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
Abstract:
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.