Filled Landau Levels Research Articles

Excitations from a filled Landau level in the two-dimensional electron gas

We consider an interacting two-dimensional electron system, with a uniform positive background, in a strong perpendicular magnetic field at zero temperature, under conditions where an integral number of Landau levels are filled and the Coulomb energy $\frac{{e}^{2}}{\ensuremath{\epsilon}{l}_{0}}$ is smaller than the cyclotron energy $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$. The elementary neutral excitations may be described alternatively as magnetoplasma modes, or as magnetic excitons---i.e., a bound state of a hole in a filled Landau level and one electron in an otherwise empty level---and they are characterized by a conserved wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$. The dispersion relations may be calculated exactly, to first order in $\frac{\frac{({e}^{2}}{\ensuremath{\epsilon}{l}_{0})}}{\ensuremath{\hbar}{\ensuremath{\omega}}_{c}}$, for the lowest magnetoplasmon band, which comes in to the cyclotron frequency at $k=0$. We also calculate the spin-wave dispersion relations for the case where one spin state of a Landau level is completely occupied, and we discuss qualitatively the exciton spectrum for a partially filled Landau level, under the conditions of the fractional quantized Hall effect.

Hall potential distribution in a thin layer as a function of its thickness

A self-consistent equation is derived for the Hall potential distribution of an electron gas with filled Landau levels in a thin layer taking into account its thickness and the magnetic field Bj generated by the current distribution inside the layer. It is found that for parameter values corresponding to quantum Hall effect experiments the weighting of the potential distribution toward the layer edges is considerably reinforced due to the field Bj. This effect increases with decreasing layer thickness.

Thermopower measurements on the two-dimensional electron gas of GaAs-Al xGa 1−xAs heterostructures

Thermopower measurements on GaAs-Al x Ga 1− x As heterostructures show that the Seebeck coefficient α xx oscillates as a function of magnetic field with peak values α max xx at half filled Landau levels. On devices with mobilities higher than μ = 41 × 10 3 cm 2 V · s , a temperature-independent value of α max xx ≈ 40 μ V K is found at helium temperatures (2 < T < 5 K) for the Landau quantum number N L = 1. However, on a sample with lower mobility (μ = 24 × 10 3 cm V·s ) , α max xx decreases with decreasing temperature and reaches a value of about 31 μ V K at T = 2.8 K. The α xy component shows a complicated oscillating behavior and changes within the experimental range ν > 2 (ν = filling factor) its sign at magnetic fields close to the filling factor ν = 3. In the plateau region of the quantized Hall resistance both α xx and α xy tend to zero.

DHVA magnetic susceptibility of a 2D free electron gas

The grand potential and energy of a noninteracting uncorrelated two-dimensional electron gas subject to Landau quantization in a magnetic field are examined here at low temperatures. The DeHaas-Van Alphen oscillatory magnetic susceptibility for the free 2D gas is calculated and the results presented here incorporate the effects of spin (by allowing that spin splitting may not, in general, equal Landau level separation) in formulae that have the same analytic structure for both even and odd numbers of filled Landau levels.

Novel features of quantum Hall plateaus for varying interface charge

A systematic study of quantum Hall plateaus has been made in Si metal-oxide-semiconductor field-effect transistors having driftable ${\mathrm{Na}}^{+}$ ions. For low interface ion densities (${N}_{\mathrm{ox}}\ensuremath{\lesssim}2\ifmmode\times\else\texttimes\fi{}{10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}2}$) the positions of plateaus for filled spin and valley levels exhibit unexpected shifts with respect to those for completely filled Landau levels, and the widths of plateaus for filled Landau levels increase more rapidly with interface charge than do those for filled spin and valley levels. These results have interesting implications for features of the density of states of the system and for aspects of interface electron scattering.

Theory of quantized Hall effect at low temperatures

At millikelvin temperatures the quantized Hall effect (QHE) is characterized by sharp steps connecting the quantized Hall resistance plateaus. We explain this behavior on the basis of the single-electron approximation and continuum percolation theory. It is shown that even when the magnetic field corresponds to partially filled Landau level on average, locally the sample breaks into patches having the occupation numbers 0 or 1. This represents a peculiar type of the metal-insulator transition, driven by disorder. Extended (global) electron states may not exist at equilibrium or arbitrarily small applied voltage $V$. Global states begin to appear at a certain critical voltage ${V}_{\mathrm{cr}}$, which is of the order of characteristic magnitude of potential fluctuations on the scale of the sample size. For small $V&gt;{V}_{\mathrm{cr}}$ the fraction of global states is still small owing to the smallness of the average electric field compared with the fluctuating field in the inversion layer. Because of this, transitions between the QHE plateaus require only a minor change in the density of states and at $T=0$ they occur in small intervals of the magnetic field. Owing to the tail of the Fermi-Dirac distribution at nonzero $T$ the deviation of the Hall conductivity from its nearest quantized value, $(\frac{{e}^{2}}{h})\ifmmode\times\else\texttimes\fi{}\mathrm{integer}$, is activated. This explains the plateau flatness and the high precision of the QHE measurements of the fine-structure constant.