In this thesis we study a variety of two- and three-dimensional (2D and 3D, respectively) nodal semimetals, subjected to local electronic interactions or disorder. Such systems constitute a minimal model for various real materials and capture a plethora of interesting physical phenomena therein. Our methodology includes an unbiased renormalization group analysis controlled by epsilon expansions about the appropriate lower critical dimension, mean-field analysis, as well as complementary numerical analyses. First, we focus on emergent symmetries at various infrared unstable quantum critical points, appearing in a renormalization group flow of interaction couplings. We investigate a 3D chiral Dirac semimetal, which in a noninteracting system enjoys a microscopic U(1)⊗SU(2) global symmetry. Though the chiral symmetry is absent in the interacting model, it gets restored (partially or fully) at various fixed points as emergent phenomena. Subsequently, we study a collection of 3D interacting effective spin-3/2 biquadratic Luttinger fermions, and demonstrate the emergence of full rotational symmetry between the distinct nematic sectors (namely Eg and T2g ) of the corresponding octahedral group. We then investigate the effects of electronic interactions at zero and finite temperature and chemical doping in a collection of (i) 2D Dirac and Luttinger fermions, constituting the linearly and quadratically dispersing low-energy excitations in monolayer and bilayer graphene, respectively, and (ii) 3D Luttinger fermions, describing a biquadratic touching of Kramers degenerate conduction and valence bands, relevant in the normal state of 227 pyrochlore iridates, and half-Heusler compounds, for example. These systems exhibit a plethora of competing broken symmetry phases (both magnetic and superconducting) when tuning the strength of interactions, temperature, and chemical doping. In this context we propose the selection rules, identifying the broken symmetry phases promoted by a given interaction channel, and the organizing principle, ordering these preselected phases along the temperature axis based on a generalized energy-entropy argument. Finally, we explore topological aspects of nodal Fermi liquids. We propose an experimentally feasible way to engineer higher-order topological phases via the application of uniaxial strain on a 3D Luttinger semimetal. Favoring a direction, strain explicitly breaks cubic symmetry. We show that the corresponding nematic orderings of Luttinger fermions result in a topological insulator or Dirac semimetal, depending on the sign (compressive or tensile, respectively) of the strain. We show that both of these phases host 1D hinge modes, localized along the edges parallel to the direction of strain, that are therefore second-order topological in nature. We then investigate the effects of disorder on such a second-order Dirac semimetal, and show its stability for weak enough disorder. At a critical disorder strength the system goes through a quantum phase transition into a diffusive metal phase and the toplogical hinge states melt into the bulk. The methodology presented in this thesis can be extended to a large family of correlated multiband systems, such as Weyl and nodal-loop semimetal.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:78568 |
| Date | 23 March 2022 |
| Creators | Szabó, András László |
| Contributors | Moessner, Roderich, Assaad, Fakher, Vojta, Matthias, Roy, Bitan, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
Page generated in 0.0058 seconds