Anomalous density of states in a metallic film in proximity with a superconductor

Abstract

We investigated the local electronic density of states in superconductor-normal metal (Nb-Au) bilayers using a very low temperature (60 mK) STM. High resolution tunneling spectra measured on the normal metal (Au) surface show a clear proximity effect with an energy gap of reduced amplitude compared to the bulk superconductor (Nb) gap. Within this mini-gap, the density of states does not reach zero and shows clear sub-gap features. We show that the experimental spectra cannot be described with the well-established Usadel equations from the quasi-classical theory.At the contact with a superconductor (S), the Andreev reflection of the electrons from a Normal metal (N) locally modifies the N metal electronic properties, including the local density of states (LDOS) [1]. The precise LDOS spectra depend on the N-S structure geometry, in particular the N metal length, and on the electron transport regime. In a diffusive N-S junction with a N metal shorter than the phase coherence length, one expects a fully opened mini-gap, which remains smaller than the superconductor's energy gap ∆ [2]. In a larger N metal, the LDOS shows, within a pseudo-gap, a linear evolution with the energy, reaching zero precisely at the Fermi level. In the ballistic regime, the same distinction holds between a chaotic (mini-gap) and an integrable (pseudogap) cavity [3]. In general terms, a mini-gap shows up if every electronic state at the Fermi level can couple to the S interface while maintaining quantum phase coherence. The order of magnitude of the energy gap E g is h/τ AR , where τ AR is the characteristic diffusion time before an electron experiences an Andreev reflection. Here, we shall consider the case of diffusive N and S metals brought in contact through a highly transparent interface. Then τ AR ≃ L 2 n /D n and the predicted gap E g is about the Thouless energyhD n /L n 2 , where L n and D n are the length and the diffusion constant of the normal metal.Recently, the LDOS of lateral S-N (Nb-Au) structures was probed with solid tunnel junctions [4] and (very) low temperature STM [5,6]. These studies focused on the pseudo-gap regime in long N metals. Also, a mini-gap was observed in a very thin (20 nm) Au layer on top of a Nb dot [5]. A good agreement with the quasi-classical theory based on the Usadel equations [2] and with the Bogoliubov-de Gennes equations [7] was obtained. In the mini-gap regime, a NbSe 2 crystal covered with a varying thickness of Au was studied by STM at 2.5 K [8] but the temperature did not allow the observation of a fully open mini-gap. Therefore, the mini-gap regime remains to be investigated, in particular its evolution with the normal metal size and the possible presence of states within the gap. A clear distinction between a fully open gap and a pseudo-gap requires a high energy resolution k B T ≪ ∆, which can be achieved only at very low temperatures (T ≪ 1K) and with a large gap ∆.In this paper, we present measurements of the local density of states at the N metal surface of S-N bilayers with a varying N m...

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