Fluctuation Conductivity of Thin Films and Nanowires Near a Parallel-Field-Tuned Superconducting Quantum Phase Transition

We calculate the fluctuation correction to the normal state conductivity in the vicinity of a quantum phase transition from a superconducting to a normal state, induced by applying a magnetic field parallel to a dirty thin film or a nanowire with thickness smaller than the superconducting coherence length. We find that at zero temperature, where the correction comes purely from quantum fluctuations, the positive “Aslamazov-Larkin” contribution, the negative “density of states” contribution, and the ”Maki-Thompson” interference contribution are all of the same order and the total correction is negative. Further, we show that, based on how the quantum critical point is approached, there are three regimes that show different temperature and field dependencies which should be experimentally accessible.

Figure 1

Phase diagram of a superconducting nanowire (thin film) in a parallel magnetic field (parametrized by $\alpha$). The boundary between the quantum and the intermediate regime, shown by a dotted line, is different for a wire and film as marked in the figure while all other boundaries coincide.

Figure 2

Dimensionless zero-temperature fluctuation conductivity correction (5) as a function of depairing parameter $\alpha$. Inset shows dependence of the resistivity on the magnetic field for temperatures $T/{\alpha }_{c0}=0.01$ (upper curves) and $T/{\alpha }_{c0}=0.1$ (lower curves). Resistivity is normalized to the high field resistivity $R_0$ while the magnetic field is normalized to the critical field $H_{c0}$ at $T=0$. The values for the high field resistivity are taken as $R_0^{-1}=e^2/c$ for a film and $R_0^{-1}=e^2(D/{\alpha }_{c0}{)}^{1/2}$ for a wire.

Figure 3

Diagrams for the fluctuation conductivity: (a) Aslamazov-Larkin diagram, (b)–(c) Maki-Thompson diagrams, and (d)–(f) density of state diagrams. The full line stands for the disorder averaged normal state Green’s function, the wavy line for the fluctuation propagator $K$, the shaded rectangle for the Cooperon $C$, and the shaded triangle for the vertex $C/2\pi \nu \tau$.