Thermopower and thermophase in a 
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-wave superconductor

Seja, Kevin Marc; Jacob, Louhane; Löfwander, Tomas

doi:10.1103/physrevb.105.104506

Cited by 6 publications

(6 citation statements)

References 55 publications

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“…We utilize the non-equilibrium quasiclassical theory of superconductivity. An overview over the relevant equations is given in appendix, see also [38,41] for more details. In short, the Eilenberger-Larkin-Ovchinnikov equations [42][43][44] for the Keldysh, retarded, and advanced quasiclassical Green's functions, equation (A2), are solved self-consistently with the superconducting order parameter ∆, impurity self-energies for arbitrary mean free path ℓ, and the local electrochemical potential ϕ(x).…”

Section: Model and Methodsmentioning

confidence: 99%

“…In the Born limit we assume u 0 small, but n imp large, keeping Γ constant, while in the unitary limit u 0 is large such that δ 0 → π/2. This homogeneous scattering model has been widely studied in unconventional, in particular d-wave, superconductors [38,41,[45][46][47][48][49][50][51]. In the bulk superconductor, the Born limit impurities simply broaden the density of states, while the unitary limit impurities introduce a sizeable impurity band of resonance states around the Fermi energy.…”

Section: Model and Methodsmentioning

confidence: 99%

“…Here, we review the key set of equations of the quasiclassical theory of superconductivity that we base our calculations on. For further details we refer to [38,41].…”

Section: Appendix Quasiclassical Theorymentioning

confidence: 99%

“…The impurity self-energies are calculated in the noncrossing approximation for the t-matrix equation [45], discussed in detail in [41]. The matrix structure is…”

Section: Appendix Quasiclassical Theorymentioning

confidence: 99%

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Self-consistent theory of current injection into d and d + is superconductors

Seja

Löfwander

2022

J. Phys.: Condens. Matter

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We present results for the steady-state nonlinear response of a dx2-y2 superconducting ﬁlm connected to normal-metal reservoirs under voltage bias, allowing for a subdominant s-wave component appearing near the interfaces. Our investigation is based on a current-conserving theory that self-consistently includes the non-equilibrium distribution functions, charge imbalance, and the voltage-dependencies of order parameters and scalar impurity self-energies. For a pure d-wave superconductor with [110] orientation of the interfaces to the contacts, the conductance contains a zero-bias peak reﬂecting the large density of zero-energy interface Andreev bound states. Including a subdominant s-wave pairing channel, it is in equilibrium energetically favorable for an s-wave order parameter component ∆sto appear near the interfaces in the time-reversal symmetry breaking combination d + is. The Andreev states then shift to ﬁnite energies in the density of states. Under voltage bias, we ﬁnd that the non-equilibrium distribution in the contact area causes a rapid suppression of the s-wave component to zero as the voltage eV → ∆s. The resulting spectral rearrangements and voltage-dependent scattering amplitudes lead to a pronounced non-thermally broadened split of the zero-bias conductance peak that is not seen in a non-selfconsistent Landauer-Büttiker scattering approach.

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Section: Model and Methodsmentioning

confidence: 99%

Section: Model and Methodsmentioning

confidence: 99%

“…Here, we review the key set of equations of the quasiclassical theory of superconductivity that we base our calculations on. For further details we refer to [38,41].…”

Section: Appendix Quasiclassical Theorymentioning

confidence: 99%

“…The impurity self-energies are calculated in the noncrossing approximation for the t-matrix equation [45], discussed in detail in [41]. The matrix structure is…”

Section: Appendix Quasiclassical Theorymentioning

confidence: 99%

See 2 more Smart Citations

Self-consistent theory of current injection into d and d + is superconductors

Seja

Löfwander

2022

J. Phys.: Condens. Matter

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“…Unconventional superconductors were also studied in a few works to enhance the thermal current i.e. the non-dissipative charge current [11,12].…”

Section: Introductionmentioning

confidence: 99%

Phase-dependent charge and heat current in thermally biased short Josephson junctions formed at helical edge states

Dutta

2023

New J. Phys.

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We explore the phase-dependent charge and heat current in short Josephson junctions with two normal metal regions attached at opposite ends, formed at helical edge states of two-dimensional topological insulators (TIs). For all finite phases, an asymmetry appears around the zero energy in the transmission spectra except for Φ=nΦ0, where n is an half-integer and Φ0 is the flux quantum. The phase-induced asymmetry plays a key role in inducing charge and heat current through the thermally biased junction. However, the current amplitudes are sensitive to the size of the junction. We show that in short Josephson junction when subject to temperature gradient, the charge current shows an odd-symmetry in phase. It indicates that the phase-tunable asymmetry around the zeroenergy is not suffcient to induce dissipative thermoelectric current in the junction. This is in contrast to the behavior of long Josephson junction as shown in the literature. The phase-tunable heat currents are obtained whose amplitudes are sensitive to the phase difference, base temperature, and system size.

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Finite element method for the quasiclassical theory of superconductivity

Seja

Löfwander

2022

Phys. Rev. B

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Thermopower and thermophase in a d -wave superconductor

Cited by 6 publications

References 55 publications

Self-consistent theory of current injection into d and d + is superconductors

Self-consistent theory of current injection into d and d + is superconductors

Phase-dependent charge and heat current in thermally biased short Josephson junctions formed at helical edge states

Finite element method for the quasiclassical theory of superconductivity

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