Large-scale superconductivity-induced conductance suppression in mesoscopic normal–superconducting structures

Abstract

Experiments on hybrid superconducting normal-metal structures have revealed that even in the absence of tunnel junctions the onset of superconductivity can lead to a decrease in the electrical conductance by an amount many orders of magnitude greater than e 2 / h. In this paper, we provide a theory of this phenomenon which shows that it originates from an instability in the four-probe conductance which is absent from two-probe measurements. We compare the zero-bias, zero-temperature four-probe conductances G N and G S of a normal diffusive metal in contact with a superconductor in both the normal (N) and superconducting (S) states, respectively. In the absence of tunnel barriers, the ensemble average of the difference δG = G S − G N vanishes, in agreement with quasiclassical theory. However, we also predict that there exist macroscopic sample specific fluctuations in δG, which lie beyond quasiclassical theory and allow large negative values of δG to occur.c 1999 Academic Press Key words: mesoscopic, superconductivity.During the past few years, studies of the subgap conductance of hybrid normal/superconductor (NS) structures have led to the identification of a small number of paradigms of phase-coherent transport. The earliest of these is the zero-bias anomaly observed in normal/insulator/superconductor (NIS) structures [1] and the related finite bias anomaly found in NS structures with clean interfaces. At high temperatures T > T * and bias voltages V > V * , where for an N-metal of length L and diffusion coefficient D,, the conductances of both types of structure vary as 1/ √ T and 1/ √ V . For a clean interface there also exists a conductance maximum at V * , T * and therefore at low temperatures and voltages a re-entrance to the low-conductance state occurs [2,3]. This re-entrance phenomenon is also observed in a second paradigm of phase-coherent transport, which arises when a normal metal is in contact with two superconductors, whose order parameter phase difference φ can be varied by some external means. In this case, the conductance is an oscillatory function of φ, with an amplitude which typically exhibits a maximum at T * and V * [2,[4][5][6][7][8][9][10]. Unlike the Josephson current which decays exponentially with T /T * , such conductance oscillations decay only as a power law. A third signature of phase-coherent transport is the long-range nature of these effects, which typically decay as a power law in L/L * , where L * = √ (D/eV ).This behaviour is in sharp contrast with the exponential decay of the Josephson effect and has been observed in a number of experiments [11,12].

Phase-coherent transport in hybrid superconducting nanostructures

“…A key prediction of [Wilhelm et al 1997] is that at zero bias and zero temperature this effect should vanish and the conductance should be unchanged by the onset of superconductivity. In contrast [Seviour et al 1997] identify an additional large-scale effect due to weak localisation, which is not contained in standard quasi-classical theory and which will survive at zero-temperature and zero-bias.…”

“…Although superconductivity-induced conductance suppression in metallic samples was predicted a number of years ago [Hui and Lambert, 1993(b)] these experiments at first sight appeared to conflict with quasi-classical theories, which universally predict that the normal-state, zerotemperature, zero-bias conductance G N is identical the conductance G N S in the superconducting state. This effect is addressed in [Hui and Lambert 1993b, Claughton et al 1995, Seviour et al 1997.…”

“…The first of these reported an increase in resistance in metallic conductors due to the onset of superconductivity and the second the discovery of a zero-bias anomaly in the dc resistance of a superconductor -semiconductor (S-Sm) contact. The former is still the subject of theoretical investigation [Wilhelm et al 1997, Seviour et al 1997, while the latter is now well-understood.…”

Conductance suppression in normal-metal–superconductor mesoscopic structures

“…͑18͒, exact results for the dc conductance can be obtained. 22,41,44 In the zero bias, zero temperature limit, Eq. ͑17͒ is greatly simplified and reduces to…”

“…The authors of Refs. 21,22 showed that the quantity R ab ϭV b /I a may exhibit an increase below T cs compared with its normal state value. In this geometry the spatial distribution of the current is nonuniform.…”