Translational symmetry breaking and the disintegration of the Hofstadter butterfly

Abstract

We study the effect of interactions on the Hofstadter butterfly of the honeycomb lattice. We show that the interactions induce charge ordering that breaks the translational and rotational symmetries of the system. These phase transitions are prolific and occur at many values of the flux and particle density. The breaking of the translational symmetry introduces a new length scale in the problem and this affects the energy band diagram resulting in the disintegration of the fractal structure in the energy flux plot, the Hofstadter butterfly. This disintegration increases with increase in the interaction strength. Many of these phase transitions are accompanied with change in the Hall conductivity. Consequently, the disintegration of the Hofstadter butterfly is manifested in the Landau fan diagram also.

11 pages, 9 figures

References in corpus (7)

• Electron fractionalization in two-dimensional graphenelike structures
• Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Hofstadter butterfly for a finite correlated system
• Self-similar occurrence of massless Dirac particles in graphene under magnetic field
• Characterizing the Hofstadter butterfly's outline with Chern numbers
• Effects of Interaction in the Hofstadter regime of the honeycomb lattice

Cited by in corpus (6)

• Fractal defect states in the Hofstadter butterfly
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Persistence of gaps in the interacting Hofstadter model
• Topological multiferroic phases in the extended Kane-Mele-Hubbard Model in the Hofstadter regime
• Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model
• Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field