Do organic and other exotic superconductors fail universal scaling relations?

Superfluid stiffness of twisted trilayer graphene superconductors

The robustness of the macroscopic quantum nature of a superconductor can be characterized by the superfluid stiffness, ρs, a quantity that describes the energy required to vary the phase of the macroscopic quantum wavefunction. In unconventional superconductors, such as cuprates, the low-temperature behaviour of ρs markedly differs from that of conventional superconductors owing to quasiparticle excitations from gapless points (nodes) in momentum space. Intensive research on the recently discovered magic-angle twisted graphene family has revealed, in addition to superconducting states, strongly correlated electronic states associated with spontaneously broken symmetries, inviting the study of ρs to uncover the potentially unconventional nature of its superconductivity. Here we report the measurement of ρs in magic-angle twisted trilayer graphene (TTG), revealing unconventional nodal-gap superconductivity. Utilizing radio-frequency reflectometry techniques to measure the kinetic inductive response of superconducting TTG coupled to a microwave resonator, we find a linear temperature dependence of ρs at low temperatures and nonlinear Meissner effects in the current-bias dependence, both indicating nodal structures in the superconducting order parameter. Furthermore, the doping dependence shows a linear correlation between the zero-temperature ρs and the superconducting transition temperature Tc, reminiscent of Uemura's relation in cuprates, suggesting phase-coherence-limited superconductivity. Our results provide strong evidence for nodal superconductivity in TTG and put strong constraints on the mechanisms of these graphene-based superconductors.

Pressure-Tuned Superconducting Dome in Chemically-Substituted κ-(BEDT-TTF)2Cu2(CN)3

The quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 has been established as the prime example of a genuine Mott insulator that can be tuned across the first-order insulator–metal transition either by chemical substitution or by physical pressure. Here, we explore the superconducting state that occurs at low temperatures, when both methods are combined, i.e., when κ-[(BEDT-TTF)1−x(BEDT-STF)x]2Cu2(CN)3 is pressurized. We discovered superconductivity for partial BEDT-STF substitution with x = 0.10–0.12 even at ambient pressure, i.e., a superconducting state is realized in the range between a metal and a Mott insulator without magnetic order. Furthermore, we observed the formation of a superconducting dome by pressurizing the substituted crystals; we assigned this novel behavior to disorder emanating from chemical tuning.

A peak in the critical current for quantum critical superconductors

Generally, studies of the critical current I_c are necessary if superconductors are to be of practical use, because I_c sets the current limit below which there is a zero-resistance state. Here, we report a peak in the pressure dependence of the zero-field I_c, I_c(0), at a hidden quantum critical point (QCP), where a continuous antiferromagnetic transition temperature is suppressed by pressure toward 0 K in CeRhIn₅ and 4.4% Sn-doped CeRhIn₅. The I_c(0)s of these Ce-based compounds under pressure exhibit a universal temperature dependence, underlining that the peak in zero-field I_c(P) is determined predominantly by critical fluctuations associated with the hidden QCP. The dc conductivity σ_dc is a minimum at the QCP, showing anti-correlation with I_c(0). These discoveries demonstrate that a quantum critical point hidden inside the superconducting phase in strongly correlated materials can be exposed by the zero-field I_c, therefore providing a direct link between a QCP and unconventional superconductivity.

Perspective on the phase diagram of cuprate high-temperature superconductors

Universal scaling laws can guide the understanding of new phenomena, and for cuprate high-temperature superconductivity the influential Uemura relation showed, early on, that the maximum critical temperature of superconductivity correlates with the density of the superfluid measured at low temperatures. Here we show that the charge content of the bonding orbitals of copper and oxygen in the ubiquitous CuO2 plane, measured with nuclear magnetic resonance, reproduces this scaling. The charge transfer of the nominal copper hole to planar oxygen sets the maximum critical temperature. A three-dimensional phase diagram in terms of the charge content at copper as well as oxygen is introduced, which has the different cuprate families sorted with respect to their maximum critical temperature. We suggest that the critical temperature could be raised substantially if one were able to synthesize materials that lead to an increased planar oxygen hole content at the expense of that of planar copper.