Masses in graphenelike two-dimensional electronic systems: Topological defects in order parameters and their fractional exchange statistics

Shinsei Ryu, Christopher Mudry, Chang Yu Hou, Claudio Chamon

Research output: Contribution to journalArticlepeer-review

137 Scopus citations

Abstract

We classify all possible 36 gap-opening instabilities in graphenelike structures in two dimensions, i.e., masses of Dirac Hamiltonian when the spin, valley, and superconducting channels are included. These 36 order parameters break up into 56 possible quintuplets of masses that add in quadrature and hence do not compete and thus can coexist. There is additionally a sixth competing mass, the one added by Haldane to obtain the quantum Hall effect in graphene without magnetic fields, which breaks time-reversal symmetry and competes with all other masses in any of the quintuplets. Topological defects in these five-dimensional order parameters can generically bind excitations with fractionalized quantum numbers. The problem simplifies greatly if we consider spin-rotation invariant systems without superconductivity. In such simplified systems, the possible masses are only 4 and correspond to the Kekulé dimerization pattern, the staggered chemical potential, and the Haldane mass. Vortices in the Kekulé pattern are topological defects that have Abelian fractional statistics in the presence of the Haldane term. We calculate the statistical angle by integrating out the massive fermions and constructing the effective field theory for the system. Finally, we discuss how one can have generically non-Landau-Ginzburg-type transitions with direct transitions between phases characterized by distinct order parameters.

Original languageEnglish (US)
Article number205319
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume80
Issue number20
DOIs
StatePublished - Nov 18 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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