Exploring linear and nonlinear electromagnetic responses in topological materials

McKay, Robert C.

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https://hdl.handle.net/2142/124302 Copy

Description

Title

Exploring linear and nonlinear electromagnetic responses in topological materials

Author(s)

McKay, Robert C.

Issue Date

2024-04-18

Director of Research (if dissertation) or Advisor (if thesis)

Bradlyn, Barry

Doctoral Committee Chair(s)

Vishveshwara, Smitha

Committee Member(s)

• Stone, Michael
• Mahmood, Fahad

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• linear response
• nonlinear response
• topological materials
• Weyl semimetal
• Weyl-CDW
• Charge-density waves
• electromagnetic response
• spatially inhomogeneous
• nonuniform
• massless mode
• massive mode
• axion
• axial anomaly
• chiral anomaly
• Kramers
• Feynman diagram
• diagrammatic response
• ARPES
• photoexcitation
• dichroism
• Maxwell's equations
• Green's functions
• Matsubara sum
• Chern insulator
• moiré
• Kerr effect
• Kerr rotation
• Kerr ellipticity
• magnetic field
• electric field
• magnetic moment
• magnetic insulator

Abstract

This dissertation serves to examine the linear and nonlinear electromagnetic response properties in topological materials.Topological materials tend to produce unique transport signatures that point to the underlying topology of its electronic energy bands.Furthermore, given the recent experimental interest in terahertz spectroscopy and nonlinear response theories, we specifically focus on the linear and nonlinear electromagnetic response properties in such materials.The particular and timely topological materials that are covered in this thesis are the conventional Weyl semimetal, the Kramers Weyl semimetal, and the moiré Chern insulator. We begin this research topic by understanding how charge-density waves impact electric field-induced transport in the topological system: the Weyl semimetal.Research over the past several years has reinvigorated the examination of how charge-density waves interact with topology. This renewed interest stems not only from advancements in optical spectroscopy experiments (i.e. more readily measurable nonlinear electromagnetic responses) but also in how materials with distinct transport signatures are impacted by charge-density wave interactions. To understand how topologically nontrivial Weyl semimetals couple to charge-density waves, we evaluate the linear and nonlinear longitudinal collective responses from perturbing electric fields, and contemplate the possible collective phonon modes mediating these responses. We consider the onset of the phase-modulating (massless) collective modes and amplitude-modulating (massive) collective modes in these responses. We find that the tilted Weyl-charge-density wave model can yield nontrivial linear longitudinal collective conductivity, mediated by the massless collective propagator mode. We also find that the untilted Weyl-charge-density wave model can yield a third-order longitudinal collective conductivity mediated by the massive collective propagator mode. Continuing our research into the electromagnetic transport in Weyl semimetals, we will also explore the angle-resolved photoemission spectroscopy of a Kramers Weyl semimetal. The Kramers Weyl semimetal is an interesting topological system with nested Fermi surfaces, stemming from chiral materials with strong spin-orbit coupling at high symmetry points. This widens the breadth of this thesis, not only in terms of exotic topological materials, but also in terms of electromagnetic-induced responses. In this chapter, we also consider the experimentally relevant system of (TaSe$_4$)$_2$I, which allows for experimental checking of our one-step photoemission model. We investigate how the spin texture of Kramers Weyl fermions affects photoexcitations in such materials. We find that a combination of time-reversal symmetry, orbital functions, and radial (pseudo-)spin texture close to the Kramers Weyl node impacts the dichroism in an asymmetric way that is consistent with experiments. In furthering our pursuit of electromagnetic response theories in topological materials, we also theorize about including spatial inhomogeneities in our nonlinear response framework. Since perturbing electromagnetic fields can transfer not only energy (via frequency) but also momentum (via wavevectors) through fermion excitations, then we adopt a response theory that accounts for excitations in wavevector. Crucially, we require that our spatially inhomogeneous response theory obeys the conservation of current. In formulating this response theory, we consider two topological material models that are experimentally relevant: the Weyl semimetal and the moiré Chern insulator. We first explore the anomalous Hall response in Weyl semimetals, subject to spatial inhomogeneities, which reveals opposing contributions between the Berry curvature and the density of states. We then apply our results to study the Kerr effect in the moiré Chern insulator, which exemplifies the experimental pertinence of spatially inhomogeneous fields in such systems, given their large effective lattice constants. We further examine the nonlinear, magnetic, and magnetoelectric phenomena in the Chern insulator. In the penultimate chapter, we apply the formulations we have developed from previous chapters (i.e. collective charge-density wave modes, Weyl semimetals, and spatially inhomogeneous electromagnetic responses) to study the axionic electromagnetic response. We specifically focus on methods for experimentally observing the axion through a collective optical response. We not only show that optical evidence of the axion is possible, but we also extend our analysis to beyond linear order in the corrections to Maxwell's equations. This result is particularly important since the experimental observation of the axion in Weyl-Charge-density wave systems has been a topic of debate. Therein, we ultimately show that the axionic corrections to Maxwell's laws can be indirectly observed in theory.

Graduation Semester

2024-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2024 Robert McKay

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