According to the BCS theory, the zero-temperature paramagnetic susceptibility of a conventional superconductor vanishes. In the presence of spin-orbit coupling (SOC), such susceptibility becomes finite, as observed a long time ago. This finite response has been theoretically explained for SOC impurities [2] and systems lacking inversion symmetry [3]. Those theories focused on infinite homogenous systems and predicted a zero-temperature magnetization along the applied field. In this talk, I discuss how finite-size effects in wires [4] and 2D superconductors [5] with intrinsic SOC modify the well-established theory of paramagnetic response. Specifically, in a quasi 1D wire, breaking the time-reversal symmetry by a Zeeman field leads to a bulk equilibrium spin current which manifests itself in a sizable edge spin polarization, transverse to the Zeeman field. The net accumulated spin does not depend on specific properties of the wire ends, being entirely determined by the bulk spin current. Similarly, in 2D samples the response to a Zeeman field leads to a spin texture with a transverse component of the spin localized near the edge on the scale of superconducting coherence length. Because of the spin-charge coupling mediated by the SOC, a nonhomogenous charge current appears in the system. Its spatial distribution depends on the direction of the applied field and the geometry of the system. For example, in a 2D superconductor with a rectangular shape, macroscopic current loops appear at the edges when the stripe is oriented along the field. Both the transverse spin and the edge currents contribute to the total magnetic moment, detectable with state-of-the-art magnetometry techniques.

[1] G. M. Androes and W. D. Knight, Phys. Rev. 121, 779 (1961); F. Reif, Phys. Rev. 106, 208 (1957).
[2] A. A. Abrikosov and L. P. Gorkov, Sov. Phys. JETP 42, 1088 (1962).
[3] L. P. Gorkov and E. I. Rashba, Phys. Rev. Lett. 87, 037004 (2001).
[4] I. V. Tokatly, B. Bujnowski, and F. S. Bergeret, Phys. Rev. B 100, 214422 (2019).
[5] F. S. Bergeret and I. V. Tokatly, Phys. Rev. B 102, 060506(R) (2020).