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A Landau Level at Zero Flux: A Minimal Exactly-Solvable Route to Magic Flat Bands

Landau levels are perfectly flat bands with a large degeneracy that textbook knowledge ties to nonzero net magnetic flux. This notion can be violated. I will construct a minimal, exactly solvable model that produces a perfectly flat, Landau-level-like band, caused by a magnetic field with zero net flux. I will present closed-form eigenstates, the simple criterion for flatness (i.e. magic), and how the degeneracy emerges while the total flux remains zero. This construction is broadly relevant to time reversal symmetric systems that form flat bands, most famously, moire superlattices. In particular we show that our simple zero flux Hamiltonian has the exact same structure of the chiral model of the twisted bilayer graphene. Thus we relate a very abstract problem in condensed matter physics (what makes the chiral model for twisted bilayer graphene "click") to a quite concrete problem that could almost be posed as a homework exercise to first-year graduate students.

Host: Hae-Young Kee
Event series  Toronto Quantum Matter Seminars