Influence of the Electron–Phonon
Interaction on the Topological Phase
Transition in BiTeI
Véronique Brousseau-Couture and Michel Côté
Abstract The topological order of a material is intrinsically related to its bulk
electronic structure. Topological phase transitions require that the bulk band gap
vanishes. However, the gap is affected by atomic motion through electron–phonon
interaction, even at T = 0 K. As a consequence, electron–phonon interaction
can either promote or suppress topologically non-trivial phases. In this work, the
temperature dependence of the pressure-induced topological phase transition in
Rashba semiconductor BiTeI is investigated through first-principles methods. We
first present an overview of electron–phonon interaction within the framework of
density-functional perturbation theory (DFPT) and derive a qualitative argument
to understand how it will affect the band gap for both typical semiconductors
and topological insulators. Then, by tracking both the pressure and temperature
dependence of the bulk band gap, we show how the Weyl semimetal and topological
insulator phases of BiTeI evolve with temperature, thus providing a guideline for
experimental detection.
Keywords Electron–phonon interaction · Density-functional theory ·
Topological phase transitions
1 Introduction
Since their theoretical prediction in the 1980s, the study of topological phases of
matter has grown to become a very active field of research in condensed matter
physics. A peculiarity of such phases resides in the fact that they cannot be
explained by Landau theory, as transitioning from a topologically trivial to a nontrivial phase does not involve any symmetry breaking. From the bulk-boundary
correspondence principle [1], the non-trivial phases are characterized by symmetryV. Brousseau-Couture () · M. Côté
Université de Montréal and Regroupement Québécois sur les Matériaux de Pointe,
Montréal, QC, Canada
e-mail: veronique.brousseau.couture@umontreal.ca; michel.cote@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_29
305
Interaction on the Topological Phase
Transition in BiTeI
Véronique Brousseau-Couture and Michel Côté
Abstract The topological order of a material is intrinsically related to its bulk
electronic structure. Topological phase transitions require that the bulk band gap
vanishes. However, the gap is affected by atomic motion through electron–phonon
interaction, even at T = 0 K. As a consequence, electron–phonon interaction
can either promote or suppress topologically non-trivial phases. In this work, the
temperature dependence of the pressure-induced topological phase transition in
Rashba semiconductor BiTeI is investigated through first-principles methods. We
first present an overview of electron–phonon interaction within the framework of
density-functional perturbation theory (DFPT) and derive a qualitative argument
to understand how it will affect the band gap for both typical semiconductors
and topological insulators. Then, by tracking both the pressure and temperature
dependence of the bulk band gap, we show how the Weyl semimetal and topological
insulator phases of BiTeI evolve with temperature, thus providing a guideline for
experimental detection.
Keywords Electron–phonon interaction · Density-functional theory ·
Topological phase transitions
1 Introduction
Since their theoretical prediction in the 1980s, the study of topological phases of
matter has grown to become a very active field of research in condensed matter
physics. A peculiarity of such phases resides in the fact that they cannot be
explained by Landau theory, as transitioning from a topologically trivial to a nontrivial phase does not involve any symmetry breaking. From the bulk-boundary
correspondence principle [1], the non-trivial phases are characterized by symmetryV. Brousseau-Couture () · M. Côté
Université de Montréal and Regroupement Québécois sur les Matériaux de Pointe,
Montréal, QC, Canada
e-mail: veronique.brousseau.couture@umontreal.ca; michel.cote@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_29
305