Berry phase effects on electronic properties

By Di Xiao, M. Chang, Q. Niu. 2009

3,626 citations recorded by the source corpus.

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/9bb25af8e69da541b758adee0acdcc00828d0561

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Spinor Bose-Einstein condensates (2010, background): “The Berry phase is a geometric phase accumulated in the parameter space of the Hamiltonian when the system undergoes an adiabatical cycle [12,13].”
Berry curvature dipole senses topological transition in a moiré superlattice (2022, background): “However, these states are symmetry equivalent and would not explain the hysteresis observed in the resistances of TDBG, which we argue to arise from two mechanisms: (1) inhomogeneous doping across the layers in the TDBG due to differences in the top and bottom doping as evident in our calculations o”
Riemannian geometry of resonant optical responses (2021, background): “As we show in Supplementary Note 3, w 1 = w n 1 − w 1 , (63) where w 1 and w m 1 are the first Stiefel-Whitney numbers of bands n and m, or equivalently, the Berry phases of bands n and m divided by π [3, 4].”
Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms (2014, background): “Considering cold atoms in optical lattices, it has been shown theoretically that semiclassical dynamics could allow for an observation of the Berry curvature through transport measurements, and could lead to a determination of the Chern number characterizing topological Bloch bands [4, 7, 10, 11].”
Thouless pumping and topology (2022, background): “The pumping mechanism can be understood from the point of view of a cycle in the parameters space (J1 − J2,∆), whose winding number is directly related to the Chern number of the pump [27].”