Bloch inductance in small-capacitance Josephson junctions

TL;DR

This paper introduces the concept of Bloch inductance in small-capacitance Josephson junctions, showing it adds an inductive component to impedance that depends periodically on quasicharge, affecting junction dynamics.

Contribution

It is the first to identify and analyze the Bloch inductance term in the impedance of small-capacitance Josephson junctions, expanding understanding of their dynamic behavior.

Findings

Bloch inductance depends periodically on quasicharge.

Maximum Bloch inductance exceeds Josephson inductance at certain quasicharges.

Bloch inductance influences the dynamics of single junctions and arrays.

Abstract

We show that the electrical impedance of a small-capacitance Josephson junction includes besides the capacitive term $-i/\omega C_B$ also an inductive term $i\omega L_B$. Similar to the known Bloch capacitance $C_B(q)$, the Bloch inductance $L_B(q)$ also depends periodically on the quasicharge $q$, and its maximum value achieved at $q=e (\textrm{mod} 2e)$ always exceeds the value of the Josephson inductance of this junction $L_J(\phi)$ at fixed $\phi=0$. The effect of the Bloch inductance on the dynamics of a single junction and a one-dimensional array is described.