Abstract

We report a study of superconductivity in the heavy fermion metal YbRh2Si2 using SQUID-based measurements of complex electrical impedance down to ultra-low temperatures [1]. The superconductivity manifests below 10 mK on the background of two magnetic phases: electronic antiferromagnetic (AFM) phase below TN = 70 mK [2,3] and electro-nuclear spin-density wave (SDW) below TA = 1.5 mK [3,4]. Our study reveals the presence of several superconducting states, that respond differently to the magnetic field. These distinct field dependencies provide the experimental measure of the Pauli limiting field and demonstrate superconductivity beyond this limit, which constitutes direct evidence for odd-parity spin-triplet superconductivity in YbRh2Si2. We examine the candidate superconducting order parameters and identify the helical state [1], the analogue of the topological planar phase of the superfluid 3He[5] A striking observation is the boost of the helical state and simultaneous suppression of other superconducting states at the onset of the electro-nuclear SDW, with signatures in critical field and kinetic inductance. We demonstrate theoretically how this selective boost can arise from the formation of a spin-triplet pair density wave (PDW) that attractively couples the magnetic and superconducting order parameters. The strong interplay between the superconductivity and magnetism in YbRh2Si2 is further demonstrated by the abrupt suppression of the superconductivity at the critical field of the electronic AFM phase. The correlations between how the superconductivity and Sommerfeld-Wilson ratio are tuned with magnetic field may point towards pairing mediated by spin fluctuations, with competition between ferro- and antiferromagnetic fluctuations. The observed superconductivity is heterogeneous [6]: high-quality single crystal samples exhibit a multitude of transport signatures, that vary from one sample to another. We discuss the possible origins of this heterogeneity and strategies for obtaining homogeneous superconducting states in YbRh2Si2. The low transition temperatures in YbRh2Si2 confer advantages through modest energy scales: the magnetism and superconductivity are effectively tuneable by modest magnetic field, uniaxial strain and Yb isotopic substitution. This flexibility makes YbRh2Si2 a promising material for topological superconducting technology. [1] L. V. Levitin et al., Nature Phys. 22, 713 (2026). [2] O. Trovarelli et al., Phys. Rev. Lett. 85, 626 (2000). [3] J. Knapp et al., Phys. Rev. Research 7, L042043 (2025). [4] J. Knapp et al., Phys. Rev. Lett. 130, 126802 (2023). [5] Yu. Makhlin, M. Silaev and G. E. Volovik, Phys. Rev. B 89, 174502 (2014). [6] M. Bachmann et al., Science 366, 221–226 (2019).