The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene

We investigate the quantum Hall (QH) states near the charge neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors $\nu=\pm1$ depend only on the perpendicular component of the field with respect to the graphene plane, indicating them to be not spin-related. A non-linear magnetic field dependence of the activation energy gap at filling factor $\nu=1$ suggests a many-body origin. We therefore propose that the $\nu=0$ and $\pm1$ states arise from the lifting of the spin and sub-lattice degeneracy of the $n=0$ LL, respectively.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Energy Spectra for Fractional Quantum Hall States

Fractional quantum Hall states (FQHS) with the filling factor nu = p/q of q < 21 are examined and their energies are calculated. The classical Coulomb energy is evaluated among many electrons; that energy is linearly dependent on 1/nu. The residual binding energies are also evaluated. The electron pair in nearest Landau-orbitals is more affected via Coulomb transition than an electron pair in non-nearest orbitals. Each nearest electron pair can transfer to some empty orbital pair, but it cannot transfer to the other empty orbital pair because of conservation of momentum. Counting the numbers of the allowed and forbidden transitions, the binding energies are evaluated for filling factors of 126 fraction numbers. Gathering the classical Coulomb energy and the pair transition energy, we obtain the spectrum of energy versus nu. This energy spectrum elucidates the precise confinement of Hall resistance at specific fractional filling factors.Comment: 5 pages, 3 figure

Electron Scattering in AlGaN/GaN Structures

We present data on mobility lifetime, $\tau_t$, quantum lifetime, $\tau_q$, and cyclotron resonance lifetime, $\tau_{CR}$, of a sequence of high-mobility two-dimensional electron gases in the AlGaN/GaN system, covering a density range of $\sim1-4.5\times10^{12}$cm$^{-2}$. We observe a large discrepancy between $\tau_q$ and $\tau_{CR}$ ($\tau_q\sim\tau_{CR}$/6) and explain it as the result of density fluctuations of only a few percent. Therefore, only $\tau_{CR}$ --and not $\tau_q$ -- is a reliable measure of the time between electron scattering events in these specimens. The ratio $\tau_t / \tau_{CR}$ increases with increasing density in this series of samples, but scattering over this density range remains predominantly in the large-angle scattering regime

Electron Depletion Due to Bias of a T-Shaped Field-Effect Transistor

A T-shaped field-effect transistor, made out of a pair of two-dimensional electron gases, is modeled and studied. A simple numerical model is developed to study the electron distribution vs. applied gate voltage for different gate lengths. The model is then improved to account for depletion and the width of the two-dimensional electron gases. The results are then compared to the experimental ones and to some approximate analytical calculations and are found to be in good agreement with them.Comment: 16 pages, LaTex (RevTex), 8 fig

Limit to 2D mobility in modulation-doped GaAs quantum structures: How to achieve a mobility of 100 millions

Considering scattering by unintentional background charged impurities and by charged dopants in the modulation doping layer as well as by GaAs acoustic phonons, we theoretically consider the practical intrinsic (phonons) and extrinsic (background and dopants) limits to carrier mobility in modulation doped AlGaAs-GaAs 2D semiconductor structures. We find that reducing background impurity density to $10^{12}$ cm$^{-3}$ along with a modulation doping separation of 1000 \AA or above will achieve a mobility of $100 \times 10^6$ cm$^2$/Vs at a carrier density of $3\times 10^{11}$ cm$^{-2}$ for T=1K. At T=4 (10)K, however, the hard limit to the 2D mobility would be set by acoustic phonon scattering with the maximum intrinsic mobility being no higher than 22 $(5) \times 10^6$ cm$^2$/Vs. Detailed numerical results are presented as a function of carrier density, modulation doping distance, and temperature to provide a quantitative guide to experimental efforts for achieving ultra-high 2D mobilities.Comment: 6 pages, 6 figure

Formation of a high quality two-dimensional electron gas on cleaved GaAs

We have succeeded in fabricating a two-dimensional electron gas (2DEG) on the cleaved (110) edge of a GaAs wafer by molecular beam epitaxy (MBE). A (100) wafer previously prepared by MBE growth is reinstalled in the MBE chamber so that an in situ cleave exposes a fresh (110) GaAs edge for further MBE overgrowth. A sequence of Si-doped AlGaAs layers completes the modulation-doped structure at the cleaved edge. Mobilities as high as 6.1×10^5 cm^2/V s are measured in the 2DEG at the cleaved interface