Charge of a quasiparticle in a superconductor

Abstract

Nonlinear charge transport in superconductor-insulator-superconductor (SIS) Josephson junctions has a unique signature in the shuttled charge quantum between the two superconductors. In the zero-bias limit Cooper pairs, each with twice the electron charge, carry the Josephson current. An applied bias VSD leads to multiple Andreev reflections (MAR), which in the limit of weak tunneling probability should lead to integer multiples of the electron charge ne traversing the junction, with n integer larger than 2Δ/eVSD and Δ the superconducting order parameter. Exceptionally, just above the gap eVSD ≥ 2Δ, with Andreev reflections suppressed, one would expect the current to be carried by partitioned quasiparticles, each with energy-dependent charge, being a superposition of an electron and a hole. Using shot-noise measurements in an SIS junction induced in an InAs nanowire (with noise proportional to the partitioned charge), we first observed quantization of the partitioned charge q = e*/e = n, with n = 1-4, thus reaffirming the validity of our charge interpretation. Concentrating next on the bias region eVSD ~ 2Δ, we found a reproducible and clear dip in the extracted charge to q ~ 0.6, which, after excluding other possibilities, we attribute to the partitioned quasiparticle charge. Such dip is supported by numerical simulations of our SIS structure.

Keywords: Andreev reflection; Josephson junction; quasiparticle charge; shot noise; superconductivity.

Fig. 1.

MAR. Illustrations of the leading processes contributing to the current as function of bias. In general, for $2\mathrm{\Delta }/\left(n-1\right)>e{V}_{SD}>2\mathrm{\Delta }/n$ the leading charge contribution to the current is ne. An electron-like quasiparticle is denoted by a full circle, whereas a hole-like quasiparticle is denoted by an empty circle. (A) When the bias is larger than the energy gap, $e{V}_{SD}>2\mathrm{\Delta }$, the leading process is a single-path tunneling of single quasiparticles from the full states (Left) to the empty states (Right). This current is proportional to the transmission coefficient t. Higher-order MAR process (dashed box), being responsible for tunneling of Cooper pairs, is suppressed as t². (B) For $2\mathrm{\Delta }>e{V}_{SD}>\mathrm{\Delta }$, the main charge contributing to the current is 2e with probability t². (C) For $\mathrm{\Delta }>e{V}_{SD}>2\mathrm{\Delta }/3$, the main charge contributing to the current is 3e with probability t³.

Fig. 2.

Scanning electron micrograph of the device and the circuit scheme. InAs NW contacted by two superconducting Al electrodes. Conductance measurement: Sourcing by ac + dc, V_ac = 0.1 μV at ∼600 kHz, with ac output on R_L. Noise measurement: sourcing by dc and measuring voltage fluctuations on R_L at a bandwidth of 10 kHz.

Fig. 3.

Shuttled charges in the MAR process. (A) Differential conductance (in units of $e^2/h$) as a function of applied bias, $V_{SD}$, normalized by $\mathrm{\Delta }/e$, where $\mathrm{\Delta }=150$μeV is the superconducting order parameter. The signature of the MAR processes is manifested by a series of peaks in bias corresponding to $e{V}_{SD}/\mathrm{\Delta }=2/n$. (B) The I-V characteristics as obtained by integrating the differential conductance. (Inset) A zoom of the small current range. (C) The shuttled charge q determined from Eq. 3 plotted as a function of $e{V}_{SD}/\mathrm{\Delta }$. The pronounced staircase demonstrates the quantization of charge involved in the MAR processes. (D) Numerical simulations of the Fano factor, F = S_exc/2eI, as function of $e{V}_{\text{SD}}/\mathrm{\Delta }$ for different values of the normal-region transmission t = 0.4, 0.2, 0.1, 0.05 (the transmission at $e{V}_{\text{SD}}>2\mathrm{\Delta }$), according to SI Appendix, section S1. (E) The normalized excess noise [after dividing the excess noise by (1 − t*)], as a function of the current. Note that the local slope at every MAR region equals the global slope (red dashed curves; see also text and Eq. 3), suggesting a dominant contribution of a single process to the current and the noise near the energy corresponding to the bias. This in turn also suggests that most of the current originates from a small energy range around the Fermi energy justifying the use of the differential conductance for extracting the transmission.

Fig. 4.

Evolution of the quasiparticles charge near the edge of the gap. (A) Differential conductance (in units of $e^2/h$) as a function of $e{V}_{\text{SD}}/\mathrm{\Delta }$ for decreasing normal-region transmission t = 0.23, 0.15, 0.1 (red, purple, and blue, respectively). As the transmission decreases (from blue to red) the conductance due to higher-order processes diminishes with $t^n$ dependence. (B) The I-V curve obtained by integrating the differential conductance. (C) The charge determined from Eq. 3 plotted as a function of $e{V}_{\text{SD}}/\mathrm{\Delta }$. As the transmission decreases, the value of the observed minima in the charge at the transition between n = 1 and n = 2 dips. (D) The measured charge q is plotted as a function of the normal-region transmission t. (E) Results of numerical calculations showing F = S_exc/2eI as function of e$V_{SD}$/Δ for low normal-region transmissions t = 0.2, 0.1, 0.05, 0.02, 0.01. (F) Evolution of the minimum value of F (F_min) as a function of transmission.

Fig. 5.

Charge measurements in an SC–normal junction. (A) The charge determined from Eq. 3 as a function of $e{V}_{\text{SD}}/\mathrm{\Delta }$ at normal-region transmission t = 0.01. The charge q increases from 1 to 2 as eV_SD crosses Δ. (B) Numerical simulations of the Fano factor, F = S_exc/2eI, as a function of $e{V}_{\text{SD}}/\mathrm{\Delta }$ at normal-region transmission t = 0.01.