Frequency dispersion of photon-assisted shot noise in mesoscopic conductors

We calculate the low-frequency current noise for ac-biased mesoscopic chaotic cavities and diffusive wires. Contrary to what happens for the admittance, the frequency dispersion in noise is determined not by the electric response time (the RC time of the circuit), but by the time that electrons need to diffuse through the structure (dwell time or diffusion time). We find that the derivative of the photon-assisted shot noise with respect to the external ac frequency displays a maximum at the Thouless energy scale of the conductor. This dispersion comes from the slow, charge-neutral fluctuations of the nonequilibrium electron distribution function inside the structure. Our theoretical predictions can be verified with present experimental technology.

Figure 1

Scheme of the system. A chaotic cavity connected to the electrodes through arbitrary coherent scatterers characterized by a set of transparencies $\left\{T_n\right\}$.

Figure 2

Frequency dependence of a differential photon-assisted shot noise in the symmetric chaotic cavity $(G_1=G_2)$ under fixed flux $A=e(V_1^0-V_2^0)∕(\hslash \Omega )$. The magnitude of $dS∕d\Omega$ is normalized to its value at $\Omega =0$. Curve (1) $A=1.0$, (2) $A=2.0$, (3) $A=3.0$, (4) $A=4.0$, and (5) $A=5.0$. For symmetric cavities the curves appear to be independent of the transmission distribution of the contacts.

Figure 3

Flux dependence of the differential photon-assisted shot noise in the symmetric chaotic cavity $(G_1=G_2)$. Curve (1) $\Omega ∕E_{\mathrm{Th}}=0.0$, (2) $\Omega ∕E_{\mathrm{Th}}=0.25$, (3) $\Omega ∕E_{\mathrm{Th}}=0.5$, and (4) $\Omega ∕E_{\mathrm{Th}}=1.0$.

Figure 4

Frequency dependence of the differential photon-noise for a diffusive wire for given values of $A=e{V}^0∕\hslash \Omega$. Here ${ϵ}_{\mathrm{Th}}=\hslash D∕L^2$ and the numerical calculation has been performed with ten nodes. The magnitude of $dS∕d\Omega$ is normalized to its value at $\Omega =0$. Curve (1) $A=1.0$, (2) $A=2.0$, (3) $A=3.0$, and (4) $A=4.0$.