Ballistic correction to the density of states in an interacting three-dimensional metal

Abstract

We study the tunneling density of states (DOS) in an interacting disordered three-dimensional metal and calculate its energy dependence in the quasiballistic regime, for the deviation from the Fermi energy, E − EF , exceeding the elastic scattering rate. In this region, the DOS correction originates from the interplay of the interaction and single-impurity scattering. Depending on the distance between the interaction point and the impurity, one should distinguish (i) the smallest scales of the order of the Fermi wavelength and (ii) larger spatial scales of the order of vF /|E − EF |. In two dimensions, the large-scale contribution prevails, resulting in a nearly universal DOS correction. The peculiarity of Friedel oscillations in three dimensions is that the contributions from small and large scales are typically comparable, making the DOS correction sensitive to the details of the interaction and demonstrating a significant particle-hole asymmetry. On the other hand, we show that the non-analytic part of the DOS is determined by large scales and can be expressed in terms of the Fermi-surface characteristics only.

Superconductivity suppression in disordered films: Interplay of two-dimensional diffusion and three-dimensional ballistics

“…This estimate can be easily obtained by cutting the 3D diffusive contribution at the ultraviolet cutoff r ∼ l. However, as shown by Belitz and Kirkpatrick in their study of weaklocalization correction to the conductivity [34], diffusive contributions in the 3D geometry are extended to the ballistic region up to the distances of the order of wavelength and have a relative order of 1/(k F l) rather than 1/(k F l) 2 . Similar extension of the interaction-induced contribution from the diffusive to the ballistic region is also known for the tunneling density of states, both in 2D [35] and 3D geometries [36,37].…”

“…The correction to the tunneling density of states in the 3D ballistic region (|ε| > 1/τ ) was studied in Refs. [36,37] and appeared to be linear in energy and generally asymmetric with respect to the Fermi level. In the case of a point-like interaction, delta-correlated disorder, and parabolic electron spectrum, it is finite only for energies below the Fermi energy and has the form δν ball (ε)/ν 0 ∼ λ|ε|θ(−ε)/(k F l) [37].…”

“…It is convenient to calculate block P (E, E ) in the coordinate representation [37]. Since the electron-electron interaction as well as the disorder correlator are assumed to be point-like, analytical expression contains only one integral over the distance r between the impurity and the interaction point, so we get:…”