Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals

Abstract

We theoretically study the stability of three dimensional Dirac semimetals against short-range electron-electron interaction and quenched time-reversal symmetric disorder (but excluding mass disorder). First we focus on the clean interacting and the noninteracting dirty Dirac semimetal separately, and show that they support two distinct quantum critical points. Using renormalization group techniques, we find that while interaction driven quantum critical points are \emph{Gaussian} (mean-field) in nature, describing quantum phase transitions into various broken symmetry phases, the ones controlled by disorder are \emph{non-Gaussian}, capturing the transition to a metallic phase. We classify such diffusive quantum critical points based on the transformation of disorder vertices under a \emph{continuous} chiral rotation. Our wek coupling renormalization group analysis suggests that two distinct quantum critical points are stable in an interacting dirty Dirac semimetal (with chiral symmetric randomness), and a multicritical point (at finite interaction and disorder) results from their interplay. By contrast, the chiral symmetry breaking disorder driven critical point is unstable against weak interactions. Effects of weak disorder on the ordering tendencies in Dirac semimetal are analyzed. The clean interacting critical points, however, satisfy the \emph{Harris criterion}, and are therefore expected to be unstable against bond disorder. Although our weak coupling analysis is inadequate to establish the ultimate stability of these fixed points in the strong coupling regime (when both interaction and disorder are strong), they can still govern crossover behaviors in Dirac semimetals over a large length scale, when either interaction or randomness is sufficiently weak.

Published Version: 28 Pages, 10 Figures, 5 Tables, added discussion, new references

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• Monte-Carlo study of Dirac semimetals phase diagram
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Exploring self-consistency of the equations of axion electrodynamics in Weyl semimetals
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Superconductivity in two-dimensional disordered Dirac semimetals
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• Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
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• Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
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• Superconductivity in doped planar Dirac insulators: A renormalization group study
• Superconductivity in three-dimensional interacting doped topological insulators
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Critical fates induced by the interaction competition in three-dimensional tilted Dirac semimetals