Anomalous Transport In Low Dimension Materials

TL;DR

This dissertation develops a theoretical framework for realizing a Chiral Magnetic Effect analogue in engineered 2D honeycomb lattices by breaking sublattice symmetry and inducing a controllable imbalance, bridging high-energy physics and condensed matter.

Contribution

It introduces a low-energy effective Hamiltonian for a 2D system with broken sublattice symmetry, enabling a CME-like effect in engineered honeycomb lattices.

Findings

Validated model consistency through angular momentum conservation.

Demonstrated controllable valley imbalance analogous to chiral chemical potential.

Established symmetry conditions necessary for 2D CME manifestation.

Abstract

This dissertation presents a systematic theoretical investigation into realizing a condensed matter analogue of the Chiral Magnetic Effect (CME) in a quasi-planar, 2+1D system. The research establishes a conceptual bridge between the anomalous transport phenomena of high-energy physics and the emergent electronic properties of engineered honeycomb lattices. The central objective is the formulation of a low-energy effective Hamiltonian that incorporates the necessary ingredients for a CME-like effect. This is achieved by moving beyond pristine graphene, whose inherent sublattice symmetry precludes the formation of a mass gap necessary for defining robust pseudo-chiral states. The core of this work is a model based on a honeycomb lattice with explicitly broken sublattice symmetry, which introduces a band gap and endows the quasi-particles system with a well-defined pseudo-chirality based on sublattice polarization. A time-reversal symmetry-breaking parameter is introduced to asymmetrically modify the valley gaps, creating a controllable non-equilibrium imbalance analogous to the chiral chemical potential in relativistic systems. A key finding is the validation of the physical model consistency; through commutator calculations, the total angular momentum - comprising both orbital and an emergent lattice spin component - is shown to be a conserved quantity. This research successfully transforms the abstract possibility of a 2D CME into a concrete, self-consistent theoretical framework, detailing the precise symmetry conditions required for its manifestation.