Concerning the theory of the Josephson effect in pureSNS junctions

Svidzinsky, A.V.; Antsygina, T. N.; Bratus, E. N.

doi:10.1007/bf00655245

Cited by 48 publications

(40 citation statements)

References 3 publications

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“…For long junctions, we observe an exponential scaling of the current through the [5, 6,10,11]. Note that in graphene v F is a constant, and δE is expected to be independent of the carrier density or the mobility , 17-21], which could be attributed to either underdamped junction dynamics [8,20], or to the self-heating by the retrapping current [1,23].…”

Section: Oct 2016mentioning

confidence: 91%

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Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes

et al. 2016

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We investigate the critical current, I C , of ballistic Josephson junctions made of encapsulated graphene/boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, I C is found to scale as ∝ exp(−k B T /δE). The extracted energies δE are independent of the carrier density and proportional to the level spacing of the ballistic cavity, as determined from Fabry-Perot oscillations of the junction normal resistance. As T → 0 the critical current of a long (or short) junction saturates at al level determined by the product of δE (or ∆) and the number of the junction's transversal modes.1 arXiv:1604.07320v3 [cond-mat.mes-hall] Oct 2016Encapsulated graphene/boron-nitride heterostructures emerged in the past year as a medium of choice for studying proximity-induced superconductivity in the ultra-clean limit [1][2][3][4]. These junctions support the ballistic propagation of superconducting currents across micron-scale graphene channels, and their critical current is gate-tunable across several orders of magnitude. In these devices, a rich phenomenology arises from the interplay of superconductivity with ballistic transport [1], cyclotron motion [2], and even the quantum Hall effect at high magnetic field [4]. In a superconductor -normal metal -superconductor (SNS) junction, single particles in the N region cannot enter the superconductor and therefore experience Andreev reflections at each S-N interface. This results in Andreev bound states (ABS), which are capable of 2 carrying superconducting current across the N region. In long ballistic junctions, the energy spectrum of the ABS is quantized with a level spacing of T is independent of V G . In the case of long ballistic graphene junctions, the inverse slope δE is expected to be independent of the carrier density and inversely proportional to L.In this work we study several ballistic junctions of different length and demonstrate that the temperature dependence of the critical current dramatically differs in the long and short regimes. For long junctions, we observe an exponential scaling of the current through the [5, 6,10,11]. Note that in graphene v F is a constant, and δE is expected to be independent of the carrier density or the mobility , 17-21], which could be attributed to either underdamped junction dynamics [8,20], or to the self-heating by the retrapping current [1,23]. As discussed in the supplementary material, the second scenario is more likely for most of the range studied here. Based on the measurements of the switching statistics [16,[24][25][26], in the following we will use the switching current to represent the true critical current of the junction, I C .In the hole-doped regime, the reflections of ballistic charge carriers from the n-doped contact interfaces yield the quantum ("Fabry-Perot") interference. A very similar oscillation pattern could be observed in the dependence of both the the normal conductance, G N , and the critica...

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Section: Oct 2016mentioning

confidence: 91%

“…For long junctions, we observe an exponential scaling of the current through the junction I C ∝ exp(−k B T /δE), where δE ≈ v F /2πL [5,6,10,11]. Note that in graphene v F is a constant, and δE is expected to be independent of the carrier density or the mobility (as long as the junction remains ballistic.)…”

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confidence: 99%

Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes

et al. 2016

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“…Let us suppose that the magnetic field is absent. Thus, in order to obtain the equation for ∆( r), it is necessary to express the function F ωn ( r, r ) from system (2) and substitute it into the selfconsistent condition (1). In the general case this problem is very complicated.…”

Section: The Common Scheme For the Investigation Of The Behavior Of Tmentioning

confidence: 99%

“…In this model a modulus of the order parameter is assumed to be a constant in the superconducting region and zero in the normal metal. Such an approach for the investigation of the current states in pure SN S junction was realized in paper [1]. The calculation of the current taking into account the reflection of electrons on the junction (junctions of SIN S, SIN IS, SN IN S type) has been made in [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

On the theory of current states in superconducting junctions of SNINS type

Sakhnyuk¹,

Svidzynskyj²

2006

Condens. Matter Phys.

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The behavior of the order parameter close to the NS interface in an SNINS junction is considered. To this end, a linear integral equation, which is valid near the superconductor-normal metal interface, is obtained and researched. The Ginzburg-Landau equation is solved taking into account the effect of the current on the space behaviour of the order parameter. Applying the method of quasiorthogonality to asymptotics, the boundary condition for the Ginzburg-Landau equation is obtained. The calculation of the current states, which can exist in an SNINS junction is carried out. We assume the normal layer thickness to be arbitrary and the temperature to be close to critical.

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“…It is known that the supercurrent can be conducted by Andreev reflections in the SNS junctions. 12,13,14,15,16,17,18,19,20,21,22,23 The supercurrent in one superconductor, for example in the left one, can transfer through the SN interface by generating the propagations of electrons and holes in the normal metal due to the Andreev refection. At another NS interface, the electrons and holes are converted into paired electrons in the right superconductor.…”

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confidence: 99%

Supercurrent transferring throughc-axis cuprate Josephson junctions with thick normal-metal bridge

Yan¹,

Ting²

2008

J. Phys.: Condens. Matter

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With a simple but exactly solvable model, we investigate the supercurrent transferring through the c-axis cuprate superconductor-normal metal-superconductor junctions with the clean normal metal much thicker than its coherence length. It is shown that the supercurrent as a function of thickness of the normal metal decreases much slower than the exponential decaying expected by the proximity effect. The present result may account for the giant proximity effect observed in the c-axis cuprate SNS junctions.

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Concerning the theory of the Josephson effect in pureSNS junctions

Cited by 48 publications

References 3 publications

Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes

Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes

On the theory of current states in superconducting junctions of SNINS type

Supercurrent transferring throughc-axis cuprate Josephson junctions with thick normal-metal bridge

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