2007/07/31 by Petra Dietl, Frederic Piechon, Gilles Montambaux
Physics and Astronomy · #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.100.236405
published as Phys. Rev. Lett. 100, 236405 (2008) · 4 pages, 4 figures
arxiv created 2007/08/31 · arxiv updated 2009/12/01
We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic in the other. We find that, in this case, the energy of the Landau levels varies with the field B as En(B) ~ [(n+γ)B]2/3. This result is obtained from the low-field study of the tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter spectrum) as well as from a calculation in the continuum approximation at low field. The latter links the new spectrum to the one of a modified quartic oscillator. The obtained value γ=1/2 is found to result from the cancellation of a Berry phase.