Ultrathin two-dimensional superconductivity with strong spin-orbit coupling

Abstract

We report on a study of epitaxially grown ultrathin Pb films that are only a few atoms thick and have parallel critical magnetic fields much higher than the expected limit set by the interaction of electron spins with a magnetic field, that is, the Clogston-Chandrasekhar limit. The epitaxial thin films are classified as dirty-limit superconductors because their mean-free paths, which are limited by surface scattering, are smaller than their superconducting coherence lengths. The uniformity of superconductivity in these thin films is established by comparing scanning tunneling spectroscopy, scanning superconducting quantum interference device (SQUID) magnetometry, double-coil mutual inductance, and magneto-transport, data that provide average superfluid rigidity on length scales covering the range from microscopic to macroscopic. We argue that the survival of superconductivity at Zeeman energies much larger than the superconducting gap can be understood only as the consequence of strong spin-orbit coupling that, together with substrate-induced inversion-symmetry breaking, produces spin splitting in the normal-state energy bands that is much larger than the superconductor's energy gap.

Keywords: Rashba; Zeeman; spin–orbit coupling; superconductivity; ultrathin film.

Fig. 1.

STS measurement of superconductivity of a 5-ML Pb film. (A) STM images of a 5-ML MBE-grown Pb(111) film on a Si(111) substrate acquired at two different locations that are 2 mm apart, showing that the uniformity of the film coverage is about ±1%. (B) STS measured at different sample temperatures. (C) Two sets of superconducting gap values as a function of temperature were taken at different locations on the same sample with different tips, respectively. Each superconducting gap value was obtained by fitting the normalized differential conductance to the BCS theory density of states. Two BCS fits are shown as solid lines with red curve labeling the fit using only data points with Δ > 0.5 meV (T_c = 5.9 K) and the light blue curve fit including all small gap data points.

Fig. 2.

Ex situ double-coil and scanning-SQUID measurements of a Ge-capped 5-ML Pb film. (A) AFM image of 5-ML Pb film after Ge capping (3 nm). (B) Temperature-dependent SFD measured on the Ge-capped sample at a frequency of 50 kHz (black) using double-coil measurements. The red curve is the real part of the film complex conductivity and the intersection between “BKT line” and SFD curve predicts BKT transition temperature. (C) Susceptometry image at T = 4.2 K in a magnetic field less than 0.3 μT using scanning-SQUID. (D) SQUID susceptibility measurements as a function of the height of the SQUID sensor. The touchdown position is of 16 μm, marked by an arrow. The solid line is a fit of data to an SQUID susceptibility expression for a uniform, thin diamagnetic sample, using the Pearl length Λ as a fitting parameter.

Fig. 3.

Transport measurements at H = 0 on Ge-capped thin Pb films. (A) R–T of 5-ML Pb film with a clean superconducting transition at T = 5.75 K and a low normal-state sheet resistance of ∼100 Ω (<<h/4e²). (B) Normal-state sheet resistances following 1/d² dependence, where d is the film thickness. (C) The mfp showing a linear dependence on d.

Fig. 4.

Magnetotransport measurements. (A and B) R–T measurements as a function of magnetic field in parallel geometry for 5-ML film (A) and 13-ML film (B), respectively. (C and D) Angular-dependent R–H measurement at T = 2 K for 5-ML film (C) and 13-ML film (D), respectively. (E) Angle-dependent critical field H_c(θ), for 5-ML (blue) and for 13-ML (red) films. Tinkham formula fit (black) to 13-ML data at T = 2 K indicates a parallel critical field of $H_{c\parallel }$ = 16 T.