Anomalous Transport In Low Dimension Materials

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.