Quantum interference correction to the shot-noise power in nonideal chaotic cavities

We present analytical results for the leading (weak-localization) quantum interference correction to the shot-noise power in a ballistic chaotic cavity coupled nonideally to two electron reservoirs via leads with an arbitrary number of open scattering channels. The calculations were performed using two independent methods: $S$-matrix diagrammatic perturbation theory and quantum circuit theory. We obtained an unexpected amplification-suppression transition as a function of both the number of open channels and the barriers’ transparencies. The effect results from a subtle combination of temporal and spatial quantum coherence in the electron propagation through the system.

Figure 1

Ladder diagrams contributing to the average shot-noise power. The maximally crossed diagrams that determine the weak-localization correction are obtained by crossing arms in each diagram.

Figure 2

Diagrams showing the transition. (1) In regions (0), (I), and (II) $p^{\text{WL}}$ has, respectively, zero, one, and two sign changes as functions of $a$ in the interval [0,1]; (2) Diagrams $\left(T_1,T_2\right)$ separating positive $(+)$ and negative $(-)$ regions for $a=3/10$ (continuous lines) and $a=6/10$ (dashed lines); (3) Diagram $\left(a,T_2\right)$ separating regions (I) and (II), where $p^{\text{WL}}$ has one and two sign changes as functions of $T_1$, respectively; (4) Positive $(+)$ and negative $(-)$ regions in the $\left(a,T_2\right)$ plane for $T_1=3/10$ (continuous lines) and $T_1=5/10$ (dashed lines); (5) Plots of $p^{\text{WL}}$ showing the sign changes as a function of $a$ for points at each region in diagram (1). (6) Plots of $p^{\text{WL}}$ showing the sign changes as functions of $T_1$ for each region in diagram (3).