Origin of Magic Angles in Twisted Bilayer Graphene Grisha Tarnopolsky Harvard University Talk at PCTS workshop ”Critical Phenomena in Statistical Mechanics and Quantum Field Theory’’ Princeton University October 4, 2018
Ashvin Vishwanath Alex Kruchkov Harvard Harvard Talk based on: GT, A. Kruchkov, A. Vishwanath arXiv:1808.05250
Plan • Graphene • Twisted Bilayer Graphene (TBG) • Continuum model for TBG and Magic angles • Origin of Magic angles
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sha1_base64="t7a0z12pa2avNaudf+gOnc1xm7Y=">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</latexit> <latexit sha1_base64="ZV4KHNqHr/IK0l9Ox3dY6xZNlY=">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</latexit> Graphene • Tight Binding Model (ignore spin) • Easy to diagonalize in Fourier space • Dirac Cones at K and K’ points P.R.Wallace, 1946
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