Synthetic magnetic fluxes on the honeycomb lattice

We devise experimental schemes able to mimic uniform and staggered magnetic fluxes acting on ultracold two-electron atoms, such as ytterbium atoms, propagating in a honeycomb lattice. The atoms are first trapped into two independent state-selective triangular lattices and are further exposed to a suitable configuration of resonant Raman laser beams. These beams induce hops between the two triangular lattices and make atoms move in a honeycomb lattice. Atoms traveling around each unit cell of this honeycomb lattice pick up a nonzero phase. In the uniform case, the artificial magnetic flux sustained by each cell can reach about two flux quanta, thereby realizing a cold atom analogue of the Harper model with its notorious Hofstadter's butterfly structure. Different condensed-matter phenomena such as the relativistic integer and fractional quantum Hall effects, as observed in graphene samples, could be targeted with this scheme.Comment: 12 pages, 14 figure

Imaging Transport Resonances in the Quantum Hall Effect

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a DC bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than four orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.Comment: 4 pages, 4 figures, submitted to PRL. For movies and additional infomation, see http://electron.mit.edu/scanning/; Added scale bars to images, revised discussion of figure 3, other minor change

A new Proposal for a Quasielectron Trial Wavefunction for the FQHE on a Disk

In this letter, we propose a new quasielectron trial wavefunction for $N$ interacting electrons in two dimensions moving in a strong magnetic field in a disk geometry. Requiring that the trial wavefunction exhibits the correct filling factor of a quasielectron wavefunction, we obtain $N+1$ angular momentum eigenfunctions. The expectation values of the energy are calculated and compared with the data of an exact numerical diagonalization.Comment: 8 page

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 resitance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave (CDW) 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 examine in detail 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.Comment: 25 pages, 6 figure

Sub-linear radiation power dependence of photo-excited resistance oscillations in two-dimensional electron systems

We find that the amplitude of the $R_{xx}$ radiation-induced magnetoresistance oscillations in GaAs/AlGaAs system grows nonlinearly as $A \propto P^{\alpha}$ where $A$ is the amplitude and the exponent $\alpha < 1$. %, with $\alpha \rightarrow 1/2$ in %the low temperature limit. This striking result can be explained with the radiation-driven electron orbits model, which suggests that the amplitude of resistance oscillations depends linearly on the radiation electric field, and therefore on the square root of the power, $P$. We also study how this sub-linear power law varies with lattice temperature and radiation frequency.Comment: 5 pages, 3 figure

Adiabatic quantization of Andreev levels

We identify the time $T$ between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent $\lambda$), coupled to a superconductor by an $N$-mode point contact. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods $T_{n}$, which in turn generate a ladder of excited states $\epsilon_{nm}=(m+1/2)\pi\hbar/T_{n}$. The largest quantized period is the Ehrenfest time $T_{0}=\lambda^{-1}\ln N$. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension $W/\sqrt{N}$, much below the width $W$ of the point contact.Comment: 4 pages, 3 figure

Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates on the surfaces of GaAs/AlGaAs heterostructures. In the low mobility regime the classical Hall resistance line is proportional to the magnetic field as measured in the high temperature limit and cuts through the center of each Hall plateau. For high mobility samples we observe in linear response measurements, that this symmetry is broken and the classical Hall line cuts the plateaus not at the center but at higher magnetic fields near the edges of the plateaus. These experimental results confirm the unconventional predictions of a model for the quantum Hall effect taking into account mutual screening of charge carriers within the Hall bar. The theory is based on solving the Poisson and Schr\"odinger equations in a self-consistent manner.Comment: EP2DS-17 Proceedings, 6 Pages, 2 Figure

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure