Structured energy distribution and coherent ac transport in mesoscopic wires

Electron energy distribution in a mesoscopic ac-driven diffusive wire generally is not characterized by an effective temperature. At low temperatures, the distribution has a form of a multistep staircase, with the step width equal to the field energy quantum. Analytic results for the field frequency high and low compared to Thouless energy are presented, while the intermediate-frequency regime is analyzed numerically. Manifestations in the tunneling spectroscopy and noise measurements are discussed.

Figure 1

The energy distribution at the wire midpoint $x=L∕2$, calculated numerically for $\hslash \omega =0.2eU$, for different values of $\omega {\tau }_D$. The height of the $\hslash \omega$ steps is a function of external voltage and other system parameters. The envelope of the staircase structure changes as the frequency of the field increases, demonstrating a crossover from the slow- to the fast-field regime.

Figure 2

Schematic representation of the measurement (Ref. 4), in which the energy distribution in a mesoscopic wire (W) is probed by a tunneling junction between the wire and the superconducting probe (SC). By changing voltage $V$ across the junction, one may scan the energy of tunneling electrons. The ac voltage $U\left(t\right)$ applied between the leads ($L$ and $R$) creates a nonequilibrium energy distribution in the wire.