2009/10/19 by C. Weeks, Conan Weeks, Marcel Franz +1 · 7 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Dirac fermion #Fermion #Lattice (music) #Massless particle #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Square lattice #Superconductivity #Topological Materials and Phenomena #Vortex #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.81.085105
published as PRB 81, 085105 (2010) · 8 pages, 4 figures
arxiv created 2009/10/19 · openalex publication_date 2010/02/05 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We explore the possible particle-hole instabilities that can arise in a system of massless Dirac fermions on both the honeycomb and \ensuremathπ-flux square lattices with short range interactions. Through analytical and numerical studies we show that these instabilities can result in a number of interesting phases. In addition to the previously identified charge and spin density wave phases and the exotic ``quantum anomalous Hall'' (Haldane) phase, we establish the existence of the dimerized ``Kekul'e'' phase over a significant portion of the phase diagram and discuss the possibility of its spinful counterpart, the ``spin Kekul'e'' phase. On the \ensuremathπ-flux square lattice we also find various stripe phases, which do not occur on the honeycomb lattice. The Kekul'e phase is described by a Z3 order parameter whose singly quantized vortices carry fractional charge \ifmmode±\else\textpm\fie/2. On the \ensuremathπ-flux lattice the analogous dimerized phase is described by a Z4 order parameter. We perform a fully self-consistent calculation of the vortex structure inside the dimerized phase and find that close to the core the vortex resembles a familiar superconducting U(1) vortex, but at longer length scales a clear Z4 structure emerges with domain walls along the lattice diagonals.