School of Physics Thesis Dissertation Defense

Xiaoyong Zhang  
Advisor: Dr. Carlos Sá de Melo, School of Physics, Georgia Institute of Technology

One-Dimensional Interacting Fermions with Spin-Orbit Coupling: Collective Excitations and Spin-Charge Hybridization

Date: Friday, November 7, 2025  
Time:  11:00 a.m.     
Location: Howey W401

Zoom link:  https://gatech.zoom.us/j/95152479502?pwd=vN0LD1PD6Zavg6qxWlYifU5Ya07pjy.1

Meeting ID: 951 5247 9502

Passcode: 191324

Committee Members:

Dr. Martin Mourigal, School of Physics, Georgia Institute of Technology

Dr. Michael Pustilnik, School of Physics, Georgia Institute of Technology

Dr. Chandra Raman, School of Physics, Georgia Institute of Technology

Dr. Luiz Santos, Department of Physics, Emory University

Abstract: 

One-dimensional fermionic systems exhibit rich collective behavior described by Tomonaga-Luttinger liquid theory, where interactions drive collective excitations into distinct charge and spin density waves that propagate at different velocities, a phenomenon known as the spin-charge separation. A natural question is how these collective modes are modified by additional effects present in those systems, such as spin-orbit coupling. Specifically, does the spin-momentum locking introduced by spin-orbit coupling dramatically influence excitations and fundamentally modify their nature?

This work aims to address these questions by showing that for SU(2) fermions, short-range interactions produce hybridized spin-charge modes with tunable velocities, while long-range Coulomb interactions give rise to a non-linear plasmon-hybrid mode and an acoustic-hybrid mode. Computation and analysis of the dynamical structure factor tensor provide a direct characterization of the hybridization among collective excitations and establish a connection between theoretical predictions and experimentally accessible observables. Extending to higher-symmetry systems, SU(3) fermions with “color-orbit coupling” are studied both with and without interactions.  The bosonization formalism is generalized to provide a method for determining the energy dispersion in the long-wavelength limit. This approach is further examined in the non–color-momentum–coupling limit, where a generalized mode separation emerges, consisting of one total-density mode and two degenerate spin-like modes. This work demonstrates that spin-orbit coupling serves as a universal mechanism for hybridizing collective modes in one-dimensional quantum liquids, providing a theoretical basis for exploring correlated quantum dynamics in engineered low-dimensional systems.