Dual Fraunhofer interference and charge fluctuations in long quantum phase slip wires

Charge interference (Aharonov-Casher effect) in a long superconducting quantum phase slip wire is considered, and from this the “dual” Fraunhofer interference effect (dual to the critical current modulation of a short Josephson junction in an external magnetic field) is derived. The device that can be used to observe this effect is proposed. Furthermore, the impact of wire inhomogeneities, charge disorder, and noise on the phase slip amplitude is investigated. Although intrinsically protected against small fluctuations, the Aharonov-Casher interference resulting from jumps of random offset charges and quasiparticles can result in significant fluctuations of the measured current-voltage characteristics of the quantum phase slip wire, similar to the effects of Joule heating when averaged out over many fluctuations. Possible ways to identify and mitigate such disorder are discussed.

Figure 1

(a) Circuit model for an array of capacitively coupled islands, in between which frequent CQPS can occur. (b) Proposed CQPS nanowire device for the observation of dual Fraunhofer interference for phase slips. (c) A modified implementation of (b) which allows for compensation of individual offset charges and local control of the phase slip rate using multiple gates separated by a characteristic distance $\zeta$.

Figure 2

Phase slip rate for a homogeneous QPS wire without charge disorder as a function of accumulated induced charge along the wire ($N=20$) according to Eq. (6) (solid black line). The approximate expression Eq. (7) is shown as the red solid line. The insets show the evolution of the phase slip rate in the complex plane where the total arc length is always the same ($=N{\nu }_0$), and the accumulated charge along the wire results in a phase factor for each individual phase slip center.

Figure 3

(a) Probability distribution for the total phase slip rate $\left|\nu \right|/N{\nu }_0$ for increasing magnitude of the random charge disorder along the nanowire $\delta q$ ($2e$). b) The same probability distributions as in (a) but with added disorder in the nanowire width. Here, the normalization in the phase slip rate is taken as the sum of individual random phase slip rates $\left|\nu \right|/{\sum }_i\left|{\nu }_i\right|$. The calculation assumes a wire with normal state per square resistance $0.3R_q,{\xi }_0=4\mathrm{nm}$ and a mean wire width $w=20\mathrm{nm}$ with a normal distributed dispersion of width $\delta w=5\mathrm{nm}$. Note that in the last two panels the probability has been multipled by a factor of 2 for enhanced visibility.

Figure 4

Simulated current voltage characteristics of a long CQPS wire with fluctuating charge disorder under the presence of microwave radiation at ${\omega }_{\mathrm{rf}}/2\pi =0.5\mathrm{GHz}$. The black solid line shows the case without disorder, and the solid red line shows the average of 20 different charge configurations with a moderate total phase slip rate dispersion of ${\sigma }_{\nu }=0.1E_{s0}$. The shaded region indicates the possible spread of parameters for the given probability distribution of phase slip rates. $E_L=e{\mathrm{\Phi }}_0^2/L=0.25,E_{s0}=2.5\mathrm{GHz},R=320\mathrm{k}\mathrm{\Omega }$.