# Berry Fermi liquid theory

## Abstract

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current–current correlator exactly matches with the result obtained from the kinetic theory. - Highlights: • We extend Landau’s kinetic theory of Fermi liquid to incorporate Berry phase. • Berry phase effects in Fermi liquid take exactly the same form as in Fermi gas. • There is a new “emergent electric dipole” contribution to the anomalous Hall effect. • Our kinetic theory is matched to field theory to all orders in Feynman diagrams.

- Authors:

- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22617474

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 377; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FERMI GAS; FERMIONS; FEYNMAN DIAGRAM; HALL EFFECT; KINETIC EQUATIONS; PERTURBATION THEORY; QUANTUM FIELD THEORY

### Citation Formats

```
Chen, Jing-Yuan, E-mail: chjy@uchicago.edu, Stanford Institute for Theoretical Physics, Stanford University, CA 94305, and Son, Dam Thanh, E-mail: dtson@uchicago.edu.
```*Berry Fermi liquid theory*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2016.12.017.

```
Chen, Jing-Yuan, E-mail: chjy@uchicago.edu, Stanford Institute for Theoretical Physics, Stanford University, CA 94305, & Son, Dam Thanh, E-mail: dtson@uchicago.edu.
```*Berry Fermi liquid theory*. United States. doi:10.1016/J.AOP.2016.12.017.

```
Chen, Jing-Yuan, E-mail: chjy@uchicago.edu, Stanford Institute for Theoretical Physics, Stanford University, CA 94305, and Son, Dam Thanh, E-mail: dtson@uchicago.edu. Wed .
"Berry Fermi liquid theory". United States.
doi:10.1016/J.AOP.2016.12.017.
```

```
@article{osti_22617474,
```

title = {Berry Fermi liquid theory},

author = {Chen, Jing-Yuan, E-mail: chjy@uchicago.edu and Stanford Institute for Theoretical Physics, Stanford University, CA 94305 and Son, Dam Thanh, E-mail: dtson@uchicago.edu},

abstractNote = {We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current–current correlator exactly matches with the result obtained from the kinetic theory. - Highlights: • We extend Landau’s kinetic theory of Fermi liquid to incorporate Berry phase. • Berry phase effects in Fermi liquid take exactly the same form as in Fermi gas. • There is a new “emergent electric dipole” contribution to the anomalous Hall effect. • Our kinetic theory is matched to field theory to all orders in Feynman diagrams.},

doi = {10.1016/J.AOP.2016.12.017},

journal = {Annals of Physics},

number = ,

volume = 377,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2017},

month = {Wed Feb 15 00:00:00 EST 2017}

}