Abstract
Motivated by recent advances in the fabrication of Josephson junctions in which the weak link is made of a low-dimensional non-superconducting material, we present here a systematic theoretical study of the local density of states (LDOS) in a clean 2D normal metal (N) coupled to two s-wave superconductors (S). To be precise, we employ the quasiclassical theory of superconductivity in the clean limit, based on Eilenberger's equations, to investigate the phase-dependent LDOS as function of factors such as the length or the width of the junction, a finite reflectivity, and a weak magnetic field. We show how the the spectrum of Andeeev bound states that appear inside the gap shape the phase-dependent LDOS in short and long junctions. We discuss the circumstances when a gap appears in the LDOS and when the continuum displays a significant phase-dependence. The presence of a magnetic flux leads to a complex interference behavior, which is also reflected in the supercurrent-phase relation. Our results agree qualitatively with recent experiments on graphene SNS junctions. Finally, we show how the LDOS is connected to the supercurrent that can flow in these superconducting heterostructures and present an analytical relation between these two basic quantities.
Highlights
If a normal metal (N) is in good electrical contact with a superconductor (S), it can acquire genuine superconducting properties
The main feature of the local density of states (LDOS) is the presence of Andreev bound states (ABSs) inside the gap that evolve with the phase difference
In the case of perfect transparency, and with the help of Eqs. (15) and (16), one can show that the energies of the ABSs for a single trajectory are given by the solutions of the following well-known equation [6]: 2E L
Summary
If a normal metal (N) is in good electrical contact with a superconductor (S), it can acquire genuine superconducting properties. The proximity effect manifests itself in a modification of the local density of states (LDOS) of the normal metal and it is mediated by the so-called Andreev reflection [5]. When the normal metal is sandwiched between two superconducting leads, multiple Andreev reflections can occur at the SN interfaces leading to the formation of Andreev bound states (ABSs) inside the gap region [6]. These ABSs are, in turn, largely responsible for the supercurrent that can flow through the superconductor–normal metal–superconductor (SNS) junction when there is a finite
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