Kinetic Inductance and Superfluid Stiffness of van der Waals Superconductors

Abstract

Elucidating the nature of unconventional superconductivity is a central focus of modern condensed matter physics. In doing so, we may identify materials with high critical temperatures $T_c$, as well as platforms for topological quantum computing. A hallmark of unconventional superconductivity is a gap which vanishes at nodal points. A powerful precedent for establishing a superconductor as nodal is observation of power law dependence of the London penetration depth $\lambda$ on applied current and temperature\cite{Prozorov.2006}. Penetration depth measurements have played a pivotal role in identifying the pairing symmetry of many unconventional superconductors\cite{Annett.1991, Hardy.1993,Hashimoto.2012,Gross.1986}. However, reliably determining such power laws requires probing the superconductor at $T\ll T_c$, necessitating very high precision and low temperature resolution when $T_c$ is not large. For this reason, low temperature studies of $\lambda$ are often ambiguous, and observation of the weak current dependence of the penetration depth in a nodal superconductor - the anomalous nonlinear Meissner effect (ANLME) - has been the subject of debate in cuprates\cite{Carrington.1999, Bidinosti.1999, Halterman.2001, Oates.2004}. This thesis presents new techniques to interrogate the pairing symmetries of novel van der Waals superconductors using kinetic inductance measurements of superfluid stiffness. We apply our technique to accurately resolve the temperature and current dependence of the penetration depth in MoTe$_2$ and moir'e graphene, providing direct evidence of unconventional superconductivity. We observe the particularly striking result of the ANLME in MoTe$_2$ - strong evidence of nodal superconductivity - and an unconventional temperature and current dependence of $\lambda$ in twisted trilayer graphene. This is the first report of the ANLME in a Weyl semimetal, and contradicts existing literature regarding the pairing symmetry of MoTe$_2$\cite{Piva.2023,Luo.2020, Guguchia.2017}. Our results demonstrate the value of our high-precision technique as a probe of the pairing symmetry in unconventional superconductors in which fragile superconducting states (with sub-dominant gaps or low density) can be difficult to probe, and invites further study of novel van der Waals superconductors.