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Quantum geometry and Landau levels of quadratic band crossings

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Title
Quantum geometry and Landau levels of quadratic band crossings
Author(s)
Junseo Jung; Hyeongmuk Lim; Bohm-Jung Yang
Publication Date
2024-01
Journal
Physical Review B, v.109, no.3
Publisher
AMER PHYSICAL SOC
Abstract
We study the relation between the quantum geometry of wave functions and the Landau level (LL) spectrum of two-band Hamiltonians with a quadratic band crossing point (QBCP) in two-dimensions. By investigating the influence of interband coupling parameters on the wave function geometry of general QBCPs, we demonstrate that the interband coupling parameters can be entirely determined by the projected elliptic image of the wave functions on the Bloch sphere, which can be characterized by three parameters, i.e., the major d1 and minor d2 diameters of the ellipse, and one angular parameter φ describing the orientation of the ellipse. These parameters govern the geometric properties of the system such as the Berry phase and modified LL spectra. Explicitly, by comparing the LL spectra of two quadratic band models with and without interband couplings, we show that the product of d1 and d2 determines the constant shift in LL energy while their ratio governs the initial LL energies near a QBCP. Also, by examining the influence of the rotation and time-reversal symmetries on the wave function geometry, we construct a minimal continuum model, which exhibits various wave function geometries. We calculate the LL spectra of this model and discuss how interband couplings give LL structure for dispersive bands as well as nearly flat bands. © 2024 American Physical Society.
URI
https://pr.ibs.re.kr/handle/8788114/14922
DOI
10.1103/PhysRevB.109.035134
ISSN
2469-9950
Appears in Collections:
Center for Correlated Electron Systems(강상관계 물질 연구단) > 1. Journal Papers (저널논문)
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