Chenggang Zhou

Laterally Modulated 2D Electron System in the Extreme Quantum Limit

We report on magnetotransport of a two-dimensional electron system (2DES), located 32 nm below the surface, with a surface superlattice gate structure of periodicity 39 nm imposing a periodic modulation of its potential. For low Landau level fillings nu, the diagonal resistivity displays a rich pattern of fluctuations, even though the disorder dominates over the periodic modulation. Theoretical arguments based on the combined effects of the long-wavelength, strong disorder and the short-wavelength, weak periodic modulation present in the 2DES qualitatively explain the data.

Effects of large disorder on the Hofstadter butterfly

Motivated by the recent experiments on periodically modulated, two-dimensional electron systems placed in large transversal magnetic fields [S. Melinte et al., Phys. Rev. Lett. 92, 036802 (2004)], we investigate the interplay between the effects of disorder and periodic potentials in the integer quantum Hall regime. In particular, we study the case where disorder is larger than the periodic modulation, but both are small enough that Landau level mixing is negligible. We carry extensive numerical calculations to understand the relevant physics in the lowest Landau level, such as the spectrum and nature (localized or extended) of the wave functions. Based on our results, we propose a qualitative explanation of the new features uncovered recently in these transport measurements.

One-dimensional chain with random long-range hopping

The one-dimensional (1D) tight-binding model with random nearest-neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effectsof random long-range (power-law) hopping with an ensemble average magnitude ‖i-j‖ - σ in the 1D chain, while maintaining the particle-hole symmetry present in the nearest-neighbor model. We find, in agreement with results of real-space renormalization-group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent σ becomes smaller than 2.

Correlated mesoscopic fluctuations in integer quantum Hall transitions

We investigate the origin of the resistance fluctuations of mesoscopic samples, near transitions between Quantum Hall plateaus. These fluctuations have been recently observed experimentally by E. Peled et al. [Phys. Rev. Lett. 90, 246802 (2003); ibid 90, 236802 (2003); Phys. Rev. B 69, R241305 (2004)]. We perform realistic first-principles simulations using a six-terminal geometry and sample sizes similar to those of real devices, to model the actual experiment. We present the theory and implementation of these simulations, which are based on the linear response theory for non-interacting electrons. The Hall and longitudinal resistances extracted from the Landauer formula exhibit all the observed experimental features. We give a unified explanation for the three regimes with distinct types of fluctuations observed experimentally, based on a simple generalization of the Landauer-Buttiker model. The transport is shown to be determined by the interplay between tunneling and chiral currents. We identify the central part of the transition, at intermediate filling factors, as the critical region where the localization length is larger than the sample size.

Resistance fluctuations near integer quantum Hall transitions in mesoscopic samples

We perform first-principles simulations to study the resistance fluctuations of mesoscopic samples, near transitions between quantum Hall plateaus. We use six-terminal geometry and sample sizes similar to those of real devices and calculate the Hall and longitudinal resistances using the Landauer formula. Our simulations recapture all the observed experimental features. We then use a generalization of the Landauer-Buttiker model, based on the interplay between tunneling and chiral currents, to explain the three regimes with distinct fluctuations observed, and identify the central regime as the critical region.

Longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two-dimensional electron system placed in a strong perpendicular magnetic field and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation. The results we present are exact for noninteracting electrons within a spin-polarized lowest Landau level: the effects of the disorder and the periodic modulation are fully accounted for. When necessary, Landau level mixing can also be incorporated straightforwardly into the same formalism. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder, when the later is dominant. This appears to be the relevant regime to understand recent experiments [S. Melinte et al., Phys. Rev. Lett. 92, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multichannel scattering problems.

Spectral weight transfer in the integer quantum Hall effect and its consequences

In the absence of disorder, the degeneracy of a Landau level (LL) is N = BA/φ0, where B is the magnetic field, A is the area of the sample and φ0 = h/e is the magnetic flux quantum. With disorder, localized states appear at the top and bottom of the broadened LL, while states in the center of the LL (the critical region) remain delocalized. This well-known phenomenology is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE) [1]. One unnoticed issue is where the new states appear as the magnetic field is increased. Here we demonstrate that they appear predominantly inside the critical region. This leads to a certain “spectral ordering” of the localized states that explains the stripes observed in measurements of the local inverse compressibility [2, 3], of two-terminal conductance [4], and of Hall and longitudinal resistances [5] without invoking interactions as done in previous work [6, 7, 8]. The spectrum and eigenstates of a disorder-broadened LL can be studied with the well-established approach of diagonalizing the single electron Hamiltonian

DISORDER AND FRUSTRATION IN DILUTED MAGNETIC SEMICONDUCTORS AT LOW CARRIER DENSITIES

We examine the effects of positional disorder of the magnetic ion in III-V Diluted Magnetic Semiconductors such as (Ga,Mn)As at low carrier densities on the nature of the low-temperature ordered magnetic state, using numerical mean field and Monte Carlo methods. We find that positional disorder leads to a highly inhomogeneous ferromagnetic order in the low carrier density limit, with unusual thermodynamic and magnetic behavior. Spin-orbit coupling presented in the valence band leads to frustration in the hole-doped system, but does not significantly affect the low temperature magnetization.