Berry Phase Physics in Free and Interacting Fermionic Systems

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dc.contributor.advisor Son, Dam T. Chen, Jingyuan 2016-10-26T21:36:38Z 2016-10-26T21:36:38Z 2016 2016
dc.identifier doi:10.6082/M11Z4295
dc.description Berry phase plays an important role in many non-trivial phenomena over a broad range of many-body systems. In this thesis we focus on the Berry phase due to the change of the particles' momenta, and study its effects in free and interacting fermionic systems. We start with reviewing the semi-classical kinetic theory with Berry phase for a non-interacting ensemble of fermions -- a Berry Fermi gas -- which might be far-from-equilibrium. We particularly review the famous Berry phase contribution to the anomalous Hall current. We then provide a concrete and general path integral derivation for the semi-classical theory. Then we turn to the specific example of Weyl fermion, which exhibits the profound quantum phenomenon of chiral anomaly; we review how this quantum effect, and its closely related chiral magnetic effect and chiral vortical effect, arise from Berry phase in the semi-classical kinetic theory. We also discuss how Lorentz symmetry in the kinetic theory of Weyl fermion, seemly violated by the Berry phase term, is realized non-trivially; we provide a physical interpretation for this non-trivial realization, and discuss its mathematical foundation in Wigner translation. Next, we turn towards interacting fermionic systems. We consider Fermi liquid near equilibrium, and propose the Berry Fermi liquid theory -- the extension to Landau Fermi liquid theory incorporating Berry phase (and other) effects. In our proposed Berry Fermi liquid theory, we can show the Berry phase is a Fermi surface property, qualitatively unmodified by interactions. But there also arise new effects from interactions, most notably the emergent electric dipole moment which contributes to the anomalous Hall current in addition to the usual Berry phase contribution. We prove our proposed Berry Fermi liquid theory from quantum field theory to all orders in Feynman diagram expansion under very general assumptions.
dc.format.extent 175
dc.format.mimetype PDF
dc.language.iso en_US
dc.publisher University of Chicago
dc.rights University of Chicago dissertations are covered by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission.
dc.subject anomalous Hall effect
dc.subject Berry curvature
dc.subject Berry phase
dc.subject Fermi liquid
dc.subject kinetic theory
dc.subject Weyl fermion
dc.title Berry Phase Physics in Free and Interacting Fermionic Systems
dc.type Dissertation
dc.contributor.department Physics Ph.D.

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