Half-filled High Landau Levels Research Articles

Anomalous Nematic States in High Half-Filled Landau Levels

It is well established that the ground states of a two-dimensional electron gas with half-filled high (N≥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 nonquantized Hall resistance R_{H}. Here, we report on emergent minima (maxima) in R_{xx} (R_{yy}) and plateaulike features in R_{H} in half-filled N≥3 Landau levels. Remarkably, these unexpected features develop at temperatures considerably lower than the onset temperature of QHSs, suggestive of a new ground state.

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.

Stripe formation driven by space noncommutativity in quantum Hall systems

We propose that the transport anisotropy observed in half-filled high Landau levels ( N ⩾ 2 ) is caused by the space noncommutativity effect, namely the Heisenberg uncertainty relation between the spatial coordinates of electrons. 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 experiments.

Metastable resistance-anisotropy orientation of two-dimensional electrons in high Landau levels.

In half-filled high Landau levels, two-dimensional electron systems possess collective phases which exhibit a strongly anisotropic resistivity tensor. A weak, but as yet unknown, rotational symmetry-breaking potential native to the host semiconductor structure is necessary to orient these phases in macroscopic samples. Making use of the known external symmetry-breaking effect of an in-plane magnetic field, we find that the native potential can have two orthogonal local minima. It is possible to initialize the system in the higher minimum and then observe its relaxation toward equilibrium.

Density-induced reorientation of the stripe at half-filled high Landau levels

The effect of a unidirectional periodic potential on the orientation of the stripe state is studied for the two-dimensional electron system at half-filled high Landau levels. By considering a quantum well with two electric subbands, it is found that the stripe is parallel to the external potential for weak modulation and is orthogonal for strong modulation. In the intermediate range, the orientation of the stripe changes from orthogonal to parallel as the electron density is increased. This result explains the recent experiment performed by J. Zhu {\it et al} that the anisotropy axis at half-filled high Landau levels rotates by $90^0$ by increasing the electron density. It also supports the suggestion that the stripes is pinned by the native surface morphology at the interface of the heterojunction.

Anisotropic transport of unidirectional lateral superlattice in high Landau levels

We report anisotropic transport observed in unidirectional lateral superlattices (LSL) with period a=92 nm , at high (6⩾ N⩾1) Landau levels (LLs). Near the half-filling of the LLs (up to filling factor ν= 25 2 ), sharp peaks are observed in the resistance traces when current is along the grating that defines the superlattice, which are not present (sometimes dips appear) for current across the grating. The peaks show alternating intensities with magnetic field: higher-magnetic-field branch spin sublevels in each LL tend to display more distinct peaks. Since the period a of LSL is close to the theoretically predicted period of the stripe phase in half-filled high LLs, the observed peaks probably represent the response of the stripe to the external periodic modulation.

Role of disorder in half-filled high Landau levels

We study the effects of disorder on the quantum Hall stripe phases in half-filled high Landau levels using exact numerical diagonalization. We show that, in the presence of weak disorder, a compressible, striped charge density wave, becomes the true ground state. The projected electron density profile resembles that of a smectic liquid. With increasing disorder strength W, we find that there exists a critical value, W_c \sim 0.12 e^2/\epsilon l, where a transition/crossover to an isotropic phase with strong local electron density fluctuations takes place. The many-body density of states are qualitatively distinguishable in these two phases and help elucidate the nature of the transition.

Density-Induced Interchange of Anisotropy Axes at Half-Filled High Landau Levels

We observe density-induced 90 degrees rotations of the anisotropy axes in transport measurements at half-filled high Landau levels in the two dimensional electron system, where stripe states are proposed ( nu = 9/2, 11/2, etc.). Using a field effect transistor, we find the transition density to be 2.9x10(11) cm(-2) at nu = 9/2. Hysteresis is observed in the vicinity of the transition. We construct a phase boundary in the filling factor magnetic field plane in the regime 4.4<nu<4.6. An in-plane magnetic field applied along either anisotropy axis always stabilizes the low density orientation of the stripes.

Reorientation of anisotropy in a square well quantum hall sample.

We have measured magnetotransport at half-filled high Landau levels in a quantum well with two occupied electric subbands. We find resistivities that are isotropic in perpendicular magnetic field but become strongly anisotropic at nu = 9/2 and 11/2 on tilting the field. The anisotropy appears at an in-plane field, B(ip) approximately 2.5 T, with the easy-current direction parallel to B(ip) but rotates by 90 degrees at B(ip) approximately 10 T and points now in the same direction as in single-subband samples. This complex behavior is in quantitative agreement with theoretical calculations based on a unidirectional charge density wave state model.

In-plane magnetic field-induced anisotropy and orientation energy of stripe phases at half-filled high Landau levels

We report on detailed Hartree–Fock calculations of the unidirectional charge density wave 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 two-dimensional electron systems we predict tilt-induced stripe states with variable anisotropy energy sign.

Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field

We report the observation of an acute sensitivity of the anisotropic longitudinal resistivity of two-dimensional electron systems in half-filled high Landau levels to the magnitude and orientation of an in-plane magnetic field. In the third and higher Landau levels, at filling fractions $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}9/2$, 11/2, etc., the in-plane field can lead to a striking interchange of the ``hard'' and ``easy'' transport directions. In the second Landau level the normally isotropic resistivity and the weak $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/2$ quantized Hall state are destroyed by a large in-plane field and the transport becomes highly anisotropic.