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Anomalous Transport In Low Dimension Materials

Leonardo Lopes

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.

Anomalous Transport In Low Dimension Materials

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.
Paper Structure (47 sections, 84 equations, 18 figures)

This paper contains 47 sections, 84 equations, 18 figures.

Table of Contents

  1. Introduction
  2. Chiral Magnetic Effect
  3. Introduction
  4. Theoretical Framework
  5. The QCD Vacuum and its Hidden Landscape
  6. A Deeper Look at Chirality and Helicity
  7. Chiral Symmetry and its Quantum Anomaly
  8. The Chiral Magnetic Effect
  9. An Idealized Picture
  10. The Real-World Scenario
  11. The Search in Heavy-Ion Collisions
  12. From a Fleeting Current to a Measurable Signal
  13. The Experimental Signature
  14. Bridge between QCD and materials
  15. Graphene and Symmetries
  16. ...and 32 more sections

Figures (18)

  • Figure 1: Representation of the QCD energy states.
  • Figure 2: An illustration of the CME in a very large, homogeneous magnetic field. The red arrows denote momentum, and the blue arrows denote spin. The figure is broken down into three stages, read from left to right. Figure extracted from the reference KHARZEEV2008227.
  • Figure 3: The measured three-particle correlator $\langle\cos(\phi_{\alpha}+\phi_{\beta}-2\Psi_{RP})\rangle$ as a function of collision centrality for $Au+Au$ and $Cu+Cu$ systems at 200 GeV. Same-charge pairs are shown with circles (red) and opposite-charge pairs with squares (blue). Figure extracted from the reference PhysRevLett.103.251601.
  • Figure 4: No predefined signatures of the CME were observed in this blind analysis. The study compared results from Ruthenium ($Ru+Ru$) and Zirconium ($Zr+Zr$) collisions. It found that the ratio of CME-sensitive measurements was below one, leading to the conclusion of a null result. The presented data distinguishes between CME-sensitive (solid symbols) and insensitive (open symbols) measures, showing both statistical and systematic uncertainties. Figure extracted from the reference PhysRevC.105.014901.
  • Figure 5: This graph is critically important as it shows that when the magnetic field is aligned parallel to the current (at an angle of $90 ^{\circ}$), the material exhibits a large negative magnetoresistance. This specific phenomenon — a decrease in resistance when electric and magnetic fields are parallel — is a key signature of the CME. Figure extracted from reference Li2016.
  • ...and 13 more figures