The specific heat of the layered organic superconductor $\kappa \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2\mathrm{Cu}(\mathrm{NCS}{)}_2$, where BEDT-TTF is bisethylenedithio-tetrathiafulvalene, has been studied in magnetic fields up to 28 T applied perpendicular and parallel to the superconducting layers. In parallel fields above 21 T, the superconducting transition becomes first order, which signals that the Pauli-limiting field is reached. Instead of saturating at this field value, the upper-critical-field increases sharply and a second first-order transition line appears within the superconducting phase. Our results give strong evidence that the phase, which separates the homogeneous superconducting state from the normal state is a realization of a Fulde-Ferrell-Larkin-Ovchinnikov state.

At the liquid–gas phase transition in water, the density has a discontinuity at atmospheric pressure; however, the line of these first-order transitions defined by increasing the applied pressure terminates at the critical point¹, a concept ubiquitous in statistical thermodynamics². In correlated quantum materials, it was predicted³ and then confirmed experimentally^4,5 that a critical point terminates the line of Mott metal–insulator transitions, which are also first-order with a discontinuous charge carrier density. In quantum spin systems, continuous quantum phase transitions⁶ have been controlled by pressure^7,8, applied magnetic field^9,10 and disorder¹¹, but discontinuous quantum phase transitions have received less attention. The geometrically frustrated quantum antiferromagnet SrCu₂(BO₃)₂ constitutes a near-exact realization of the paradigmatic Shastry–Sutherland model^12,13,14 and displays exotic phenomena including magnetization plateaus¹⁵, low-lying bound-state excitations¹⁶, anomalous thermodynamics¹⁷ and discontinuous quantum phase transitions^18,19. Here we control both the pressure and the magnetic field applied to SrCu₂(BO₃)₂ to provide evidence of critical-point physics in a pure spin system. We use high-precision specific-heat measurements to demonstrate that, as in water, the pressure–temperature phase diagram has a first-order transition line that separates phases with different local magnetic energy densities, and that terminates at an Ising critical point. We provide a quantitative explanation of our data using recently developed finite-temperature tensor-network methods^17,20,21,22. These results further our understanding of first-order quantum phase transitions in quantum magnetism, with potential applications in materials where anisotropic spin interactions produce the topological properties^23,24 that are useful for spintronic applications.

The realization of superconductivity at the interface between a topological insulator and an iron-chalcogenide compound is highly attractive for exploring several recent theoretical predictions involving these two new classes of materials. Here we report transport measurements on a Bi₂Te₃/FeTe heterostructure fabricated via van der Waals epitaxy, which demonstrate superconductivity at the interface, which is induced by the Bi₂Te₃ epilayer with thickness even down to one quintuple layer, though there is no clear-cut evidence that the observed superconductivity is induced by the topological surface states. The two-dimensional nature of the observed superconductivity with the highest transition temperature around 12 K was verified by the existence of a Berezinsky–Kosterlitz–Thouless transition and the diverging ratio of in-plane to out-plane upper critical field on approaching the superconducting transition temperature. With the combination of interface superconductivity and Dirac surface states of Bi₂Te₃, the heterostructure studied in this work provides a novel platform for realizing Majorana fermions.