We report on transport signatures of hidden quantum Hall stripe (hQHS) phases in high ($N > 2$) half-filled Landau levels of Al$_{x}$Ga$_{1-x}$As/Al$_{0.24}$Ga$_{0.76}$As quantum wells with varying Al mole fraction $x < 10^{-3}$. Residing between the conventional stripe phases (lower $N$) and the isotropic liquid phases (higher $N$), where resistivity decreases as $1/N$, these hQHS phases exhibit isotropic and $N$-independent resistivity. Using the experimental phase diagram we establish that the stripe phases are more robust than theoretically predicted, calling for improved theoretical treatment. We also show that, unlike conventional stripe phases, the hQHS phases do not occur in ultrahigh mobility GaAs quantum wells, but are likely to be found in other systems.
We study the transport properties of pinned striped quantum Hall phases. We show that under quite general assumptions, the macroscopic conductivity tensor satisfies a semicircle law. In particular, this result is valid for both smectic and nematic stripe phases, independent of the presence of topological defects such as dislocations and grain boundaries. As a special case, our results explain the experimental validity of a product rule for the dissipative part of the resistivity tensor, which was previously derived by MacDonald and Fisher for a perfect stripe structure.
We study the quantum anomalous Hall effect in a strip of stripes model coupled to a magnetic texture with zero total magnetization and in the presence of strong electron-electron interactions. A helical magnetization along the stripes and a spin-selective coupling between the stripes gives rise to a bulk gap and chiral edge modes. Depending on the ratio between the period of the magnetic structure and the Fermi wavelength, the system can exhibit the integer or fractional quantum anomalous Hall effect. In the fractional regime, the quasiparticles have fractional charges and non-trivial Abelian …
We develop a sine-Gordon model of layered systems of two-dimensional modulated surfaces and one dimensional stripes, and demonstrate that these systems can undergo a Kosterlitz-Thouless transition in which the modulations unlock as a result of thermal or quantum fluctuations, respectively. The unlocked phase is interpreted as an anisotropic crystal in which soliton-antisoliton pairs proliferate. The properties of such a state for modulated stripes in quantum Hall systems and its possible relevance to recent anomalies in transport data are discussed.
We launch surface acoustic waves (SAW) along both the $<110>$ and the $<1\bar{1}0>$ directions of a Hall bar and measure the anisotropic conductivity in a high purity GaAs 2-D electron system in the Quantum Hall regime of the stripe and the bubble phases. In the anisotropic stripe phase, SAW propagating along the "easy" $<110>$ direction sense a compressible behavior (finite resistance) which is seen in standard transport measurement only if current flows along the "hard" $<1\bar{1}0>$ direction. In the isotropic bubble phase, the SAW data show compressible behavior in both directions, in mark…
We investigate the effect of the filling factor on transport anisotropies, known as stripes, in high Landau levels of a two-dimensional electron gas. We find that at certain in-plane magnetic fields, the stripes orientation is sensitive to the filling factor within a given Landau level. This sensitivity gives rise to the emergence of stripes away from half-filling while an orthogonally-oriented, native stripes reside at half-filling. This switching of the anisotropy axes within a single Landau level can be attributed to a strong dependence of the native symmetry breaking potential on the filli…
The collective modes of striped phases in a quantum Hall system are computed using the time-dependent Hartree-Fock approximation. Uniform stripe phases are shown to be unstable to the formation of modulations along the stripes, so that within the Hartree-Fock approximation the groundstate is a stripe crystal. Such crystalline states are generically gapped at any finite wavevector; however, in the quantum Hall system the interactions of modulations among different stripes is found to be remarkably weak, leading to an infinite collection of collective modes with immeasurably small gaps. The resu…
Our magnetotransport measurements of quantum Hall stripes in a high-quality GaAs quantum well in a slightly tilted magnetic field reveal that the orientation of stripes can be changed by temperature. Field-cooling and field-warming measurements, as well as observation of hysteresis at intermediate temperatures allow us to conclude that the observed temperature-induced reorientation of stripes is owing to the existence of two distinct minima in the symmetry-breaking potential. We also find that the native symmetry-breaking mechanism does not depend on temperature and that low-temperature magnet…
We analyze various properties of the visibility diagrams that can be used in the context of modular symmetries and confront them to some recent experimental developments in the Quantum Hall Effect. We show that a suitable physical interpretation of the visibility diagrams which permits one to describe successfully the observed architecture of the Quantum Hall states gives rise naturally to a stripe structure reproducing some of the experimental features that have been observed in the study of the quantum fluctuations of the Hall conductance. Furthermore, we exhibit new properties of the visibi…
We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe wit…
We consider quantum spin Hall effect in an anisotropic strip of stripes and address both integer and fractional filling factors. The first model is based on a gradient of spin-orbit interaction in the direction perpendicular to the stripes. The second model is based on two weakly coupled strips with reversed dispersion relations. We demonstrate that these systems host helical modes, modes in which opposite spins propagate in opposite directions. In the integer regime, the modes carry an elementary electron charge whereas in the fractional regime they carry fractional charges, and their excitat…
Recent experiments seem to confirm predictions that interactions lead to charge density wave ground states in higher Landau levels. These new ``correlated'' ground states of the quantum Hall system manifest themselves for example in a strongly anisotropic resistivity tensor. We give a brief introduction and overview of this new and emerging field.
Recently reported giant anisotropy in the longitudinal resistivity of a 2D electron system with valence Landau level index $N \ge 2$ has been interpreted as a signal of unidirectional charge density wave (UCDW) ground states. We report on detailed Hartree-Fock calculations of the UCDW orientation energy induced by a tilted magnetic field. We find that for current experimental samples stripes are oriented perpendicular to the in-plane field, consistent with experiment. For wider 2D electron systems we predict tilt-induced stripe states with variable anisotropy energy sign.
We examine the effect of disorder on the electromagnetic response of quantum Hall stripes using an effective elastic theory to describe their low-energy dynamics, and replicas and the Gaussian variational method to handle disorder effects. Within our model we demonstrate the existence of a depinning transition at a critical partial Landau level filling factor $Δν_c$. For $Δν<Δν_c$, the pinned state is realized in a replica symmetry breaking (RSB) solution, and the frequency-dependent conductivities in both perpendicular and parallel to the stripes show resonant peaks. These peaks shift to zero…
Quantum Hall stripe phases near half-integer filling factors $ν\ge 9/2$ were predicted by Hartree-Fock (HF) theory and confirmed by discoveries of giant resistance anisotropies in high-mobility two-dimensional electron gases. A theory of such anisotropy was proposed by MacDonald and Fisher, although they used parameters whose dependencies on the filling factor, electron density, and mobility remained unspecified. Here, we fill this void by calculating the hard-to-easy resistivity ratio as a function of these three variables. Quantitative comparison with experiment yields very good agreement wh…
We have investigated the effect of unidirectional periodic potential modulation on the fractional quantum Hall (FQH) state at filling factors nu=5/3 and 4/3. For large enough modulation amplitude, we find that the resistivity minimum at nu=5/3 gives way to a peak that grows with decreasing temperature. Density matrix renormalization group calculation reveals that phase transition from FQH state to unidirectional striped state having a period sim 4 l (with l the magnetic length) takes place at nu=1/3 (equivalent to nu=5/3 by the particle-hole symmetry) with the increase of the modulation amplit…
We present results of a study of double layer quantum Hall systems in which each layer has a high-index Landau level that is half-filled. Hartree-Fock calculations indicate that, above a critical layer separation, the system becomes unstable to the formation of a unidirectional coherent charge density wave (UCCDW), which is related to stripe states in single layer systems. The UCCDW state supports a quantized Hall effect when there is tunneling between layers, and is {\it always} stable against formation of an isotropic Wigner crystal for Landau indices $N \ge 1$. The state does become unstabl…
Much of the present day qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the interactions between composite fermions altogether. For example the fractional quantum Hall effect at $ν=n/(2pn\pm 1)$ corresponds to filled composite-fermion Landau levels,and the compressible state at $ν=1/2p$ to the Fermi sea of composite fermions. Away from these filling factors, the residual interactions between composite fermions will determine the nature of the ground state. In this article, a model is constructed for the residual interaction between composite ferm…
We investigate nuclear spin effects in a two-dimensional electron gas in the quantum Hall regime modeled by a weakly coupled array of interacting quantum wires. We show that the presence of hyperfine interaction between electron and nuclear spins in such wires can induce a phase transition, ordering electrons and nuclear spins into a helix in each wire. Electron-electron interaction effects, pronounced within the one-dimensional stripes, boost the transition temperature up to tens to hundreds of millikelvins in GaAs. We predict specific experimental signatures of the existence of nuclear spin …
We investigate quantum Hall stripes under in-plane magnetic field $B_\parallel$ in a variable-density two-dimensional electron gas. At filling factor $ν= 9/2$, we observe one, two, and zero $B_\parallel$-induced reorientations at low, intermediate, and high densities, respectively. The appearance of these distinct regimes is due to a strong density dependence of the $B_\parallel$-induced orienting mechanism which triggers the second reorientation, rendering stripes \emph{parallel} to $B_\parallel$. In contrast, the mechanism which reorients stripes perpendicular to $B_\parallel$ showed no noti…
Quantum Hall stripe (QHS) phases, predicted by the Hartree-Fock theory, are manifested in GaAs-based two-dimensional electron gases as giant resistance anisotropies. Here, we predict a ``hidden'' QHS phase which exhibits \emph{isotropic} resistivity whose value, determined by the density of states of QHS, is independent of the Landau index $N$ and is inversely proportional to the Drude conductivity at zero magnetic field. At high enough $N$, this phase yields to an Ando-Unemura-Coleridge-Zawadski-Sachrajda phase in which the resistivity is proportional to $1/N$ and to the ratio of quantum and …
The collective modes of stripes in double layer quantum Hall systems are computed using the time-dependent Hartree-Fock approximation. It is found that, when the system possesses spontaneous interlayer coherence, there are two gapless modes, one a phonon associated with broken translational invariance, the other a pseudospin-wave associated with a broken U(1) symmetry. For large layer separations the modes disperse weakly for wavevectors perpendicular to the stripe orientation, indicating the system becomes akin to an array of weakly coupled one-dimensional XY systems. At higher wavevectors th…
In ultra-clean 2D electron systems on (001) GaAs/AlGaAs upon filling high Landau levels, it was recently observed a new class of collective states, which can be related to the spontaneous formation of a charge density wave (``striped phase''). We address to the following unsolved problem: what is the reason for stripe pinning along the crystallographic direction [110]? It is shown that in a single heterojunction (001) III-V the effective mass of 2D electrons is anisotropic. This natural anisotropy is due to the reduced (C_{2v}) symmetry of the heterojunction and, even being weak (0.1 percent),…
Nature of the fractional quantum Hall state at Landau level filling factor 5/2 remains elusive despite intensive experimental and theoretical work. While the leading theoretical candidates are Moore-Read Pfaffian (Pf) and its particle-hole conjugate anti-Pfaffian (APf), neither received unambiguous experimental support. We show that a state that is intermediate between them, made of alternating stripes of Pf and APf in the bulk, is a viable candidate. Such a state is shown to be incompressible and thus a charge insulator in the bulk, but a heat conductor due to the presence of gapless neutral …
We report on quantum Hall stripes (QHSs) formed in higher Landau levels of GaAs/AlGaAs quantum wells with high carrier density ($n_e > 4 \times 10^{11}$ cm$^{-2}$) which is expected to favor QHS orientation along unconventional $\left < 1\bar{1}0 \right >$ crystal axis and along the in-plane magnetic field $B_{||}$. Surprisingly, we find that at $B_{||} = 0$ QHSs in our samples are aligned along $\left < 110 \right >$ direction and can be reoriented only perpendicular to $B_{||}$. These findings suggest that high density alone is not a decisive factor for either abnormal native QHS orientation…
There is growing experimental and theoretical evidence that very clean two dimensional electron systems form unidirectional charge density waves (UCDW) or ``striped'' states at low temperatures and at Landau level filling fractions of the form nu = M + x with 4 < M < 10 an integer and 0.4 < x < 0.6. Following previous work, we model the striped state using a Hartree-Fock approach. We construct the low energy excitations of the system by making smooth deformations of the stripe edges analogous to the construction of edge state excitations of quantum Hall droplets. These low energy excitations a…
Anomalous nematic states, recently discovered in ultraclean two-dimensional electron gas, emerge from quantum Hall stripe phases upon further cooling. These states are hallmarked by a local minimum (maximum) in the hard (easy) longitudinal resistance and by an incipient plateau in the Hall resistance in nearly half-filled Landau levels. Here, we demonstrate that a modest in-plane magnetic field, applied either along $\left < 110 \right >$ or $\left < 1\bar10 \right >$ crystal axis of GaAs, destroys anomalous nematic states and restores quantum Hall stripe phases aligned along their native $\le…
A strong anisotropy in the longitudinal resistivity of a 2D electron system has been observed at half-filled high Landau levels. We report on detailed Hartree-Fock calculations of the unidirectional charge density wave (UCDW) orientation energy induced by a tilted magnetic field. We find that stripes can orient both parallel or perpendicular to the in-plane field depending on the sample parameters and field strength. The close agreement between complex experimental data on different sample geometries and our theoretical results strongly support the UCDW picture as the origin of the observed an…
We present recent experimental results confirming previously predicted strong asymmetries of the current distribution in narrow Hall bars under the conditions of the integer quantum Hall effect (IQHE). Using a previously developed self-consistent screening and transport theory of the IQHE, we investigate how these asymmetries, which are due to a non-linear feedback effect of the imposed current on the electron distribution in the sample, depend on relevant parameters, such as the strength of the imposed current, the magnetic field, the temperature, and the collision broadening of the Landau-qu…
We analyze the quantum Hall effect in single layer graphene with bilayer stripe defects. Such defects are often encountered at steps in the substrate of graphene grown on silicon carbide. We show that AB or AA stacked bilayer stripes result in large Hall conductivity fluctuations that destroy the quantum Hall plateaux. The fluctuations are a result of the coupling of edge states at opposite edges through currents traversing the stripe. Upon rotation of the second layer with respect to the continuous monolayer (a twisted-bilayer stripe defect), such currents decouple from the extended edge stat…
In some range of interlayer distances, the ground state of the two-dimensional electron gas at filling factor nu =4N+1 with N=0,1,2,... is a coherent stripe phase in the Hartree-Fock approximation. This phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton-antisoliton pairs using a supercell microscopic unrestricted Hartree-Fock approach. We study this gap as a function of interlayer distance and tunneling amplitude. Our calculations…
We present a brief survey of the charge density wave phases of a two-dimensional electron liquid in moderate to weak magnetic fields where several higher Landau levels are occupied. The review follows the chronological development of this new and emerging field: from the ideas that led to the original theoretical prediction of the novel ground states, to their dramatic experimental discovery, to the currently pursued directions and open questions.
We report on the effect of in-plane magnetic field $B_\parallel$ on stripe phases in higher ($N=2,3$) Landau levels of a high-mobility 2D electron gas. In accord with previous studies, we find that a modest $B_\parallel$ applied parallel to the native stripes aligns them perpendicular to it. However, upon further increase of $B_\parallel$, stripes are reoriented back to their native direction. Remarkably, applying $B_\parallel$ perpendicular to the native stripes also aligns stripes parallel to it. Thus, regardless of the initial orientation of stripes with respect to $B_\parallel$, stripes ar…
Anisotropic states at half-filled third and higher Landau levels are investigated in the system with a finite electric current. We study the response of the striped Hall state and the anisotropic charge density wave (ACDW) state against the injected current using the effective action. Current distributions and a current dependence of the total energy are determined for both states. With no injected current, the energy of the ACDW state is lower than that of the striped Hall state. We find that the energy of the ACDW state increases faster than that of the striped Hall state as the injected cur…
In higher Landau levels (N>0) and around filling factors nu =4N+1, a two-dimensional electron gas in a double-quantum-well system supports a stripe groundstate in which the electron density in each well is spatially modulated. When a parallel magnetic field is added in the plane of the wells, tunneling between the wells acts as a spatially rotating effective Zeeman field coupled to the ``pseudospins'' describing the well index of the electron states. For small parallel fields, these pseudospins follow this rotation, but at larger fields they do not, and a commensurate-incommensurate transition…
We develop a Chern-Simons theory to describe a two-dimensional electron gas in intermediate magnetic fields. Within this approach, inhomogeneous states emerge in analogy to the intermediate state of a superconductor. At half filling of the highest Landau level we find unidirectional charge-density-wave (CDW) solutions. With a semiclassical calculation we give an intuitive explanation of the change of CDW orientation in the presence of an in-plane magnetic field. An anisotropy in the electron band mass is suggested as a possible source of the reproducible orientation of the CDW.
We consider stripe formation in quantum Hall systems at integer filling factors. We use Hartree-Fock calculations to obtain the phase diagram of bilayer quantum Hall systems at $ν=4n+1$ in a tilted magnetic field. We derive and analyze an effective low energy theory for the stripe phases which may be present in such systems. We discuss the possibility of stripe formation in wide well systems in a tilted magnetic field and suggest that the resistance anisotropy, observed recently by W. Pan et.al. [phys. Rev. B 64 (2001) 121305], may be due to the existence of a skyrmion stripe phase.
We study fluctuations and topological melting transitions of quantum Hall stripes near half-filling of intermediate Landau levels. Taking the stripe state to be an anisotropic Wigner crystal (AWC) allows us to identify the quantum Hall nematic state conjectured in previous studies of the 2D electron gas as an {\em anisotropic hexatic}. The transition temperature from the AWC to the quantum Hall nematic state is explicitly calculated, and a tentative phase diagram for the 2D electron gas near half-filling is suggested.
We study a paired state at the half-filled Landau level using a mean field theory on the von Neumann lattice. We obtain a microscopic model which shows a continuous transition from the compressible stripe state to the paired state. The energy gap in the paired state is calculated numerically at the half-filled second Landau level.
We determine conditions for the formation of compressible stripes near the quantum Hall effect (QHE) edges of top-gated epitaxial graphene on Si-terminated SiC (G/SiC) and compare those to graphene exfoliated onto insulating substrate in the field-effect-transistor (GraFET) geometry. For G/SiC, a large density of localised surface states on SiC just underneath graphene layer and charge transfer between them lead both to doping of graphene and to screening of potential profile near its edge. This suppresses formation of compressible stripes near QHE edges in graphene, making them much narrower …
We present a microscopic derivation of the hydrodynamic theory of the Quantum Hall smectic or stripe phase of a two-dimensional electron gas in a large magnetic field. The effective action of the low energy is derived here from a microscopic picture by integrating out high energy excitations with a scale of the order the cyclotron energy.The remaining low-energy theory can be expressed in terms of two canonically conjugate sets of degrees of freedom: the displacement field, that describes the fluctuations of the shapes of the stripes, and the local charge fluctuations on each stripe.
We study striped states in the quantum Hall system around half-filled high Landau levels and obtain the optimal orientation of the striped state in the presence of an external unidirectional periodic potential. It is shown that the optimal orientation is orthogonal to the external modulation in the Coulomb dominant regime (the orthogonal phase) and is parallel in the external modulation dominant regime (the parallel phase). The phase boundary of these two phases is determined numerically in the parameter space of the strength and wave number of the external modulation at the half-filled third …
We examine the influence of the edge electronic density profile and of dissipation on edge magnetoplasmons in the quantum Hall regime, in a semiclassical calculation. The equilibrium electron density on the edge, obtained using a Thomas-Fermi approach, has incompressible stripes produced by energy gaps responsible for the quantum Hall effect. We find that these stripes have an unobservably small effect on the edge magnetoplasmons. But dissipation, included phenomenologically in the local conductivity, proves to produce significant oscillations in the strength and speed of edge magnetoplasmons …
We propose that the transport anisotropy observed in half-filled high Landau levels ($N \geq 2$) is caused by the space noncommutativity effect, namely the Heisenberg uncertainty relation between the spatial coordinates of electrons. The stripe corresponds to a limit that one coordinate of a large number of particles is fixed at a certain value while its conjugate coordinate is completely uncertain. We make a renormalization group analysis and find that the noncommutativity effect is able to drive the stripe formation only at half-fillings $ν= 9/2, 11/2, 13/2,$ etc., in agreement with experime…
We use a fully self-consistent laterally resolved Hartree-Fock approximation for numerically addressing the electron configurations at higher Landau levels in the quantum Hall regime for near-macroscopic sample sizes. Our results give microscopic details of stripe- and bubble-like charge density modulations and show how these emerge depending on the filling factor. We find that there exists a region at the boundaries of the stripes and bubbles with a density modulation that corresponds to a filling factor around half filling. The microscopic details of these boundary regions determine the geom…
We have performed an exact diagonalization study of up to N=12 interacting electrons on a disk at filling $ν={1/3}$ for both Coulomb and $V_1$ short-range interaction for which Laughlin wave function is the exact solution. For Coulomb interaction and $N\geq 10$ we find persistent radial oscillations in electron density, which are not captured by the Laughlin wave function. Our results srongly suggest formation of a chiral edge striped phase in quantum Hall systems. The amplitude of the charge density oscillations decays slowly, perhaps as a square root of the distance from the edge; thus the s…
In a 2D electron system in (001) GaAs/AlGaAs upon filling high Landau levels, it was recently observed a new class of collective states, which are recognized now to relate to the spontaneous formation of a charge density wave (``stripe phase''). Here we analyze one of the possible mechanisms of the stripe pinning along the crystallographic direction [110]--the native effective mass anisotropy of 2D electrons. It is shown that for a symmetric quantum well this anisotropy is a linear function of applied perpendicular-to-plane electric field. So, if it is the anisotropy that defines the direction…
The physical properties of striped Hall state in the presence of an external unidirectional periodic potential is investigated. The study of searching the optimal orientation of the state is reported for the state at filling factor $ν=2+1/2$ and for the state at higher Landau levels at $l+1/2$ where $l=3,4,5,6,7,8$. It is predicted that two phases of the orientation, parallel phase and perpendicular phase, exist and a phase transition from one to another phase occurs.
State of the art computing opens now a new window to the integer quantum Hall effect (IQHE) regime, which enforces a major revision of the common knowledge accumulated so far. In our record-breaking application of the Hartree-Fock method we use up to 3000 electrons distributed over up to 5000 states for almost macroscopic system size of 1000x1000nm. In particular, the formation of compressible and in-compressible edge stripes turns out to develop essentially different from the common picture used so far. Oppositely to the theory of Chklovskii, Shklovskii and Glazman (CSG), the narrow channels,…
Transport experiments provide conflicting evidence on the possible existence of fractional order within integer quantum Hall systems. In fact integer edge states sometimes behave as monolithic objects with no inner structure, while other experiments clearly highlight the role of fractional substructures. Recently developed low-temperature scanning probe techniques offer today an opportunity for a deeper-than-ever investigation of spatial features of such edge systems. Here we use scanning gate microscopy and demonstrate that fractional features were unambiguously observed in every integer quan…
The quantum Hall effect is generally understood for free electron gases, in which topologically protected edge states between Landau levels (LLs) form conducting channels at the edge of the sample. In periodic crystals, the LLs are imprinted with lattice properties; plateaus in the transverse Hall conductivity are not equidistant in energy anymore. Herein, crystals with a polyatomic basis are considered. For a stripe arrangement of different atoms, the band structure resorts nontrivially and exhibits strong oscillations that form a salient pattern with very small bandgaps. The Hall conductivit…
A comprehensive study of magnetoresistance and Hall effect has been performed for the set of the single crystals of non-magnetic metal LuB12 with the Jahn-Teller instability of the boron cage and dynamic charge stripes forming along <110> direction. Anomalous positive contribution to Hall effect for particular direction of magnetic field H//[001] is found in the single crystals of LuB12 of the highest quality. This contribution arising at T~ 150 K is shown to increase drastically when approaching the disordered ground state below 60 K. The Hall effect anomaly is shown to appear in combination …
We consider the two lowest Landau levels at half filling. In the higher Landau level (nu =5/2), we find a first order phase transition separating a compressible striped phase from a paired quantum Hall state, which is identified as the Moore-Read state. The critical point is very near the Coulomb potential and the transition can be driven by increasing the width of the electron layer. We find a much weaker transition (either second order or a crossover) from pairing to the composite fermion Fermi liquid behavior. A very similar picture is obtained for the lowest Landau level but the transition…
We numerically investigate the interplay of disorder and electron-electron interactions in the integer quantum Hall effect. In particular, we focus on the behaviour of the electronic compressibility as a function of magnetic field and electron density. We find manifestations of non-linear screening and charging effects around integer filling factors, consistent with recent imaging experiments. Our calculations exhibit $g$-factor enhancement as well as strong overscreening in the centre of the Landau bands. Even though the critical behaviour appears mostly unaffected by interactions, important …
Anisotropic states at half-filled higher Landau levels are investigated in the system with a finite electric current. We study the response of the striped Hall state and the anisotropic charge density wave (ACDW) state against the injected current using the effective action. Current distributions and a current dependence of the total energy are determined for both states. With no injected current, the energy of the ACDW state is lower than that of the striped Hall state. We find that the energy of the ACDW state increases faster than that of the striped Hall state as the injected current incre…
We use dynamic scanning capacitance microscopy (DSCM) to image compressible and incompressible strips at the edge of a Hall bar in a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives access to the complex local conductance, Gts, between a sharp metallic tip scanned across the sample surface and ground, comprising the complex sample conductance. Near integer filling factors we observe a bright stripe along the sample edge in the imaginary part of Gts. The simultaneously recorded real part exhibits a sharp peak at the boundary between the sample inter…
We present a detailed theory for finite-frequency conductivities Re$[σ_{αβ}(ω)]$ of quantum Hall stripes, which form at Landau level $N\geq 2$ close to half filling, in the presence of weak Gaussian disorder. We use an effective elastic theory to describe the low-energy dynamics of the stripes with the dynamical matrix being determined through matching the density-density correlation function obtained in the microscopic time-dependent Hartree-Fock approximation. We then apply replicas and the Gaussian variational method to deal with the disorder. Within this method, a set of saddle point equat…
We study the problem of a single Dirac fermion in a quantizing orbital magnetic field, when the chemical potential is at the Dirac point. This can be realized on the surface of a topological insulator, such as Bi2Se3, tuned to neutrality. We study the effect of both long range Coulomb interactions (strength alpha=e^2/(epsilon hbar v_F).) and local repulsion U which capture the effect of electron correlations. Interactions resolve the degeneracy of free fermions in the zeroth Landau level at half filling, but in a manner different from that in graphene. For weak interactions, U=0 and alpha<<1, …
A transport study of two-dimensional (2D) holes confined to wide GaAs quantum wells provides a glimpse of a subtle competition between different many-body phases at Landau level filling $ν=3/2$ in tilted magnetic fields. At large tilt angles ($θ$), an anisotropic, stripe (or nematic) phase replaces the isotropic compressible Fermi sea at $ν=3/2$ if the quantum well has a symmetric charge distribution. When the charge distribution is made asymmetric, instead of the stripe phase, an even-denominator fractional quantum state appears at $ν=3/2$ in a range of large $θ$, and reverts back to a compre…
In this report we summarize a recent progress in exploration of correlated two-dimensional electron states in partially filled high Landau levels. At a mean-field Hartree-Fock level they can be described as charge-density waves, either unidirectional (stripes) or with the symmetry of the triangular lattice (bubbles). Thermal and quantum fluctuations have a profound effect on the stripe density wave and give rise to novel phases, which are quite similar to smectic and nematic liquid crystals. We discuss the effective theories for these phases, their collective modes, and phase transitions betwe…
