Zero-Bias Transport Anomaly in Metallic Nanobridges

Abstract

It is well known that in bulk metals and semiconductors with diffusive transport the electron-electron interaction causes an anomaly in the electronic density of states (DOS) at the Fermi level. As explained by Aronov and Al’tshuler (A-A) in the 1980s [1, 2], this correction is induced by the long-range, retarded character of the dynamically screened Coulomb interaction in a diffusive system. It has been observed in thermodynamic equilibrium by tunneling spectroscopy on disordered metals [3, 4]. In the present article we address the question how this anomaly is modified in a nanoscopic sample or metal bridge whose size L is smaller than the dephasing length L _ϕ (and all inelastic relaxation lengths) and which is driven out of equilibrium by a finite bias voltage U applied between the ends of the sample. Since in such a situation energy relaxation is negligible for electrons traversing the system, no local equilibrium is reached at any point in the bridge. Rather, the electron liquids penetrating from the left and right leads into the bridge remain at their respective electrochemical potentials μ _L and μ _R . Consequently, the quasiparticle distribution function is a linear superposition of Fermi distributions in the left and right leads and displays a doublestep form (see Fig. 1). This fact has been claimed theoretically [5] and has recently been observed experimentally by tunneling spectroscopy [6] (where in addition the steps were rounded due to interactions in long wires). It should be distinguished from the hot-electron regime [7], where local thermalization in a current-carrying system occurs.