Research ArticleSUPERCONDUCTIVITY

Resolving thermoelectric “paradox” in superconductors

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Science Advances  26 Feb 2016:
Vol. 2, no. 2, e1501250
DOI: 10.1126/sciadv.1501250
  • Fig. 1 Bimetallic superconducting loop and experimental setup for thermoelectric flux measurements.

    (A) Bimetallic superconducting loop in the temperature gradient. Thermoelectric quasiparticle current, Iq, in the bulk of the superconductor with a smaller gap is opposed by counterflowing supercurrent Is with superconducting phase difference, Δθ, created and circulating current Ics induced within the penetration depth, Λ; with an increase in average temperature, the penetration depth acquires an increment, δΛ, that results in an increase in the effective area of the loop; the screening current I2 keeps the total magnetic flux through the bimetallic loop constant. (B) Diagram of experimental setup. A bimetallic loop made of different superconductors is placed within a loop of a hybrid quantum interferometer a-b-c-d. The total flux through the bimetallic loop, Φ2, is created by the external magnetic field B and the fields BTh and B2 induced by thermoelectric circulating current Ics and screening current I2. The interferometer measures the superconducting phase difference φ between c and d that is proportional to the total magnetic flux through the interferometer loop. This includes the flux through the bimetallic loop and externally induced flux that is partially screened by the current I1. (C) False-colored scanning electron micrograph of a bimetallic loop coupled to a heater and hybrid quantum interference device (HyQUID). (D) A fluxless heater f generating a temperature gradient in the bimetallic loop by local spot heating of the contact e. The temperature T1 at e is measured by superconductor/normal/superconductor (SNS) thermometer g. (E) The HyQUID measuring a superconducting phase difference between c and d with folded normal wires insulated by a spacer [see (B) for details].

  • Fig. 2 Phase shifts in oscillations at different k numbers and heater currents.

    (A) Oscillations at different k numbers of magnetic flux quanta trapped in the bimetallic loop with the heater current OFF. Left maximum corresponds to k = 4; middle, k = 5; right, k = 6; 1, n = 8.5; 2, n = 9.5; 3, n = 10.5. A change in k number introduces constant phase shift, leaving the period intact. (B) Oscillations with the heater current OFF (red line) and with the heater current ON (black line). (C) The shifts ΔBn,k [as in (B)] of the values Bn,k with the heater current ON versus the total flux Φ1 = nΦ0 at different fixed k numbers of the trapped flux quanta. (D) The shifts ΔBn,k versus k number at a fixed total flux. (E) Three-dimensional (3D) representation of the shifts ΔBn,k versus k number and the total flux Φ1 = nΦ0 through the measurement loop. The planes correspond to different fixed heater currents Ih = 10, 15, 20, and 25 μA.

  • Fig. 3 Thermoelectric phase shifts and magnetic flux at different heater currents and hot contact temperatures.

    (A) The values of ΔBn,k versus p at different k and n values close to the line ΔBn,k = 0 in Fig. 2E with Λ effect excluded. (B) The measured thermoelectric flux values at different hot spot temperatures for two samples with opposite direction of the temperature gradient (symbols). Curves are theory predictions according to Eq. 2.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/2/e1501250/DC1

    Calculating thermoelectric flux

    Thermometry

    Fig. S1. Conversion of currents at the interface between two superconductors, S and S′, with different energy gaps, Δ and Δ′.

    Fig. S2. Calculated dependence of the thermoelectric flux scaling factors on the quasiparticle temperature normalized to critical temperature, Tc.

    Fig. S3. Calculated temperature dependence of thermoelectric flux, Φth, normalized to its value, Φth(Tc), at critical temperature with different values of critical current, I0, and electron-phonon parameter, n.

    Fig. S4. Dependence of critical current in the SNS thermometer on the length of the normal element at base temperature T = 245 mK.

    Fig. S5. Differential resistance versus bias current curves for an SNS thermometer at different bath temperatures.

    Fig. S6. Differential resistance versus bias current curves for an SNS thermometer at different heater currents.

    Fig. S7. Temperature calibration curve.

    Fig. S8. Determination of the heater current corresponding to the onset of superconductivity in the bimetallic loop.

    Reference (34)

  • Supplementary Materials

    This PDF file includes:

    • Calculating thermoelectric flux
    • Thermometry
    • Fig. S1. Conversion of currents at the interface between two superconductors, S and S', with different energy gaps, Δ and Δ′.
    • Fig. S2. Calculated dependence of the thermoelectric flux scaling factors on the quasiparticle temperature normalized to critical temperature, Tc.
    • Fig. S3. Calculated temperature dependence of thermoelectric flux, Φth, normalized to its value, Φth(Tc), at critical temperature with different values of critical current, I0, and electron-phonon parameter, n.
    • Fig. S4. Dependence of critical current in the SNS thermometer on the length of the normal element at base temperature T = 245 mK.
    • Fig. S5. Differential resistance versus bias current curves for an SNS thermometer at different bath temperatures.
    • Fig. S6. Differential resistance versus bias current curves for an SNS thermometer at different heater currents.
    • Fig. S7. Temperature calibration curve.
    • Fig. S8. Determination of the heater current corresponding to the onset of superconductivity in the bimetallic loop.
    • Reference (34)

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