Shot Noise in the Chaotic-to-Regular Crossover Regime

We investigate the shot noise for phase-coherent quantum transport in the chaotic-to-regular crossover regime. Employing the modular recursive Green’s function method for both ballistic and disordered two-dimensional cavities, we find the Fano factor and the transmission eigenvalue distribution for regular systems to be surprisingly similar to those for chaotic systems. We argue that, in the case of regular dynamics in the cavity, diffraction at the lead openings is the dominant source of shot noise. We also explore the onset of the crossover from quantum-to-classical transport and develop a quasiclassical transport model for shot noise suppression which agrees with the numerical quantum data.

Figure 1

Rectangular quantum billiard with tunable shutters and tunable disorder potential (gray shaded area). Electrons are injected from the left into the cavity region of size $A=2d^2$, width $2d$, and height $d$. Tuning the opening of the shutters $w$ and the strength of the disorder potential $V_0$, the onset of the crossover from quantum-to-classical and chaotic-to-regular scattering can be investigated, respectively.

Figure 2

(a) Fano factor $F$ for the cavity depicted in Fig. 1 as a function of the shutter opening ratio $w/d$. Curves for different disorder amplitudes: $V_0/E_{\mathrm{F}}=0.1$ (■), 0.07 (□), 0.05 (●), 0.03 (○), 0.015 (▲), 0 (△). (b) Fano factor as a function of the disorder amplitude $V_0$. Curves for different shutter openings: $w/d=0.1$ (■), 0.2 (□), 0.3 (●), 0.4 (○), 0.5 (▲), 0.55 (△). Insets of (a) and (b) depict the fit parameter-free prediction with diffractive corrections [Eq. (5)]. (c) Distribution of transmission eigenvalues $\rho (T)$ for different values of $w$: $w/d=15$ (▼), 50 (▽), and $V_0/E_{\mathrm{F}}=0$ (▼), 0 (▽). (d) $\rho (T)$ for different values of $V_0$: $V_0/E_{\mathrm{F}}=0.1$ (◆), 0 (⋄) and $w/d=50$ (◆), 50 (⋄).

Figure 3

(a) Fano factor $F$ for scattering systems with chaotic (stadium) and regular (circle, rectangle) classical dynamics as a function of $k_{\mathrm{F}}$, in units of the number of open modes $N=\mathrm{int}(k_{\mathrm{F}}b/\pi )$ (each data point is averaged over 200 equidistant $k_{\mathrm{F}}$ values). The inset shows the fit parameter-free prediction with diffractive corrections [see Eq. (5)]. (b)–(d) Distribution of transmission eigenvalues $\rho (T)$ averaged over the $k_{\mathrm{F}}$ range depicted in (a). Remarkably the obtained values for $\rho (T)$ correspond very closely to the RMT prediction ${\rho }^{\mathrm{RMT}}(T)$, irrespective of the chaoticity in the cavity. The insets show the cavity geometries.