Low-Frequency Imaginary Impedance at the Superconducting Transition of $2H$-${\mathrm{Nb}\mathrm{Se}}_{2}$

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Low-Frequency Imaginary Impedance at the Superconducting Transition of $2 H$ - ${Nb Se}_{2}$

David Perconte, Samuel Mañas-Valero, Eugenio Coronado, Isabel Guillamón, and Hermann Suderow

Phys. Rev. Applied 13, 054040 – Published 18 May 2020

Abstract

The superconducting transition leads to a sharp resistance drop in a temperature interval that can be a small fraction of the critical temperature $T_{c}$ . A superconductor exactly at $T_{c}$ is thus very sensitive to all kinds of thermal perturbation, including the heat dissipated by the measurement current. We show that the interaction between electrical and thermal currents leads to a sizable imaginary impedance at frequencies of the order of tens of hertz at the resistive transition of single crystals of the layered material $2 H$ - ${Nb Se}_{2}$ . We explain the result using models developed for transition-edge sensors. By measuring under magnetic fields and at high currents, we find that the imaginary impedance is strongly influenced by the heat associated with vortex motion and out-of-equilibrium quasiparticles.

Received 6 November 2019
Revised 6 April 2020
Accepted 13 April 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.054040

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Heat transfer Optoelectronics Phase slips Superconducting phase transition Vortices in superconductors

Solid-state detectors Superconducting devices Transition metal dichalcogenides

Particles & FieldsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

David Perconte¹, Samuel Mañas-Valero ², Eugenio Coronado ², Isabel Guillamón ^1,3, and Hermann Suderow ^1,3,*

¹Departamento de Física de la Materia Condensada, Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid E-28049, Spain
²Instituto de Ciencia Molecular (ICMol), Universidad de Valencia, Catedrático José Beltrán 2, Paterna 46980, Spain
³Unidad Asociada de Bajas Temperaturas y Altos Campos Magnéticos, UAM, CSIC, Cantoblanco, Madrid E-28049, Spain

^*hermann.suderow@uam.es

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Vol. 13, Iss. 5 — May 2020

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Figure 1
(a) Electrical scheme of our setup. A current source ( $I_{source}$ ) is connected to the $2 H$ - ${Nb Se}_{2}$ sample, with impedance $Z$ , through wiring that has a finite resistance $R_{cir}$ and an inductance $L_{cir}$ . $I (t)$ follows Eq. (1). (b) Thermal scheme. An electrical power $P_{elec}$ is introduced by an electrical current in the $2 H$ - ${Nb Se}_{2}$ sample (box). This produces heat that flows to the thermal bath ( $P_{th}$ ) through the thermal connection $G$ . $T (t)$ follows Eq. (2) and is connected to $I (t)$ through $P_{elec} = R I (t)^{2}$ .
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Figure 2
(a) Real impedance versus temperature for different magnetic fields (lines from blue to red, 0, 152, 304, 759, 1519, 2278, and 3038 Oe). (b) Imaginary impedance versus temperature for the same magnetic fields. The data in (a),(b) are taken at 20 mA and a frequency of 70 Hz. (d) Real impedance for different values of the current (from blue to red, 5, 10, 15, 20, 25, 30, 40, and 50 mA). (e) Imaginary impedance versus temperature for the same values of current. The data in (d),(e) are taken at zero magnetic field and a frequency of 70 Hz. (g) Real impedance versus temperature for different frequencies (from blue to red, 7, 32, 64, 89, 289, 689, and 989 Hz). (h) Imaginary impedance for the same frequencies. The data in (g),(h) are taken at zero magnetic field and a current of 20 mA. (c),(f),(i) Imaginary impedance obtained using Eq. (4) and the approximations described in the text. For clarity, we show the color scale used in each set of figures as bars on the right.
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Figure 3
(a) Curve of thermal conductance versus exchange-gas pressure deduced from Eq. (4). (b) Imaginary impedance as a function of frequency at about 7.2 K. The exchange-gas pressure varies from 0.01 to 5 mbar. The colors of the lines in (b),(c) correspond to the values shown in (a). (c) Results of the calculation described in the text using Eq. (4).
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Figure 4
The top panels of each part show the temperature dependence of the resistance (left $y$ axis, red lines) and of $d R / d T$ (right $y$ axis, blue lines). The bottom panels show the value of $C$ obtained as discussed in the text (black lines). Notice that the temperature range shown in each part corresponds to the range where the reactance is finite. (a) Results obtained at 10 mA and zero magnetic field [blue curves in Figs. 2 and 2], (b) results obtained at 10 mA and 2300 Oe [orange curves in Figs. 2 and 2], and (c) results obtained at 40 mA and zero magnetic field [orange curves in Figs. 2 and 2]. The temperature range shaded green corresponds to the temperature region where at least part of the sample is superconducting, and the red shading corresponds to the normal region dominated by fluctuation and dissipation.
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Figure 5
The blue points show the reactance versus frequency, and the fit to the model described in the text is shown in green. The measurement temperature is 7.2 K, and the exchange-gas residual pressure is below 0.01 mbar.
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Physical Review Applied

Low-Frequency Imaginary Impedance at the Superconducting Transition of 2H-NbSe2

David Perconte, Samuel Mañas-Valero, Eugenio Coronado, Isabel Guillamón, and Hermann Suderow

Phys. Rev. Applied 13, 054040 – Published 18 May 2020

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Low-Frequency Imaginary Impedance at the Superconducting Transition of $2 H$ - ${Nb Se}_{2}$