PIRSA:13110070

Hofstadter’s Butterfly and interaction driven quantum Hall ferromagnetism in graphene

Kim, P. (2013). Hofstadter’s Butterfly and interaction driven quantum Hall ferromagnetism in graphene. Perimeter Institute. https://pirsa.org/13110070

Kim, Philip. Hofstadter’s Butterfly and interaction driven quantum Hall ferromagnetism in graphene. Perimeter Institute, Nov. 07, 2013, https://pirsa.org/13110070 

          @misc{ pirsa_PIRSA:13110070,
            doi = {10.48660/13110070},
            url = {https://pirsa.org/13110070},
            author = {Kim, Philip},
            keywords = {},
            language = {en},
            title = {Hofstadter{\textquoteright}s Butterfly and interaction driven quantum Hall ferromagnetism in graphene},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {nov},
            note = {PIRSA:13110070 see, \url{https://pirsa.org}}
          }

Philip Kim Columbia University

DOI 10.48660/13110070
Collection
Talk Type Conference

Abstract

Electrons moving in a periodic electric potential form Bloch energy bands where the mass of electrons are effectively changed. In a strong magnetic field, the cyclotron orbits of free electrons are quantized and Landau levels forms 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 spectrum known as “Hofstadter’s Butterfly.” Experimental efforts to demonstrate this fascinating electron energy spectrum have continued ever since. Recent advent of graphene, where its Bloch electrons can be described by Dirac feremions, provides a new opportunity to investigate this half century old problem experimentally. In this presentation, I will discuss the experimental realization Hofstadter’s Butterfly via substrate engineered graphene under extremely high magnetic fields controlling two competing length scales governing Dirac-Bloch states and Landau orbits, respectively. In addition, the strong Coulomb interactions and approximate spin-pseudo spin symmetry are predicted to lead to a variety of integer quantum Hall ferromagnetic and fractional quantum Hall states and the quantum phase transition between them in graphene. I will discuss several recent experimental evidences to demonstrate the role of the electron interaction in single and bilayer graphene.