Renormalization group analysis of Dirac fermions with random mass

Abstract

Two-dimensional (2D) disordered superconductor (SC) in class D exhibits a disorder-induced quantum multicritical phenomenon among diffusive thermal metal (DTM), topological superconductor (TS), and conventional localized (AI) phases. To characterize the quantum tricritical point where these three phases meet, we carry out a two-loop renormalization group (RG) analysis for 2D Dirac fermion with random mass in terms of the $\epsilon$-expansion in the spatial dimension $d=2-\epsilon$. In 2D ($\epsilon =0$), the random mass is marginally irrelevant around a clean-limit fixed point of the gapless Dirac fermion, while there exists an IR unstable fixed point at finite disorder strength that corresponds to the tricritical point. The critical exponent, dynamical exponent, and scaling dimension of the (uniform) mass term are evaluated around the tricritical point by the two-loop RG analysis. Using a mapping between an effective theory for the 2D random-mass Dirac fermion and the (1+1)-dimensional Gross-Neveu model, we further deduce the four-loop evaluation of the critical exponent, and the scaling dimension of the uniform mass around the tricritical point. Both the two-loop and four-loop results suggest that criticalities of a AI-DTM transition line as well as TS-DTM transition line are controlled by other saddle-point fixed point(s) at finite uniform mass.

arXiv comment21 pages, 14 figures

References in corpus (51)

• Anyons in an exactly solved model and beyond
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Anderson Transitions
• Evidence for Majorana bound state in an iron-based superconductor
• Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Quantum criticality between topological and band insulators in $(3+1)$-dimensions
• Quasiparticle localization in superconductors with spin-orbit scattering
• Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Non-Majorana Origin of the Half-Quantized Conductance Plateau in Quantum Anomalous Hall Insulator and Superconductor Hybrid Structures
• Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals
• Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors
• Disordered weak and strong topological insulators
• Thermal metal in network models of a disordered two-dimensional superconductor
• Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry
• Effect of Disorder in a Three-Dimensional Layered Chern Insulator
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• Criticality in the two-dimensional random-bond Ising model
• Phase diagrams of disordered Weyl semimetals
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
• Diffusive Quantum Criticality in Three Dimensional Disordered Dirac Semimetals
• Unconventional localisation transition in high dimensions
• Ballistic transport in disordered graphene
• Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures
• Four loop renormalization of the Gross-Neveu model
• Learning Disordered Topological Phases by Statistical Recovery of Symmetry
• Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality
• Disorder-induced Majorana metal in interacting non-Abelian anyon systems
• Critical exponents at the unconventional disorder-driven transition in a Weyl semimetal
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• Effective mass and tricritical point for lattice fermions localized by a random mass
• Quantum phase transition of chiral Majorana fermion in the presence of disorder
• Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• Temperature enhancement of thermal Hall conductance quantization
• Note on "Diffusive quantum criticality in three-dimensional disordered Dirac semimetals"
• The renormalization group flow in field theories with quenched disorder
• Anderson-Kitaev spin liquid
• Critical behavior of the 2D Ising model with long-range correlated disorder
• Quantum Multicriticality in Disordered Weyl Semimetal
• Multicriticality of Two-dimensional Class D Disordered Topological Superconductors
• On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model
• Universal critical exponent in class D superconductors
• Griffiths phase in the thermal quantum Hall effect
• Critical fixed points in class D superconductors
• Unconventional scaling theory in disorder-driven quantum phase transition
• The phase diagram of a two-dimensional dirty tilted Dirac semimetal
• Localization properties of random-mass Dirac fermions from real-space renormalization group

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