Tunable backscattering in quantum Hall systems induced by neighbouring gates

doi:10.1016/S0921-4526(99)02892-6

Physica B: Condensed Matter

Volumes 284–288, Part 2, July 2000, Pages 1728-1729

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Abstract

Using focussed ion beam writing we define an in-plane gate (IPG) modified with a bay. Biasing this IPG modifies on the one hand the edge potential and on the other hand the bay width. The first effect governs the interchannel scattering, the second one the backscattering in general. We measure the longitudinal resistance R_xx(B) for different gate voltages V_Gate. In the quantum regime both effects are responsible for an increased dependence of the R_xx(x)-peaks and especially of the neighbouring spin-split maxima ratio on V_Gate compared to a simple IPG. A structure with a longer slit realized with two neighbouring IPGs is used to examine the backscattering in the bay region.

Introduction

The lateral field effect is a powerful tool to tune the edge potential of two-dimensional electron systems: using focused ion beams insulating lines are patterned, forming in-plane gates (IPG) [1]. For the depletion length holds l_depl∝V_Gate [2] if a gate voltage V_Gate is applied over the IPG. According to Ref. [2] the edge potential depends on the depletion length. Fig. 1(a) shows the measurement of R_xx(B) for a structure with a simple IPG patterned at the side of a Hall bar (Fig. 2(a)). We recognize that the maxima height depends on the applied gate voltage. Also, the spin-up maximum is more influenced by V_Gate than the spin-down maximum that belongs to the same main quantum number (MQN). Heidtkamp et al. [3] explained this by a dependence of the maxima height on the short-range scattering rate between the two innermost edge channels $1/τ_{el}^{in.} : 1/τ_{el}^{in.}$ depends on the spin-dependent energy gap ΔE=γℏω_c between them and on the depletion length l_depl: $1/τ_{el}^{in.} ∝ exp (− const γn_{2D} l_{depl}).$ In our experiments, we study the effect of slightly modified IPG geometries. These modifications lead to a stronger dependence of the maxima height on the gate voltage.

Section snippets

Experiments

The R_xx(B)-peaks depend on the backscattering rate very sensitively. To increase the backscattering rate we added a small bay ( $10 μm$ wide, $30 μm$ deep) (Fig. 2(b)): in the bay, the backscattering rate per unit length is much higher than along the IPG, i.e. the bay yields a non-negligible contribution to R_xx. Furthermore, for the bay region holds $1/τ_{el}^{in.} ∝ exp (− const γn_{2D} ×2×l_{depl})$ (Eq. (1)) because the depletion zone depends on V_Gate at both sides: Thus, the change of R_xx(B) with the gate voltage is

Acknowledgements

We gratefully acknowledge support from DFG-GRK 50, the Evangelisches Studienwerk Haus Villigst and the DFG-GRK 384.

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