Electrical Conductivity in Quantum Materials

Abstract

In recent years, there is an increasing interest in transport phenomena that are fundamentally linked to the presence of multiple bands. In this thesis, we develop, discuss, and apply a theory of the electrical conductivity that includes interband contributions within a microscopic approach. We derive formulas of the conductivity tensor ${\sigma }^{\alpha \beta }$ and the Hall conductivity tensor ${\sigma }_{\text{H}}^{\alpha \beta \eta }$ for a general two-band model. This minimal model of a multiband system captures a broad variety of very different physical phenomena ranging from spiral spin density waves to Chern insulators. We motivate and derive a unique and physically transparent decomposition of the conductivity tensors by identifying intra- and interband contributions as well as symmetric and antisymmetric contributions under the exchange of the current and the electric field directions. Using these criteria, we find that the symmetric interband contribution of ${\sigma }^{\alpha \beta }$ is connected to the quantum metric, whereas the antisymmetric part involves the Berry curvature and captures the intrinsic anomalous Hall effect. We include a phenomenological relaxation rate $\Gamma$ of arbitrary size to study the relevance of the interband contributions systematically. Our conductivity formulas are applied to models and experiments of recent interest. We identify typical scaling behaviors of the conductivities with respect to $\Gamma$ in agreement with theoretical and experimental results. Recent experiments on hole-doped cuprates under very high magnetic fields show a drastic change of the Hall number when entering the pseudogap regime, which is shown to be consistent with the onset of spiral magnetic order. We analyze the experimental results with our formulas of the longitudinal and the Hall conductivity and clarify the validity of the broadly used Boltzmann-like conductivity formulas.

PhD Thesis (2021)

References in corpus (21)

• Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals
• Universal Scaling Behavior of Anomalous Hall Effect and Anomalous Nernst Effect in Itinerant Ferromagnets
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Anomalous Hall Effect in Weyl Metals
• Semiclassical theories of the anomalous Hall effect
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Optical properties of correlated materials -- Generalized Peierls approach and its application to VO2
• Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi d-orbital tight-binding model
• Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance
• Fermi surface reconstruction and drop of Hall number due to spiral antiferromagnetism in high-$T_c$ cuprates
• The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
• Interplay between incommensurate phases in the cuprates
• Streda-like formula in spin Hall effect
• Destruction of Neel order and local spin spirals in insulating La_{2-x}Sr_xCuO_4
• Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal
• Saturation of the Anomalous Hall Effect in Critically Disordered Ultra-thin CNi3 Films
• Incommensurate spiral magnetic order on anisotropic triangular lattice: Dynamical mean field study in a spin-rotating frame
• Hall effect in cuprates with incommensurate spin-density wave
• Optical conductivity of unconventional charge density wave systems: Role of vertex corrections
• Effective masses in a strongly anisotropic Fermi liquid
• Simultaneous drop in mean free path and carrier density at the pseudogap onset in high-$T_c$ cuprates