Benjamin Fregoso (Kent State University)

Date: Mon. October 27th, 2025, 12:45 pm-1:45 pm
Location: Rockefeller 221 (Foldy Room) & Zoom
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Nonlinear response of Bloch electrons to a magnetic field: average density

Professor Benjamin Fregoso
Kent State University

(Host: Shulei Zhang)

Abstract: Strong magnetic fields in crystals can confine electrons to tight regions of space, e.g. in the quantum Hall effects. Here we ask the question, what is the average density of a 3D crystal in the regime where the magnetic field is not so strong but beyond the linear response. We develop a general formalism to compute the average electron density of a clean crystal (of any space group, considering intraband and interband on equal footing) in terms of unperturbed Bloch wave functions. To first order, we recover Streda-like formulas with an additional contribution from the orbital magnetic moments at the Fermi sea. Implications of the existence of this additional term are discussed. If there is time reversal symmetry or the magnetic field is stronger, the second order term becomes important. To second order the expressions are more complex and naturally depend on geometric aspects of the wave functions such as the quantum metric tensor. Our expressions can be used to compute electron density of materials using large scale numerical codes, and, similar to the Streda formula, be used as a diagnostic tool for the existence (or lack thereof) of topological states.