Long-range thermoelectric effects in mesoscopic superconductor–normal metal structures

Volkov, A. N.; Павловский, В.

doi:10.1103/physrevb.72.014529

Cited by 18 publications

(19 citation statements)

References 27 publications

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“…Moreover, previous works have considered analytical solutions of the Usadel equation using the so-called θ -parametrization in SN bilayers161718 and also approximate solutions in the SNS case192021, whereas in our work the analytical solution is exact for the key cases of (i) and (ii) for phase differences nπ between the terminals.…”

Section: Theorymentioning

confidence: 99%

Analytically determined topological phase diagram of the proximity-induced gap in diffusive n-terminal Josephson junctions

Amundsen

Ouassou

Linder

2017

Sci Rep

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Multiterminal Josephson junctions have recently been proposed as a route to artificially mimic topological matter with the distinct advantage that its properties can be controlled via the superconducting phase difference, giving rise to Weyl points in 4-terminal geometries. A key goal is to accurately determine when the system makes a transition from a gapped to non-gapped state as a function of the phase differences in the system, the latter effectively playing the role of quasiparticle momenta in conventional topological matter. We here determine the proximity gap phase diagram of diffusive n-terminal Josephson junctions ( ∈ N n ), both numerically and analytically, by identifying a class of solutions to the Usadel equation at zero energy in the full proximity effect regime. We present an analytical equation which provides the phase diagram for an arbitrary number of terminals n. After briefly demonstrating the validity of the analytical approach in the previously studied 2-and 3-terminal cases, we focus on the 4-terminal case and map out the regimes where the electronic excitations in the system are gapped and non-gapped, respectively, demonstrating also in this case full agreement between the analytical and numerical approach.The interest in topological quantum phases of matter has grown steadily in recent years, and the fundamental importance of this topic in physics was recently recognized by Thouless, Haldane, and Kosterlitz being awarded the 2016 Nobel prize in physics for their contribution to this field. So far, specific material classes such as telluride-based quantum wells (HgTe, CdTe), bismuth antimony (Bi 1−x Sb x ) and bismuth selenide (Bi 2 Se 3 ) have received the most attention in the pursuit of symmetry-protected topological phases and excitations 1-4 . However, it was recently proposed 5 that similar physics could be obtained using conventional superconducting materials. More specifically, by using multiterminal Josephson junctions, the authors of ref. 5 showed that it was possible to create an artificial topological material displaying Weyl singularities under appropriate conditions. In multiterminal Josephson junctions hosting well-defined Andreev bound states, the crossing of these states with the Fermi level has been shown to be analogous to Weyl points in 3D solids with the Andreev bound state taking on the role of energy bands and the superconducting phase differences corresponding to quasiparticle momenta. A considerable advantage in utilizing multiterminal Josephson junctions rather than 3D solids to study exotic phenomena such as Weyl singularities and topologically different phases is that the phase differences are much more easily controlled experimentally than the quasiparticle momenta.In order to probe electronic excitations with topological properties, a key goal is to map out the phase diagram of the system in terms of when it is gapped or not. A gapped system here means that there are no available excitations in a finite interval around the Fermi level. The reason for why this...

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Section: Theorymentioning

confidence: 99%

Analytically determined topological phase diagram of the proximity-induced gap in diffusive n-terminal Josephson junctions

Amundsen

Ouassou

Linder

2017

Sci Rep

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“…Long-range phase coherent thermoelectricity. Applying a thermal gradient to normal terminals N 1 and N 2 one induces thermoelectric voltages V 1 and V 2 at these terminals [7][8][9][10][11][12][13]. These voltage signals are in general not small and depend periodically on the phase χ, as it was repeatedly observed in experiments [14][15][16][17].…”

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confidence: 97%

Phase-sensitive thermoelectricity and long-range Josephson effect supported by thermal gradient

2020

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We demonstrate that thermoelectric signal as well as dc Josephson current may be severely enhanced in multi-terminal superconducting hybrid nanostructures exposed to a temperature gradient. At temperatures T strongly exceeding the Thouless energy of our device both the supercurrent and the thermo-induced voltage are dominated by the contribution from non-equilibrium low energy quasiparticles and are predicted to decay slowly (algebraically rather than exponentially) with increasing T . We also predict a non-trivial current-phase relation and a transition to a π-junction state controlled by both the temperature gradient and the system topology. All these features are simultaneously observable in the same experiment.

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“…At high temperatures where it vanishes exponentially, other sources become more important. 10,12,13 However, validity of Eqs. (2) is somewhat restricted, since they are correct only in the linear response and to the first order in the proximity corrections, additionally assuming that the energy gap |∆| of the nearby superconductors satisfies k BT ≪ |∆|.…”

Section: Figmentioning

confidence: 99%

“…in terms of the biases ∆V j = V j −V , ∆T j = T j −T and the modified response coefficients L. The proximityinduced changes in the conductance 8,9,10,11,12,13,14,15,16,17 have recently been investigated both experimentally and theoretically. Behavior of the remaining off-diagonal coefficient L ij 21 has previously been discussed in Ref.…”

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confidence: 99%

Peltier effects in Andreev interferometers

Virtanen¹,

Heikkilä²

2007

Phys. Rev. B

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The superconducting proximity effect is known to modify transport properties of hybrid normal--superconducting structures. In addition to changing electrical and thermal transport separately, it alters the thermoelectric effects. Changes to one off-diagonal element $L_{12}$ of the thermoelectric matrix $L$ have previously been studied via the thermopower, but the remaining coefficient $L_{21}$ which is responsible for the Peltier effect has received less attention. We discuss symmetry relations between $L_{21}$ and $L_{12}$ in addition to the Onsager reciprocity, and calculate Peltier coefficients for a specific structure. Similarly as for the thermopower, for finite phase differences of the superconducting order parameter, the proximity effect creates a Peltier effect significantly larger than the one present in purely normal-metal structures. This results from the fact that a nonequilibrium supercurrent carries energy.Comment: 5 pages, 4 figure

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Long-range thermoelectric effects in mesoscopic superconductor–normal metal structures

Cited by 18 publications

References 27 publications

Analytically determined topological phase diagram of the proximity-induced gap in diffusive n-terminal Josephson junctions

Analytically determined topological phase diagram of the proximity-induced gap in diffusive n-terminal Josephson junctions

Phase-sensitive thermoelectricity and long-range Josephson effect supported by thermal gradient

Peltier effects in Andreev interferometers

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