Microscopic origin of residual dissipation in Nb-contacted InAs quantum-well weak-link arrays

Series arrays of superconducting weak links, built from a high-mobility InAs quantum well contacted by niobium (Nb) electrodes with a micrometre-scale grating period, show Josephson transport yet retain a finite zero-bias resistance $R_0(T)$ below the Nb transition. Its Arrhenius activation energies (about 0.7 to 24 meV for array widths of 16 to 200 µm) are hundreds of times smaller than the Josephson energy scale $ℏI_c/e$ evaluated with the measured corner current, so standard thermal-fluctuation pictures (Nyquist-activated phase slips or thermally generated Josephson vortices) fail by factors of hundreds. The activation energy grows with array width but is independent of the number of junctions in series, and strong sample-to-sample variability tracks the processing-dependent Nb-InAs interface transparency. Neither the dissipation mechanism nor this geometric scaling has an accepted microscopic explanation; the question, posed by the 1996-1998 UCSB Nb/InAs program (Kroemer-Thomas 1997 and companion papers), remains open. In the same program, microwave irradiation of these arrays revealed an anomalous response dominated by a step at half the usual voltage, $V = N hν/(4e)$, persisting up to the Nb transition (Drexler et al. 1996); for related Nb-InAs-Nb single junctions this half-integer-step phenomenology was later accounted for by a nonequilibrium Andreev-bound-state model (Kroemer 1999; Lehnert et al. 1999), while anomalously large $sin(2φ)$ harmonics and charge-4e supercurrents in modern epitaxial InAs/Al junctions remain microscopically unexplained.

Background

A Josephson weak link is a short conductor joining two superconducting electrodes, through which a dissipationless supercurrent flows up to a critical current $I_c$; the current-phase relation (CPR) gives the supercurrent as a function of the superconducting phase difference $Φ$ across the link, and is sinusoidal ($j_c sin Φ$) for an opaque tunnel junction but strongly non-sinusoidal for a transparent one. When an electron in a normal conductor hits a superconductor interface it can be Andreev-reflected: it is converted, together with a second electron, into a Cooper pair (the charge-2e boson carrying the supercurrent), leaving a retro-reflected hole; repeated Andreev reflection is the microscopic basis of the superconducting proximity effect, the induction of superconducting correlations into a non-superconducting region. A semiconductor two-dimensional electron gas (2DEG) is an attractive weak-link material because it can be ballistic (mean free path longer than the electrode spacing) and because InAs, unlike GaAs, pins its surface Fermi level inside the conduction band so that metal contacts can be nearly transparent rather than blocked by Schottky barriers. The UCSB program around H. Kroemer and E. L. Hu grew InAs quantum wells (QWs; a thin InAs layer confined between AlSb barrier layers by molecular beam epitaxy) with electron sheet densities near $10^{13}$ cm$^{-2}$ and mobilities of order $10^{5}$ cm$^2$V$^{-1}$s$^{-1}$, contacted by sputtered Nb electrodes. Early work found strongly enhanced subgap conductance attributed to multiple Andreev reflections (MAR; Andreev reflection repeated between the two electrodes, producing conductance structure at submultiples of the superconducting gap voltage) in these structures, including a planar backplane-enhancement mechanism (Nguyen, Kroemer and Hu 1992), and Josephson-type current-voltage characteristics in submicrometre gaps (Kroemer et al. 1994). A key device class was the grating array: about 300 Nb-InAs-Nb weak links in series, with Nb stripes of period about 1 µm and InAs gaps of about 0.3 µm, spanning device widths from 16 to 200 µm; the series connection multiplies the per-junction voltage so that millivolt-scale signals are resolvable. Below the Nb transition (about 8 K) these arrays show Josephson-like current-voltage curves with a supercurrent branch ending at a corner (critical-like) current $I_c$, but a finite small-signal zero-bias resistance $R_0(T)$ that decreases over orders of magnitude with cooling in a thermally activated (Arrhenius) fashion. Standard theory for such residual resistance is thermal activation: in the Ambegaokar-Halperin picture, Nyquist current fluctuations thermally activate phase diffusion over a barrier set by the Josephson energy scale $ℏI_c/e$, and in two-dimensional arrays the moving agents can be thermally generated Josephson vortices (a phase winding of the superconducting order parameter localized in the junction region); both pictures tie the activation energy to $ℏI_c/e$. Under microwave irradiation of frequency $ν$, a Josephson system displays Shapiro steps: constant-voltage plateaus at $V = n hν/(2e)$ per junction ($n$ integer), or $N n hν/(2e)$ for $N$ phase-locked series junctions. In the same NbInAsNb grating arrays, the measured ac Josephson response was instead dominated by a step at half the usual voltage, $V = N hν/(4e)$ (for $ν$ = 120 to 360 GHz), persisting up to the Nb transition temperature and interpreted at the time as a Josephson coupling dominated by a second harmonic of the current-phase relation, $j_c sin(2Φ)$ (Drexler et al., Surface Science 361-362, 306, 1996); for related Nb-InAs-Nb single junctions of the same program, this half-integer-step phenomenology was subsequently accounted for by a nonequilibrium dynamical model based on time-dependent Andreev bound states (Kroemer 1999; Lehnert et al., Physical Review Letters 82, 1265, 1999). This microwave line of work is related to, but separate from, the residual-dissipation question posed below. The unresolved target is a microscopic account of what the experiments actually showed: activation energies far below every standard scale, an unexplained geometry dependence, and uncontrolled interface effects.

Problem Statement

Provide a microscopic, quantitatively validated explanation, or a decisive experimental discrimination, for the following jointly measured phenomenology of series arrays of superconducting weak links formed between Nb electrodes bridged by a high-mobility InAs quantum well (grating period about 1 µm, about 300 junctions in series, array widths 16 to 200 µm). The phenomenology comprises three parts: (1) below the Nb transition (about 8 K) the zero-bias resistance $R_0(T)$ decreases over orders of magnitude in Arrhenius fashion with activation energies $E_a$ of about 0.7 to 24 meV, yet these energies are hundreds of times smaller than the Josephson energy scale $ℏI_c/e$ evaluated with the measured array corner current, so that neither Nyquist-current thermal activation (Ambegaokar-Halperin-type phase diffusion) nor the motion of thermally generated Josephson vortices can account for the magnitude; (2) $E_a$ grows approximately in proportion to array width but is independent of the number of junctions in series (identical $E_a$ at 300 and 425 µm probe spacings); and (3) the strong sample-to-sample variability correlates with processing-dependent residual barriers at the Nb-InAs interface, so the separation of intrinsic ballistic-proximity dissipation from extrinsic contact-limited dissipation is undetermined. A microscopic account is sought that quantitatively reproduces the measured activation-energy range (about 0.7 to 24 meV), the several-hundredfold ratio of $ℏI_c/e$ to $E_a$ evaluated with the measured array corner current, and the array-width dependence for the stated geometry; the intrinsic-versus-extrinsic separation of part (3) remains an open sub-question.

References

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