Novel Quantum Criticality in Two Dimensional Topological Phase transitions

TL;DR

This paper uncovers a new type of quantum criticality in two-dimensional topological phase transitions involving anisotropic dispersion and long-range Coulomb interactions, with implications for various materials.

Contribution

It introduces a novel quantum critical point in 2D topological transitions with anisotropic dispersion, considering Coulomb interactions beyond conventional models.

Findings

Discovery of anisotropic Coulomb interaction effects.

Marginal modification of electronic excitations.

Predicted observable effects in experiments.

Abstract

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO${}_2$-VO${}_2$ heterostructure to organic material $\alpha$-(BEDT-TTF)${}_2$ I${}_3$ under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the 1/r long-range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality.