Onset of superconductivity in a voltage-biased normal-superconducting-normal microbridge

Abstract

We study the stability of the normal state in a mesoscopic NSN junction biased by a constant voltage V with respect to the formation of the superconducting order. Using the linearized timedependent Ginzburg-Landau equation, we obtain the temperature dependence of the instability line, Vinst(T ), where nucleation of superconductivity takes place. For sufficiently low biases, a stationary symmetric superconducting state emerges below the instability line. For higher biases, the normal phase is destroyed by the formation of a non-stationary bimodal state with two superconducting nuclei localized near the opposite terminals. The low-temperature and large-voltage behavior of the instability line is highly sensitive to the details of the inelastic relaxation mechanism in the wire. Therefore, experimental studies of Vinst(T ) in NSN junctions may be used as an effective tool to access parameters of the inelastic relaxation in the normal state.PACS numbers: 74.40. Gh, 74.78.Na, 72.15.Lh, 72.10.Di Nonequilibrium superconductivity has being attracting significant experimental and theoretical attention over decades [1][2][3], ranging from vortex dynamics [4] to the physics of the resistive state in current-carrying superconductors [5][6][7][8][9]. It was recognized long ago [10] that a superconducting wire typically has a hysteretic current voltage characteristic specified by several "critical" currents. In an up-sweep, a current exceeding the thermodynamic depairing current, I c (T ), does not completely destroy superconductivity but drives the wire into a nonstationary resistive state [11], with the excess phase winding relaxing through the formation of phase slips [12]. The resistive state continues until I 2 (T ) > I c (T ), when the wire eventually becomes normal. In the down-sweep of the current voltage characteristic, the wire remains normal until I 1 (T ) < I 2 (T ) when an emerging order parameter leads to the reduction of the wire resistance.The theoretical description of a nonequilibrium superconducting state is a sophisticated problem, requiring a simultaneous account of the nonlinear order parameter dynamics and quasiparticle relaxation under nonstationary conditions. The resulting set of equations is extremely complicated [1,4] and can be treated only numerically [13-15] (even then the stationarity of the superconducting state is often assumed [13,14]). A more intuitive but somewhat oversimplified approach is based on the a time-dependent Ginzburg-Landau (TDGL) equation for the order parameter field ∆(r, t). The TDGL approach which is generally inapplicable in the gapped phase [16], can be justified only in a very narrow vicinity of the critical temperature, T c , provided that the electron-phonon (e-ph) interaction is sufficiently strong to thermalize quasiparticles [17]. These generalized TDGL equations are analyzed numerically in Refs. [5,18].While the applicability of the TDGL equation in the superconducting region is a controversal issue, its lin-earized form can be safely employed to find the line I i...

PTrestoration via increased loss and gain in thePT-symmetric Aubry-André model

“…) and the enhanced PT -breaking threshold, γ P T /J ∼ 0.3, is consistent with a linear-potential threshold [36]. For an even lattice, the average of the gain-potential is given by…”

$${\mathcal{P}}{\mathcal{T}}$$-Symmetric Effective Model for Nonequilibrium Phase Transitions in a Dissipative Fermionic Mott Insulator Chain

“…At the PT symmetry-breaking transition the eigenvalues of the non-Hermitian Hamiltonian acquire finite imaginary components 5 implying that the system transits from stationary to non-stationary dynamics. This approach has been employed in quantum optics and photonic systems [6][7][8][9][10][11] , microwave cavities 12 , superfluid dynamics 13,14 , vortex depinning 15,16 , and remarkably enabled the quantitative description of the dynamic Mott transition [17][18][19][20] , resistive transitions in current-biased superconducting wires 1,21 , and dynamic phase transitions in spin systems 22,23 .…”

“…In all the above developments, except 21 , where an imaginary term in the Hamiltonian for a superconducting wire appeared in the linear approximation with respect to the applied electric field, the non-Hermiticity have been introduced on a phenomenological level, whereas the microscopic origin of the imaginary drive has remained an open question. However, the successful description of such a rich diversity of physical systems, indicates a possible generality in underlying microscopic mechanisms behind the non-Hermiticity.…”

Single Charge Current in a Normal Mesoscopic Region Attached to Superconductor Leads via a Coupled Poisson Nonequilibrium Green Function Formalism

“…In these systems, the energy level discreteness is quite important since level spacing is comparable with other energy scales [3,4]. Indeed, the coupling with the bath modifies drastically the properties of an otherwise uncoupled nanometer system in a sharp contrast with similar non-Figure 1: Set-up: single level quantum dot connected with two superconducting leads via coupling constants Γ s equilibrium macroscopic systems [5,6,7,8,9,10,11,12,13]. They constitutes hybrid systems.…”