layers) and gives rise to a sharp peak in the temperature dependence at $T$ of the order of the Landau level width.
The intense search for topological superconductivity is inspired by the prospect that it hosts Majorana quasiparticles. We explore in this work the optimal design for producing topological superconductivity by combining a quantum Hall state with an ordinary superconductor. To this end, we consider a microscopic model for a topologically trivial two-dimensional p-wave superconductor exposed to a magnetic field, and find that the interplay of superconductivity and Landau level physics yields a rich phase diagram of states as a function of $mu/t$ and $Delta/t$, where $mu$, $t$ and $Delta$ are the chemical potential, hopping strength, and the amplitude of the superconducting gap. In addition to quantum Hall states and topologically trivial p-wave superconductor, the phase diagram also accommodates regions of topological superconductivity. Most importantly, we find that application of a non-uniform, periodic magnetic field produced by a square or a hexagonal lattice of $h/e$ fluxoids greatly facilitates regions of topological superconductivity in the limit of $Delta/trightarrow 0$. In contrast, a uniform magnetic field, a hexagonal Abrikosov lattice of $h/2e$ fluxoids, or a one dimensional lattice of stripes produces topological superconductivity only for sufficiently large $Delta/t$.
It is commonly believed that a non-interacting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localisation that have manifestations in the disorder-averaged density of states, conductivity and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors and all sufficiently high-dimensional systems. Moreover, such systems exhibit unconventional behaviour of Lifshitz tails, energy-level statistics and ballistic-transport properties. Here we review recent progress and the status of results on non-Anderson disorder-driven transitions and related phenomena.
It is well established that the ground states of a two-dimensional electron gas with half-filled high ($N ge 2$) Landau levels are compressible charge-ordered states, known as quantum Hall stripe (QHS) phases. The generic features of QHSs are a maximum (minimum) in a longitudinal resistance $R_{xx}$ ($R_{yy}$) and a non-quantized Hall resistance $R_H$. Here, we report on emergent minima (maxima) in $R_{xx}$ ($R_{yy}$) and plateau-like features in $R_H$ in half-filled $N ge 3$ Landau levels. Remarkably, these unexpected features develop at temperatures considerably lower than the onset temperature of QHSs, suggesting a new ground state.
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