Nonequilibrium Zero-Bias Anomaly in Disordered Metals

Abstract

The non-equilibrium zero bias anomaly (ZBA) in the tunneling density of states of a diffusive metallic film is studied. An effective action describing virtual fluctuations out-of-equilibrium is derived. The singular behavior of the equilibrium ZBA is smoothed out by real processes of inelastic scattering.PACS numbers: 73.40.Gk, 73.50.Td The suppression of tunneling current at low bias due to electron-electron interaction is known as the zero bias anomaly (ZBA). The theory of ZBA for disordered metals at thermal equilibrium has been developed, on a perturbative level, by Altshuler and Aronov [1,2]. The nonperturbative generalization of this theory was achieved by Finkelstein [3]. Measurements of the tunneling density of states (DOS) in biased quasi-one-dimensional wires [4] call for an extension of the theory to non-equilibrium setups. In this work we study the ZBA for disordered metallic films out of equilibrium, in both the perturbative and the non-perturbative (in interaction) limits.Besides the experimental motivation, the problem of ZBA in a non-equilibrium system is of fundamental theoretical interest. At equilibrium, the distribution of electrons in phase space has a single edge at the Fermi surface. The Coulomb interaction between the tunneling electron and the electrons in the Fermi sea excites virtual particle-hole pairs around the Fermi edge, leading to the suppression of the tunneling DOS, similarly to the Debye-Waller factor. The suppression gets stronger when the electron energy approaches the Fermi energy. Out of equilibrium, the distribution of particles may have several sharp edges rather than a single one at the Fermi surface, which poses important questions addressed in this work: How will the excitation of electron-hole pairs in this situation affect the tunneling DOS? Will there be an interpaly between the two edges? We show that the two edges are not independent: one edge affects the ZBA near the other via real interaction-induced scattering processes governing the dephasing of electrons in the non-equlibrium regime. From this point of view the problem we are considering is a representive of a class of phenomena that involve renormalization away from thermal equilibrium, such as the Fermi edge singularity [5] and the Kondo effect [6].What makes the ZBA particularly interesting is its deep connection to various conceptually important phenomenological ideas. At equilibrium, the nonperturbative results [3] have been reproduced by quantum hydrodynamical methods [7], and, within the framework of the theory of dissipation [8], by methods that rely on the fluctuation-dissipation theorem. Our work

Theory of the nonequilibrium electronic Mach-Zehnder interferometer

“…(20). One can show that taking into account corrections of order τ 2 which follow from the exact non-linear equation of motion would lead to a contribution of order τ 4 to the tunneling action.…”

Relaxation processes in a disordered Luttinger liquid

“…A conceptually similar formalism has been applied earlier for higher-dimensional disordered conductors in the study of the single-particle density of states out of equilibrium in Ref. [33]. The nonequilibrium tunneling density of states in the clean LL has been considered within the functional bosonization approach in Ref.…”

Universal Dephasing in a Chiral 1D Interacting Fermion System

“…Using a physically transparent semiclassical ansatz, we find a power-law decay of the coherence at high energies and zero temperature (T = 0), with a universal asymptotic exponent of 1, independent of the interaction strength. We obtain the dephasing rate at T > 0 and the fluctuation spectrum acting on an electron.Studying the loss of quantum coherence is important both for fundamental reasons (quantum-classical transition, measurement process, equilibration) and with regard to possible applications of quantum mechanics (interferometry, quantum information processing).Dephasing of electrons in Luttinger liquids is interesting as an example of a non-perturbative, strongly correlated model case [1,2,3,4,5,6]. In contrast, the situation for (spinless) chiral interacting fermion systems, such as edge states in the integer quantum Hall effect (QHE), seems to be clear.…”

“…Dephasing of electrons in Luttinger liquids is interesting as an example of a non-perturbative, strongly correlated model case [1,2,3,4,5,6]. In contrast, the situation for (spinless) chiral interacting fermion systems, such as edge states in the integer quantum Hall effect (QHE), seems to be clear.…”