Probing the sensitivity of electron wave interference to disorder-induced scattering in solid-state devices

The study of electron motion in semiconductor billiards has elucidated our understanding of quantum interference and quantum chaos. The central assumption is that ionized donors generate only minor perturbations to the electron trajectories, which are determined by scattering from billiard walls. We use magnetoconductance fluctuations as a probe of the quantum interference and show that these fluctuations change radically when the scattering landscape is modified by thermally induced charge displacement between donor sites. Our results challenge the accepted understanding of quantum interference effects in nanostructures.

Figure 1

Schematics of (a) GaAs/(AlGa)As and (b) (GaIn)As/InP billiards. The 2DEG (white) is located near the lower GaAs/(AlGa)As interface for (a) and in the (GaIn)As layer for (b). The modulation doping (red) consists of a 40-nm (AlGa)As layer with a Si donor density of $1.2\times {10}^{18}$ cm${}^{-3}$ for (a) and a 1-nm InP layer with a Si density of $5\times {10}^{18}$ cm${}^{-3}$ for (b). The billiard walls (light blue) are defined by surface gates (yellow) in (a) and by etched trenches in (b). The heterostructure in (b) has a uniform top gate separated from the surface by a 1-$\mu$m insulating layer (not shown). (c) Simulation of the energy band structure for the GaAs/(AlGa)As heterostructure, plotting the conduction band edge $E_C$ v. distance from the 2DEG. (d) Magnetoconductance traces for a 1-$\mu$m (GaIn)As/InP billiard measured at temperatures $T$ of (top to bottom) 12 K, 5 K, 1 K, and 240 mK. The traces are offset for clarity. Inset: A plot of the electron phase coherence length ${\ell }_{\phi }$ as a function of $T$, and associated fit line, for the (GaIn)As/InP billiard.

Figure 2

Comparison of MCF for the (GaIn)As/InP billiard after being warmed to three intermediate temperatures $T_i$. Top to bottom, the $T_i$ values for the pairs of traces are 300 K, 115 K, and 240 mK. The traces are offset for clarity. Top: Magnified comparison of traces taken with $T_i$ $=$ 115 K (lower [black] and middle [green]) and $T_i$ $=$ 300 K (lower [black] and upper [red]).

Figure 3

Comparison of MCF for the GaAs/(AlGa)As billiard after being warmed to three intermediate temperatures $T_i$. Top to bottom, the $T_i$ values for the pairs of traces are 300 K, 115 K, and 240 mK. The traces are offset for clarity. Top: Magnified comparison of traces taken with $T_i$ $=$ 115 K (lower [black] and middle [green]) and $T_i$ $=$ 300 K (lower [black] and upper [red]).

Figure 4

A plot of $F$ v. $T_i$ for the GaAs wire (red circles), the (GaIn)As/InP billiard (light blue squares), and the GaAs/(AlGa)As billiard (green diamonds). The insets show the annealing function's form as $\beta$ and $\eta$ are varied (see text).

Figure 5

A plot of $F$ (left axis) v. $T_i$ (bottom axis) for the (GaIn)As/InP billiard (light blue squares), as well as $n_{\text{norm}}$ (right axis) v. $T$ (top axis) for the (GaIn)As/InP billiard (blue crosses). The decorrelation data for the (GaIn)As/InP are identical to those shown in Fig. 4.