TY - JOUR

T1 - Disorder-induced quantum phase transitions in three-dimensional topological insulators and superconductors

AU - Ryu, Shinsei

AU - Nomura, Kentaro

PY - 2012/4/26

Y1 - 2012/4/26

N2 - We discuss the effects of disorder in time-reversal-invariant topological insulators and superconductors in three spatial dimensions. For three-dimensional topological insulator in the symplectic (AII) symmetry class, the phase diagram in the presence of disorder and a mass term, which drives a transition between trivial and topological insulator phases, is computed numerically by the transfer matrix method. The numerics is supplemented by a field-theory analysis (the large-N f expansion, where N f is the number of valleys or Dirac cones), from which we obtain the correlation length exponent, and several anomalous dimensions at a nontrivial critical point separating a metallic phase and a Dirac semimetal. A similar-field theory approach is developed for disorder-driven transitions in symmetry classes AIII, CI, and DIII. For these three symmetry classes, where topological superconductors are characterized by integer topological invariant, a complementary description is given in terms of the nonlinear sigma model supplemented with a topological term, which is a three-dimensional analog of the Pruisken term in the integer quantum Hall effect.

AB - We discuss the effects of disorder in time-reversal-invariant topological insulators and superconductors in three spatial dimensions. For three-dimensional topological insulator in the symplectic (AII) symmetry class, the phase diagram in the presence of disorder and a mass term, which drives a transition between trivial and topological insulator phases, is computed numerically by the transfer matrix method. The numerics is supplemented by a field-theory analysis (the large-N f expansion, where N f is the number of valleys or Dirac cones), from which we obtain the correlation length exponent, and several anomalous dimensions at a nontrivial critical point separating a metallic phase and a Dirac semimetal. A similar-field theory approach is developed for disorder-driven transitions in symmetry classes AIII, CI, and DIII. For these three symmetry classes, where topological superconductors are characterized by integer topological invariant, a complementary description is given in terms of the nonlinear sigma model supplemented with a topological term, which is a three-dimensional analog of the Pruisken term in the integer quantum Hall effect.

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U2 - 10.1103/PhysRevB.85.155138

DO - 10.1103/PhysRevB.85.155138

M3 - Article

AN - SCOPUS:84860477374

SN - 1098-0121

VL - 85

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 15

M1 - 155138

ER -