2019_EJRNL_PP_GRIGORY_TARNOPOLSKY_1.pdf
Terbatas Ratnasari
» ITB
Terbatas Ratnasari
» ITB
Twisted bilayer graphene (TBG) was recently shown to host superconductivity when tuned to special
“magic angles” at which isolated and relatively flat bands appear. However, until now the origin of the
magic angles and their irregular pattern have remained a mystery. Here we report on a fundamental
continuum model for TBG which features not just the vanishing of the Fermi velocity, but also the perfect
flattening of the entire lowest band. When parametrized in terms of ? ? 1=?, the magic angles recur with a
remarkable periodicity of ?? ? 3=2.We show analytically that the exactly flat band wave functions can be
constructed from the doubly periodic functions composed of ratios of theta functions—reminiscent of
quantum Hall wave functions on the torus. We further report on the unusual robustness of the
experimentally relevant first magic angle, address its properties analytically, and discuss how lattice
relaxation effects help justify our model parameters.