High-resolution calorimetry and thermal-expansion data on the high-temperature superconductor YBa2Cu3O7−δ with weak point disorder showed that the superconducting transition in a magnetic field behaves as an extremely fragile kinetic glass transition of the vortex liquid rather than an equilibrium phase transition. Whether the in-field superconducting transition of disordered cuprates is genuinely kinetic or is a true thermodynamic vortex-glass transition remains undecided, and the microscopic origin of the anomalously large vortex-liquid heat-capacity jump that produces the extreme fragility is unknown. The problem is to determine the equilibrium status of this transition in weakly point-disordered YBa2Cu3O7−δ and to identify the mechanism behind the anomalous liquid thermodynamics—strong thermal phase fluctuations, vortex-loop excitations, a nearby liquid–liquid critical point, or combinations thereof.

Background

In a type-II superconductor in a magnetic field, magnetic flux penetrates as quantized filaments (vortices) that form a distinct thermodynamic phase of matter, 'vortex matter', with its own solid, liquid and glassy states. In clean high-TcT_c cuprates the vortex lattice melts in a first-order transition, seen calorimetrically as a latent heat and an entropy jump ΔSm\Delta S_m. With weak random point disorder (pinning), the first-order melting line terminates and the resistive transition of the mixed state is widely described using the vortex-glass idea of Fisher, Fisher and Huse: quenched disorder destroys vortex-lattice positional order at all scales, and a true second-order thermodynamic transition separates a dissipative vortex liquid from a vortex-glass phase with zero linear resistivity. Whether the observed in-field transition is such an equilibrium critical phenomenon or merely a kinetic arrest—like the glass transition of a supercooled structural liquid, which is kinetic rather than thermodynamic—has been debated since the early 1990s. Lortz, Meingast, Rykov and Tajima (2006) addressed this with high-resolution thermal expansion and magnetization of slightly disordered YBa2Cu3O7−δ. They showed that the vortex-liquid entropy, extrapolated below the melting temperature TmT_m, would fall below that of the vortex solid at a Kauzmann temperature TKT_K (the temperature at which the supercooled liquid's entropy would equal the crystal's, a classic paradox of glass physics), and that the relaxation of the vortex system freezes in with the highly non-Arrhenius, Vogel–Fulcher–Tammann-type kinetics that define an extremely 'fragile' glass former in Angell's strong/fragile classification. They concluded that the field-tuned superconducting transition of disordered YBa2Cu3O7−δ is a kinetic glass transition, and identified its thermodynamic driver: an anomalously large heat-capacity jump ΔCp\Delta C_p of the vortex liquid (measured calorimetrically by Schilling et al.), whose origin is unknown. Candidate explanations they list are strong thermal phase fluctuations of the superconducting order parameter, describable as closed vortex-loop excitations (treated theoretically by Tešanović and by Nguyen and Sudbø), or the vicinity of a liquid–liquid transition or critical point in the vortex phase diagram (anomalous second liquid phases were reported in YBa2Cu3O7 by Bouquet et al. and by Kwok et al.), or a combination. Later work has deepened the neighboring landscape without deciding the question: simulations remain split, with some finding genuine vortex-glass order and others no thermodynamic transition driven by proliferation of closed vortex loops; quantitative melting-thermodynamics theory (Li and Rosenstein) and specific-heat theories of the vortex liquid do not reproduce the full anomaly; and in two-dimensional weakly pinned films fragile-glass (Vogel–Fulcher–Tammann) dynamics and hexatic intermediate fluids (phases with sixfold bond-orientational order but no long-range positional order) are now documented, showing the glass-dynamics phenomenology is real but leaving the three-dimensional disordered cuprate case, and the role of pinning versus intrinsic fluctuations, unsettled.

Problem Statement

Determine the equilibrium nature of the superconducting transition in a magnetic field of weakly point-disordered YBa2Cu3O7−δ—kinetic glass arrest of the vortex liquid or true thermodynamic vortex-glass transition—and identify the microscopic origin of the anomalously large vortex-liquid heat-capacity jump ΔCp\Delta C_p and the resulting extreme fragility. Concretely, as posed by the source work: (i) identify the mechanism—strong thermal phase fluctuations of the superconducting order parameter, vortex-loop excitations, a nearby liquid–liquid critical point, or a combination—that produces the excess heat capacity and entropy of the vortex liquid; (ii) establish whether random pinning alone suffices to produce the observed kinetic arrest, or whether intrinsic fluctuation degrees of freedom (phase fluctuations, vortex-loop excitations, vortex entanglement) are required; and (iii) determine whether a liquid–liquid transition or critical point exists in the vortex phase diagram near the Kauzmann point, and whether it causes the large ΔCp\Delta C_p and the fragile kinetics.

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