Effect of Disorder on the Quantum Coherence in Mesoscopic Wires

We present phase coherence time measurements in quasi-one-dimensional mesoscopic wires made from high mobility two-dimensional electron gas. By implanting gallium ions into a $\mathrm{GaAs}/\mathrm{AlGaAs}$ heterojunction we are able to vary the diffusion coefficient over 2 orders of magnitude. We show that in the diffusive limit, the decoherence time follows a power law as a function of diffusion coefficient as expected by theory. When the disorder is low enough so that the samples are semiballistic, we observe a new and unexpected regime in which the phase coherence time is independent of disorder. In addition, for all samples the temperature dependence of the phase coherence time follows a power law down to the lowest temperatures without any sign of saturation and this strongly suggests that the frequently observed low temperature saturation is not intrinsic.

Figure 1

Magnetoconductance curves of 2DEG wires with $w=1130\mathrm{nm}$ for (a) $D=290{\mathrm{cm}}^2/\mathrm{s}$ ($l_e=0.34\mu \mathrm{m}$) and (b) $3500{\mathrm{cm}}^2/\mathrm{s}$ ($4.0\mu \mathrm{m}$) at different temperatures. The broken lines show theoretical fits to weak localization theory for (a) the diffusive and (b) the semiballistic regimes.

Figure 2

Phase coherence length $L_{\varphi }$ for different $D$ as a function of $T$ ($w=1130\mathrm{nm}$). The solid lines are the best fits with Eq. (3) adding an extra term $\propto T^{-1}$ for high energy processes [16]. The open and closed symbols are used for the semiballistic and diffusive regimes, respectively. The inset shows 2DEG wires with $W=1500\mathrm{nm}$ and a Hall bar.

Figure 3

Phase coherence length $L_{\varphi }$ as a function of $D$ ($w=1130\mathrm{nm}$) at a temperature of $T=60\mathrm{mK}$. The solid and broken lines represent $D^{1/2}$ and $D^{2/3}$ laws, respectively.

Figure 4

Top figure shows the experimental coefficients $a_{\exp }$ of Eq. (3) scaled by ${\alpha }_{\mathrm{AAK}}$ as a function of $D$. The dashed line represents $D^{-1/3}$. The experimental values of $k_F{l}_e$ are shown in the bottom part of the figure.