Title: Wave function geometry and anomalous Landau levels of flat bands
Date/Time: Tuesday, 13 April, 2021 / 5:00 p.m
Speaker: Bohm Jung Yang
Semiclassical quantization of electronic states under magnetic field describes not only the Landau level spectrum but also the geometric responses of metals under a magnetic field. However, it is unclear whether this semiclassical idea is valid in dispersionless flat-band systems, in which an infinite number of degenerate semiclassical orbits are allowed. Here we show that the semiclassical quantization rule breaks down for a class of flat bands including singular flat bands and isolated flat bands. The Landau levels of such a flat band develop in the empty region in which no electronic states exist in the absence of a magnetic field, and exhibit an unusual dependence on the Landau level index n, which results in anomalous orbital magnetic susceptibility. The total energy spread of the Landau levels of flat bands is determined by the quantum geometry of the relevant Bloch states, which is characterized by their Hilbert–Schmidt quantum distance and fidelity tensors. The results indicate that the anomalous Landau level spectrum of flat bands is promising for the direct measurement of the quantum geometry of wavefunctions in condensed matter.