^{1}, Sean Byrnes

^{1}, Sergey Vitkalov

^{1,a)}, A. V. Goran

^{2}and and A. A. Bykov

^{2}

### Abstract

Quantum oscillations of dissipative resistance are observed in response to electric current applied to a GaAs quantum well with variable two dimensional electron density placed in quantizing magnetic fields. At a fixed magnetic field, the period of the current induced oscillations depends linearly on the electron density. The observed behavior is in accord with a recently proposed model that considers the DC bias-induced spatial re-population of Landau levels as the origin of the resistance oscillations. It indicates the important role of the electron screening in the vicinity of the quantum well, which significantly enhances the nonlinear response.

Work was supported by National Science Foundation (DMR 1104503) and the Russian Foundation for Basic Research, Project No. 12-02-31709.

I. INTRODUCTION

II. EXPERIMENTAL SETUP

III. MODEL

IV. RESULTS AND DISCUSSION

V. CONCLUSION

### Key Topics

- Electric currents
- 21.0
- Electrical resistivity
- 16.0
- Magnetic fields
- 16.0
- Direct current power transmission
- 11.0
- Quantum wells
- 10.0

## Figures

(a) Schematic diagram of GaAs quantum well with AlAs/GaAs short-period superlattice barriers. The two lower plots show the Fermi energy level *E _{F} *, the edges of the conduction band and

*U*and the density distributions of Γ and

_{X}*X*electrons. (b) Approximation of the structure shown in (a) by an “effective” capacitor.

^{ 25 }Two dimensional electron gas (2DEG) is sandwiched between two screening superlattices (SL) placed at an effective distance

*d*from the 2D electron gas. The SL layers screen electric charges induced by applied dc bias inside the conducting 2DEG. Placed at a distance

_{eff}*d*gate controls the averaged density

_{gate}*n*across the structure. An antisymmetric application of the dc bias to current leads (not shown) produces an antisymmetric distribution of the Hall potential across 2DEG (y-direction). The potential is induced by an antisymmetric redistribution of the electron density with a net variation . In a general case the electron redistribution and the Hall potential can be quite complex.

^{ 35 }At small dc biases the electric potential is shown in the upper part of the plot.

(a) Schematic diagram of GaAs quantum well with AlAs/GaAs short-period superlattice barriers. The two lower plots show the Fermi energy level *E _{F} *, the edges of the conduction band and

*U*and the density distributions of Γ and

_{X}*X*electrons. (b) Approximation of the structure shown in (a) by an “effective” capacitor.

^{ 25 }Two dimensional electron gas (2DEG) is sandwiched between two screening superlattices (SL) placed at an effective distance

*d*from the 2D electron gas. The SL layers screen electric charges induced by applied dc bias inside the conducting 2DEG. Placed at a distance

_{eff}*d*gate controls the averaged density

_{gate}*n*across the structure. An antisymmetric application of the dc bias to current leads (not shown) produces an antisymmetric distribution of the Hall potential across 2DEG (y-direction). The potential is induced by an antisymmetric redistribution of the electron density with a net variation . In a general case the electron redistribution and the Hall potential can be quite complex.

^{ 35 }At small dc biases the electric potential is shown in the upper part of the plot.

(a) Longitudinal resistance *R _{xx} * shown versus gate voltage

*V*. Open circles present the experimental data. Solid line is a spline interpolation, B = 1.95 (T); (b) Hall resistance

_{g}*R*shown versus magnetic field B for varying gate voltages as labeled. (c) Dependence of the electron density on the gate. Open squares present electron density obtained from the slope of the magnetic field dependence of the Hall resistance shown in (b). Solid line presents the electron density obtained from the Hall resistance measured at a fixed magnetic field B = 0.89 (T) and varying gate voltage. T = 5 K.

_{xy}(a) Longitudinal resistance *R _{xx} * shown versus gate voltage

*V*. Open circles present the experimental data. Solid line is a spline interpolation, B = 1.95 (T); (b) Hall resistance

_{g}*R*shown versus magnetic field B for varying gate voltages as labeled. (c) Dependence of the electron density on the gate. Open squares present electron density obtained from the slope of the magnetic field dependence of the Hall resistance shown in (b). Solid line presents the electron density obtained from the Hall resistance measured at a fixed magnetic field B = 0.89 (T) and varying gate voltage. T = 5 K.

_{xy}(a) Contour plot showing longitudinal differential resistance as a function of gate voltage and DC bias. (b) Horizontal cuts of the contour plot in (a) taken at different gate voltages as labeled. B = 1.95 (T). T = 5 (K).

(a) Contour plot showing longitudinal differential resistance as a function of gate voltage and DC bias. (b) Horizontal cuts of the contour plot in (a) taken at different gate voltages as labeled. B = 1.95 (T). T = 5 (K).

(a) Contour plot showing longitudinal differential resistance as a function of electron density and DC bias. (b) Vertical cut of the contour plot showing longitudinal differential resistance versus electron density corresponding to the red dotted line in (a) taken at *I _{dc} * = 0. The differential resistance oscillations demonstrate high periodicity as compared to Fig. 1(a) .

(a) Contour plot showing longitudinal differential resistance as a function of electron density and DC bias. (b) Vertical cut of the contour plot showing longitudinal differential resistance versus electron density corresponding to the red dotted line in (a) taken at *I _{dc} * = 0. The differential resistance oscillations demonstrate high periodicity as compared to Fig. 1(a) .

Longitudinal differential resistance versus DC bias shown for various electron densities labeled from the top down to the bottom. Top (bottom) panel presents data obtained at minima (maxima) of SdH oscillations at . Open circles indicate the resistance maxima used for the analysis in Fig. 6 .

Longitudinal differential resistance versus DC bias shown for various electron densities labeled from the top down to the bottom. Top (bottom) panel presents data obtained at minima (maxima) of SdH oscillations at . Open circles indicate the resistance maxima used for the analysis in Fig. 6 .

DC bias *I* _{0} corresponding to differential resistance peaks labeled by open circles in Fig. 5 are plotted as a function of electron density. Closed (open) circles indicate the differential resistance maxima obtained from the top (bottom) panel in Fig. 5 . Solid straight lines present linear fits drawn in accordance with Eq. (6) . Slopes *m* of these fits are indicated at corresponding lines.

DC bias *I* _{0} corresponding to differential resistance peaks labeled by open circles in Fig. 5 are plotted as a function of electron density. Closed (open) circles indicate the differential resistance maxima obtained from the top (bottom) panel in Fig. 5 . Solid straight lines present linear fits drawn in accordance with Eq. (6) . Slopes *m* of these fits are indicated at corresponding lines.

Dependence of dissipative differential resistance on Hall voltage *V _{H} * and electron density. B = 1.95(T). T = 5 K.

Dependence of dissipative differential resistance on Hall voltage *V _{H} * and electron density. B = 1.95(T). T = 5 K.

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