Helical metals and insulators and sheet singularity of inflated Berry monopole

Abstract

We study the new phases of interacting Dirac matter that host novel Berry signatures. We predict a topological Lifshitz phase transition caused by the changes of a Dirac cone intersection from a semimetalic phase to helical insulating or metallic phases. These helical phases provide the examples of gapless topological phase where spectral gap is not required for a topological protection. To realize nodal helical phases one would need to consider isotropic infinite-range inter-particle interaction. This interaction could emerge because of a momentum conserving scattering of electron from a bosonic mode. For repulsive/attractive interactions in density/pseudospin channel system undergoes a transition to helical insulator phase. For an attractive density-density interaction, a new metallic phase forms that hosts {\it nodal circle} and {\it nodal sphere} in two and three dimensions, respectively. A {\it sheet singularity} of Berry curvature is highlighted as a peculiar feature of the nodal sphere phase in 3D and represent the extension of the Berry monopole singularities into inflated monopole. To illustrate the properties of these helical phases we investigate Landau levels in both metallic and insulating phases. Our study provides an extension of the paradigm in the interacting Dirac matter and makes an interesting connection to inflated topological singularities in cosmology.

17 pages, 5 figures

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