Topological Landau Theory

TL;DR

This paper extends Landau's phase transition theory by incorporating the topology of the order parameter, revealing how nontrivial topology and Berry phases influence superconducting phase transitions and can be experimentally detected.

Contribution

It introduces a topological extension to Landau's theory, demonstrating the emergence of Berry phases in order parameters with multiple components and analyzing their effects in superconducting systems.

Findings

Order parameters can acquire a Berry phase during cyclic parameter evolution.

Topological features such as Dirac and Weyl points influence phase diagrams.

Experimental signatures of topology are observable in Josephson junctions.

Abstract

We present an extension of Landau's theory of phase transitions by incorporating the topology of the order parameter. When the order parameter comprises several components arising from multiplicity in the same irreducible representation of symmetry, it can possess a nontrivial topology and acquire a Berry phase under the variation of thermodynamic parameters. To illustrate this idea, we investigate the superconducting phase transition of an electronic system with tetragonal symmetry and an attractive interaction involving two partial waves, both transforming in the trivial representation. By analyzing the time-dependent Ginzburg-Landau equation in the adiabatic limit, we show that the order parameter acquires a Berry phase after a cyclic evolution of parameters. We study two concrete models -- one preserving time-reversal symmetry and one breaking it -- and demonstrate that the nontrivial topology of the order parameter originates from thermodynamic analogs of gapless Dirac and Weyl points in the phase diagram. Finally, we identify an experimental signature of the topological Berry phase in a Josephson junction.