Theory of the sign of multi-probe conductances for normal and superconducting materials

Allsopp, N. K.; Hui, Victor; Lambert, Colin J.; Robinson, S. J.

doi:10.1088/0953-8984/6/48/009

Cited by 24 publications

(31 citation statements)

References 19 publications

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“…In contrast with the normal case however, the 'conductances' G i j (i = j) are not necessarily positive. Furthermore, as noted in Refs [20,21]…”

mentioning

confidence: 78%

“…The a i j values are linear combinations of the normal and Andreev scattering coefficients and in the absence of superconductivity satisfy As an aid to comparing transport coefficients in the normal and superconducting states, it is convenient to eliminate v from eqn (1) by the following procedure suggested in Refs [20,21], which yields…”

mentioning

confidence: 99%

“…Setting I 1 = −I 2 = I , I 3 = I 4 = 0 and solving eqn (2) for the four-probe conductance yields [20] …”

mentioning

confidence: 99%

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

Seviour

Lambert

Leadbeater

1999

Superlattices and Microstructures

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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].

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“…In contrast with the normal case however, the 'conductances' G i j (i = j) are not necessarily positive. Furthermore, as noted in Refs [20,21]…”

mentioning

confidence: 78%

mentioning

confidence: 99%

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

Seviour

Lambert

Leadbeater

1999

Superlattices and Microstructures

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“…More generally I 1 and I 2 will have opposite signs whenever Andreev transmission dominates normal transmission. As noted in ref 20 , this can occur even if the current carrying wires are not ferromagnetic.In the absence of a normal region in front of the superconductor (ie L = 0) and in the presence of tunnel junctions at the F-S interfaces, the analysis of ref predicts that both I 1 and I 2 decay as exp −(2L/πξ), where ξ is the superconducting coherence length. To analyze this structure for finite L we solve the Bogoliubovde Gennes equation on a square tight binding lattice and compute the scattering matrix using an exact recursive Green's function technique.…”

mentioning

confidence: 81%

Non-local current correlations in ferromagnet/superconductor nanojunctions

Lambert¹,

Koltai²,

Cserti³

2003

Toward the Controllable Quantum States

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When two fully polarized ferromagnetic (F) wires with opposite polarizations make contact with a spin-singlet superconductor, a potential-induced current in wire 1 induces a non-local current of equal magnitude and sign in wire 2. The magnitude of this current has been studied in the tunneling limit and found to decay exponentially with the distance between the contact. In this paper we propose a new structure in which this novel non-local effect is increased by orders of magnitude. We study the spin-dependent electronic transport of a diffusive nanojunction and demonstrate that when a normal diffusive region is placed between the F leads and superconductor, the non-local initially increases with the separation between the F leads, achieving a maximum and decays as a power law with increasing separation.Experimental studies of electronic transport properties of nanostructures containing both ferromagnets (F) and superconductors (S) 1,2,3,4,5,6,7,8,9,10,11 . reveal novel features, not present in normal-metal/superconductor (N/S) junctions, due to the suppression of electron-hole correlations in the ferromagnet. When spin-flip processes are absent, further effects are predicted, including the suppression of the conventional giant magnetoresistance ratio in diffusive magnetic multilayers 12 and the appearance of non-local currents when two fully polarized ferromagnetic (F) wires with opposite polarizations make contact with a spin-singlet superconductor 13,14 . The latter effect has been highlighted, because of interest in the possibility of generating entangled pairs of electrons at a superconductor (S) interface 15,16,17 . A recent study of such a junction in the tunneling limit predicts that the magnitude of the non-local current will decrease exponentially with the distance between the F contacts. It is therefore of interest to ask how the magnitude of this novel effect can be enhanced.In this paper we propose a hybrid nanostructure in which the non-local current is enhanced by orders of magnitude compared with the geometry of ref.13 . The proposed structure is sketched in figure 1 and comprises two clean F wires, each of width M f , separated by a distance M , in contact with a diffusive, normal metallic region of area A = L.(2M f + M ), which in turn makes contact with a spin-singlet superconductor.In the linear response limit, the current-voltage relation of a such a hybrid structure connected by non-superconducting wires to normal reservoirs was first presented in ref 18 . If I 1 , I 2 are the currents leaving reservoirs 1 and 2, and v 1 , v 2 1 their respective voltages, then at zero temperatureandwhere v is the condensate potential. In this expression R 0 is the coefficient for an electron from reservoir 1 to be reflected as an electron back into reservoir 1, while T 0 is the coefficient for an electron from reservoir 1 to be transmitted as an electron into reservoir 2. R a is the coefficient for an electron from reservoir 1 to be Andreev reflected as a hole into wire 1 and T a is the coefficient for an e...

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“…The a ij 's are linear combinations of the normal and Andreev scattering coefficients and in the absence of superconductivity satisfy Setting I 1 = −I 2 = I and solving equation 1 for the 2 probe conductance yields [15],…”

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confidence: 99%

Transport across a normal-superconducting interface: a novel probe of electron-electron interactions in the normal metal

Dolby

Seviour

Lambert

2001

J. Phys.: Condens. Matter

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In this letter, we examine the effect of Coulomb interactions in the normal region of a normalsuperconducting (N/S) mesoscopic structure, here the change from an attractive to a repulsive coulombic interaction, at the N/S interface, causes a shift in the order parameter phase. We show that this shift has a pronounced effect on Andreev bound states and demonstrate that the effect on Andreev scattering of non-zero order-parameter tails, can be used to probe the sign of the interaction in the normal region.Recent advances in material technology have enabled the fabrication of normal/superconducting (N/S) mesoscopic hybrid structures with well defined dimensions and interfaces [1][2][3][4]. Due to the proximity of the normal material to the superconductor the pairing field f (x) = ψ ↑ (x)ψ ↓ (x) , in the normal region, decays to zero on the scale of a coherence length ξ [5]. During the past decade this proximity effect has been extensively investigated both experimentally and theoretically (see for example [6][7][8][9]).In contrast to the pairing field f (x), the effective electron-electron interaction, V (x), changes abruptly at the S/N interface, from an attractive interaction in the superconductor to either zero, a much diminished attractive interaction or to a repulsive interaction, in the normal (N) material. Consequently the order parameter, ∆ = V (x)f (x), of a s-wave superconductor also changes abruptly at the S/N interface, as shown in figure 1. To date theoretical research into the transport properties of N/S interfaces have mainly considered the order parameter in the normal region to be zero (figure 1a) [10,11].In this letter we consider the effect of an attractive or repulsive electron-electron interaction (V (x) = 0), as shown in 1b and 1c. The difference between figures 1b and 1c is the π phase shift in ∆(x), induced by the cross-over from an attractive to a repulsive interaction at the N/S interface. In what follows we examine how this phase shift affects the transport properties associated with Andreev bound states.To investigate this regime we adopt a general scattering approach to dc transport, which was initially developed to describe phase-coherent transport in dirty mesoscopic superconductors [12]. For simplicity in this letter, we focus solely on the zero-voltage, zero-temperature conductance, for the structure shown in figure 2. In the linear-response limit, at zero temperature, the conductance of a phase-coherent structure may be calculated from the fundamental current voltage relationship [13,14],The above expression relates the current I i from a normal reservoir i to the voltage differences (v j − v), where v = µ/e and the sum is over the 2 normal leads connected to the scattering region. The a ij 's are linear combinations of the normal and Andreev scattering coefficients and in the absence of superconductivity satisfy where G is the conductance in units ofh . As noted in [15] the various transmission and reflection coeffcients can be computed by solving the Bogoliubov -de Gennes equatio...

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Theory of the sign of multi-probe conductances for normal and superconducting materials

Cited by 24 publications

References 19 publications

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

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

Non-local current correlations in ferromagnet/superconductor nanojunctions

Transport across a normal-superconducting interface: a novel probe of electron-electron interactions in the normal metal

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