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Journal of Physics C Solid State Physics

Phase transitions in model superconductors

Ian D. Lawrie

Published Sep 10, 1982• 10 citations
Publisher

Abstract

Recent Monte Carlo simulations by Dasgupta and Halperin (1981) of a lattice model for superconductivity indicate a continuous transition, but do not rule out a first-order transition for sufficiently small electric charge. The author shows conversely that earlier arguments for a first-order transition in the continuum model fail when the charge exceeds a certain maximum value, which he calculates at first order of the epsilon expansion.

DOI
10.1088/0022-3719/15/25/006

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Recent Monte Carlo simulations by Dasgupta and Halperin (1981) of a lattice model for superconductivity indicate a continuous transition, but do not rule out a first-order transition for sufficiently small electric charge. The author shows conversely that earlier arguments for a first-order transition in the continuum model fail when the charge exceeds a certain maximum value, which he calculates at first order of the epsilon expansion.
Monte Carlo data and duality arguments, applied to a lattice model, are presented which indicate that a three-dimensional type-II superconductor should have a transition asymptotically equivalent to that of a superfluid with reversed temperature axis, and not a first-order transition. Results may apply to the nematic---smectic-AAA transition.
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Quantum phase transitions of a q-state Potts model in fractal lattices are studied using a continuous-time quantum Monte Carlo simulation technique. For small values of q, the transition is found to be second order and critical exponents of the quantum critical point are calculated. The dynamic critical exponent z is found to be greater than one for all fractals studied, which is in contrast to integer-dimensional regular lattices. When q is greater than a certain value q_{c}, the phase transition becomes first order, where q_{c} depends on the lattice. Further analysis shows that the characteristics of phase transitions are more sensitive to the average number of nearest neighbors than the Hausdorff dimension or the order of ramification.
In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d -wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.