Quantum Tunneling between Paramagnetic and Superconducting States of a Nanometer-Scale Superconducting Grain Placed in a Magnetic Field

We consider the process of quantum tunneling between the superconducting and paramagnetic states of a nanometer-scale superconducting grain placed in a magnetic field. The grain is supposed to be weakly coupled to a normal metallic contact that plays the role of the spin reservoir. Using the instanton method, we find the probability of the quantum tunneling process and express it in terms of the applied magnetic field, order parameter of the superconducting grain, and conductance of the tunneling junction between the grain and metallic contact.

Figure 1

Energy of an isolated superconducting grain as a function of its total spin. The inset shows a possible experimental setup: An STM tip (3) and superconducting grain separated by an insulating layer from metallic plate (2).

Figure 2

Dependence of the order parameter $\Delta$ on time $\tau$. The region $\tau >0$ is the mirror reflection of the “physical” region $\tau <0$. The superconducting state corresponds to the regions $|\tau |>T$ while the paramagnetic one to $|\tau |<T$.

Figure 3

The normalized order parameter $\Delta (\tau )/{\Delta }_0$ (dashed line) and the normalized total spin $2S(\tau )/N$ of the grain as functions of ${\tau }^{\prime }=\tau -T$ at the boundary $\tau \sim T$ between the superconducting (left) and paramagnetic (right) states.