Tunable crossovers for the quantum interference correction to conductance and shot-noise power in chaotic quantum dots with nonideal contacts

We study a large class of tunable crossovers between the three Dyson universality classes for electron transport through chaotic quantum dots with nonideal contacts. We present analytical expressions for the leading quantum interference corrections to both the conductance and the shot-noise power as a function of the transparencies of the contacts and some tunable crossover parameters, such as a perpendicular magnetic field and spin-orbit coupling strengths. Our results apply both to metallic grains with isotropic spin-orbit coupling and to GaAs heterostructures, in which spin-orbit coupling arises from both the asymmetry of the confining potential and crystal inversion asymmetry. We found that, for nonideal contacts and in the absence of spin-orbit coupling, a perpendicular magnetic field can induce a surprising change of sign in the leading quantum interference correction to the shot-noise power. The results for metallic grains are recovered by independent calculations using quantum circuit theory.

Figure 1

Weak-localization correction to the average conductance as a function of the magnetic field parameter $x$ for fixed values of the spin-orbit parameter $a$. The full lines correspond to the isotropic model, while the symbols correspond to the anisotropic model. In both cases, we used ${\Gamma }_1=0.8$, ${\Gamma }_2=0.9$, and $N_2/N_1\approx 0.67$.

Figure 2

Weak-localization correction to the average shot-noise power as a function of the magnetic field parameter $x$ for fixed values of the spin-orbit parameter $a$. The full lines correspond to the isotropic model, while the symbols correspond to the anisotropic model. In both cases, we used ${\Gamma }_1=0.8$, ${\Gamma }_2=0.9$, and $N_2/N_1\approx 0.67$. Note the change of sign in the WL correction as a function of $x$.

Figure 3

Diagrams showing the depletion-amplification transition for $N_2/N_1\approx 0.67$. (a) Diagrams ($x$, $a$) separating positive ($+$) (amplification) and negative ($-$) (depletion) regions for ${\Gamma }_1=1$ with ${\Gamma }_2=0,3$ (continuous lines) and ${\Gamma }_2=0,7$ (dashed lines); (b) positive (+) and negative ($-$) regions in the plane (${\Gamma }_1,{\Gamma }_2$) for $x=2$ with $a=6$ (continuous lines) and $a=10$ (dashed lines); (c) diagram in the plane ($\Gamma$, $x$), obtained by setting ${\Gamma }_1={\Gamma }_2=\Gamma$ and by taking the limit $a\to 0$; (d) diagram similar to (c), obtained by taking the limit $a\to \infty$; (e) diagram in the plane ($\Gamma$, $a$), obtained by setting ${\Gamma }_1={\Gamma }_2=\Gamma$ and by taking the limit $x\to 0$.