Long-lived nonequilibrium superconductivity in a noncentrosymmetric Rashba semiconductor

V. Narayan, P. C. Verpoort, J. R. A. Dann, D. Backes, C. J. B. Ford, M. Lanius, A. R. Jalil, P. Schüffelgen, G. Mussler, G. J. Conduit, and D. Grützmacher

Phys. Rev. B 100, 024504 – Published 10 July 2019

Abstract

We report nonequilibrium magnetodynamics in the Rashba-superconductor GeTe, which lacks inversion symmetry in the bulk. We find that at low temperature the system exhibits a nonequilibrium state, which decays on timescales that exceed conventional electronic scattering times by many orders of magnitude. This reveals a nonequilibrium magnetoresponse that is asymmetric under magnetic-field reversal and, strikingly, induces a nonequilibrium superconducting state distinct from the equilibrium one. We develop a model of a Rashba system in which nonequilibrium configurations relax on a finite timescale that captures the qualitative features of the data. We also obtain evidence for the slow dynamics in another nonsuperconducting Rashba system. Our work provides insights into the dynamics of noncentrosymmetric superconductors and Rashba systems in general.

Received 24 November 2018
Revised 5 April 2019

DOI:https://doi.org/10.1103/PhysRevB.100.024504

Physics Subject Headings (PhySH)

Rashba coupling Spin-orbit coupling Superconducting fluctuations Superconducting phase transition

Low-temperature superconductors Semiconductor compounds Thin films

Methods in superconductivity

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. Narayan ^1,*, P. C. Verpoort¹, J. R. A. Dann¹, D. Backes^1,†, C. J. B. Ford¹, M. Lanius², A. R. Jalil², P. Schüffelgen², G. Mussler², G. J. Conduit¹, and D. Grützmacher²

¹Department of Physics, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
²Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich & Jülich-Aachen Research Alliance (JARA-FIT), 52425 Jülich, Germany

^*Author to whom all correspondence should be addressed: vn237@cam.ac.uk
^†Present address: Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom.

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Vol. 100, Iss. 2 — 1 July 2019

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Images

Figure 1
GeTe: a semiconducting, spin-orbit-coupled superconductor. (a) The ultrathin GeTe films show semiconducting characteristics at high $T$ with a band gap of $\approx 0.1 eV$ . Below $100 K$ , the $T$ dependence weakens significantly, being indicative of 2D metallic states. (b) The spin-orbit coupling in GeTe manifests as WAL, i.e., positive quantum corrections to the electrical conductivity $Δ σ_{xx} = σ_{xx} (B) - σ_{xx} (0)$ . These characteristics are well described by the Hikami-Larkin-Nagaoka (HLN) [13] formula valid for 2D systems (see also Fig. S2 [14]). (c) There is a broad superconducting transition between 0.2 and $0.1 K$ below which we note that $R_{xx}$ does not go completely to zero (see Fig. S3 [14] for possible explanation). Inset: superconductivity is suppressed when the sample is cooled in the presence of a constant magnetic field perpendicular to the plane of the film. The data are consistent with a field offset of $\approx 15 mT$ , which can arise due to trapped flux in the external superconducting magnet (see Fig. S4 [14] for details of how these data are collected). (d) The dependence of the critical field $B_{c}$ on $T$ reveals $B_{c} (0 K) = 70 mT$ and $T_{c} = 140 mK$ . Here the superconducting transition is defined as $R_{xx} < R_{N} / 2$ (where $R_{N}$ is the normal-state resistance).
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Figure 2
Long-lived nonequilibrium magnetodynamics. (a) Starting in the superconducting state, as $B$ is ramped toward $- 1 T$ at $d B / d t = 5 T h^{- 1}$ ( $1.4 mT s^{- 1}$ ), there is a sharp transition to the normal state at $- 15 mT$ . However, the “forward $B$ sweep” from $- 1$ to $1 T$ shown in (b) is distinctly dissimilar to the previous trace, showing an initial increase in $R_{xx}$ followed by an almost complete transition to superconductivity beginning at $B = - 250 mT$ , well above the previously estimated values of $B_{c}$ . The sweep is not symmetric about $R_{\min}$ or about $B = 0 T$ . In contrast, at $B = 0 T$ , the value $R_{xx}$ is now finite and close to $R_{N}$ . (c) The shape of $R_{xx}$ as $B$ is swept in the opposite direction from 1 to $- 1 T$ is precisely the mirror image of the forward sweep when reflected about $B = 0 T$ . The gray arrows indicate the direction of the $B$ sweep. (d) When the sweep is stopped at $B = 0 T$ the nonequilibrium state persists for $\approx 100 s$ before relaxing to the equilibrium zero-resistance state over a further $300 s$ . (e) Over the range of sweep rates explored, $R_{xx}$ is seen to show a lower minimum $R_{\min}$ for slower sweep rates. Inset: $R_{\min} / R_{N}$ as a function of sweep rate. (f)–(i) The apparent nonequilibrium superconducting state is visible even above $T_{c}$ .
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Figure 3
Nonequilibrium butterfly hysteresis. (a) The magnetoresistance of a model Rashba system subjected to a $B$ field, in which interband relaxation processes occur on a finite timescale $τ$ . The two traces compare the behavior when $τ$ is changed by a factor of 2. Superconductivity is induced locally depending on the instantaneous carrier concentration. The model correctly captures the difference between traces with differing sign of $d B / d t$ as well as $R (B) \neq R (- B)$ for a given sign of $d B / d t$ . (b) The asymmetric $ρ (B)$ and mirror symmetry between the forward and reverse $B$ sweeps are clearly seen in a heterostructure of $p$ - and $n$ -type topological insulators. (c) The characteristic “butterfly” shape of $ρ (B)$ can be captured within a model of a Rashba material.
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