Studies of Quantum Phase Transitions in Dirac Electron Systems

  • Author / Creator
    Yerzhakov, Hennadii
  • This thesis is dedicated to the study of quantum phase transitions in 2D Dirac semimetals. In Chapter 1, we first briefly review how Dirac fermions emerge in condensed matter systems and then briefly review the physics of quantum phase transitions. Chapter 2 is devoted to the field-theoretic study of the isotropic-nematic phase transition on the surface of a 3D topological insulator with a single Dirac cone in its band structure. Unlike spin-degenerate Fermi liquids, due to the spin-orbit-coupled nature of topological insulators, the nematic order parameter necessarily mixes spin and spatial degrees of freedom. First, using mean-field theory, we find that the system undergoes a first-order phase transition at zero temperature in the undoped limit, which then becomes continuous at a finite-temperature tricritical point. In the doped limit, the phase transition is continuous at zero temperature. We discuss several signatures of the nematic order, among which is the partial breakdown of spin-momentum locking. In many regards, the effects of fluctuations about the mean-field solution are qualitatively the same as for spin-degenerate Fermi liquids. However, we show that nematic fluctuations may induce spin fluctuations. In Chapter 3, we use the double epsilon expansion method of renormalization group theory to study the interplay of interactions and weak uncorrelated disorder on the superconducting phase transition in a 2D Dirac semimetal described by the chiral XY Gross-Neveu-Yukawa model. When the number of fermion flavors in the system is greater than one, we find new disordered quantum critical points, some of which are of stable-focus type. In Chapter 4, we extend this study to the Ising and Heisenberg Gross-Neveu-Yukawa models, appropriate to charge-density-wave and spin-density-wave transitions, and include long-range correlated disorder. A controlled treatment of the latter requires the introduction of another small parameter; the double epsilon expansion method is thus generalized into the triple epsilon expansion method. We find new short- and long-range disordered fixed points and show that for some regions of physical parameters, the critical behavior is controlled by a stable limit cycle.

  • Subjects / Keywords
  • Graduation date
    Spring 2021
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.