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Bloch, Landau, and Dirac: Hofstadter’s Butterfly in Graphene

Philip Kim, Department of Physics, Columbia University
Monday, November 5, 2012 - 4:00pm to 5:00pm
PAA A-102

In periodic electric potential, electrons form Bloch energy bands where their masses are effectively changed. In a strong magnetic field, the cyclotron orbits of electrons are quantized and Landau levels form with a massive degeneracy within. In 1976, Hofstadter showed that for 2-dimensional electronic system, the intriguing interplay between these two quantization effects can lead into a self-similar fractal set of energy spectra known as the“Hofstadter’s Butterfly.” Experimental efforts to demonstrate this fascinating electron energy spectrum have continued ever since. Graphene, in which Bloch electrons can be described by Dirac feremions, provides a new opportunity to investigate this nearly 40 year old problem experimentally. In this lecture I will discuss the experimental realization of Hofstaders butterfly in graphene. By using nanoscaled substrate engineering and extremely high magnetic fields, we can control length scales governing Dirac-Bloch states and Landau orbits in graphene, demonstrating the importance of the interplay between the two competing energy gaps.

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