Topological Landau Theory
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909657188007936 |
|---|---|
| author | Sun, Canon Maciejko, Joseph |
| author_facet | Sun, Canon Maciejko, Joseph |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Landau Theory Sun, Canon Maciejko, Joseph Superconductivity Mesoscale and Nanoscale Physics Other Condensed Matter Statistical Mechanics 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. |
| title | Topological Landau Theory |
| topic | Superconductivity Mesoscale and Nanoscale Physics Other Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2412.15103 |