Characterizing the Hofstadter butterfly's outline with Chern numbers

Details Characterizing the Hofstadter butterfly's outline with Chern numbers Characterizing the Hofstadter butterfly's outline with Chern numbers

2008-08-11

arxiv.org/abs/0808.1440v3

J. Phys. B: At. Mol. Opt. Phys. 42 (2009) 055302

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Accepted for publication in J. Phys. B (Jan 2009)

Scientific paper

10.1088/0953-4075/42/5/055302

In this work, we report original properties inherent to independent particles subjected to a magnetic field by emphasizing the existence of regular structures in the energy spectrum's outline. We show that this fractal curve, the well-known Hofstadter butterfly's outline, is associated to a specific sequence of Chern numbers that correspond to the quantized transverse conductivity. Indeed the topological invariant that characterizes the fundamental energy band depicts successive stairways as the magnetic flux varies. Moreover each stairway is shown to be labeled by another Chern number which measures the charge transported under displacement of the periodic potential. We put forward the universal character of these properties by comparing the results obtained for the square and the honeycomb geometries.

Affiliated with

Also associated with

No associations

Rating

Characterizing the Hofstadter butterfly's outline with Chern numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Characterizing the Hofstadter butterfly's outline with Chern numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Characterizing the Hofstadter butterfly's outline with Chern numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-492630