Topological semimetallic states with magnetic order: electronic states and collective excitations

Abstract

The discovery of linear band crossings at the Fermi level in graphene, protected by symmetry and topology, marked a transformative milestone in condensed matter physics. This novel quantum phase, termed the topological semimetal (TSM), has catalyzed extensive exploration in a wide array of material systems. Characterized by exotic and robust electronic properties, topological semimetals have opened new frontiers in next-generation electronic and spintronic technologies, enabling the manipulation of multiple degrees of freedom in a fundamentally new manner. Among various classes, Dirac and Weyl semimetals have emerged as key representatives, where the protection and breaking of fundamental symmetries—such as time-reversal and inversion—govern the emergence of Dirac or Weyl points. While Dirac semimetals require these symmetries (or sometimes, non-symmorphic lattice symmetries) to protect the four-fold degenerate Dirac points, Weyl semimetals arise when either symmetry is broken, resulting in pairs of Weyl nodes carrying opposite topological charges (Chern numbers). Although substantial focus has been given to three-dimensional semimetals, their two-dimensional counterparts have garnered increasing attention due to promising potential for miniaturized device applications. Notably, magnetic monolayers like FeSe and TaCoTe2 have been proposed as candidates to host two-dimensional Dirac fermions. This thesis explores the emergence and tunability of topological semimetallic phases within two-dimensional magnetically ordered systems. The first system considered is the spin-density wave (SDW) state in iron pnictides, which hosts Dirac-like features near the Fermi level. Experimentally observed metallic SDW state dictates the presence of additional pockets at the Fermi level. However, no attempt has been made in exploring the possibility of Dirac points at the Fermi level. We demonstrate that the Dirac points in this phase can be brought precisely to the Fermi level by tuning the orbital splitting between the dxz and dyz orbitals of iron. This tuning simultaneously suppresses non-Dirac Fermi pockets, stabilizing a Dirac semimetallic state with (π, 0) SDW state. The orbital character and slopes of bands forming the Dirac cone are shown to be key parameters in controlling this behavior. Additionally, by eliminating second-neighbor intraorbital hopping, we reveal a perfectly nested (π, π) ordered phase in a two-orbital Hubbard model, analyze the semimetallic state, and discuss its topological characteristics. The second system involves an antiferromagnetically (AFM) ordered state with Rashba-type spin-orbit coupling, where a Dirac semimetallic phase is realized under specific symmetry constraints on magnetic moment orientation using the Rashba- Hubbard model. Upon introducing an in-plane magnetic field like term aligned with the moment direction, Dirac points split into Weyl points, thereby realizing a Weyl semimetallic phase. Subsequently, we also investigate collective excitations using two primary probes: quasiparticle interference and optical conductivity. These tools elucidate the interplay between correlations, symmetry, and band topology in the ordered systems, and thereby provide insights into the possible anisotropic electronic states. The research work presented in the thesis is organized and structured in the form of seven chapters, which are briefly described as follows: i) Chapter 1 introduces the fundamental concepts of topology in condensed matter physics, reviews the development of topological insulators and semimetals, and outlines the two magnetically ordered 2D systems that form the focus of this thesis. ii) Chapter 2 develops the theoretical framework, employing the Hubbard model for systems with broken time-reversal (T ) and inversion (P) symmetries. It demonstrates how Dirac and Weyl semimetallic phases emerge under specific symmetry constraints and external tuning in an antiferromagnetically ordered non-symmorphic lattice. Topological invariants (Chern numbers) and edge-state dispersions are computed to confirm non-trivial band topology. iii) Chapter 3 examines collective excitations in AFM–TSM phases within a nonsymmorphic crystal, focusing on optical conductivity and quasiparticle interference for both magnetic and non-magnetic impurities, revealing strong anisotropy in the electronic responses. iv) Chapter 4 addresses the realization of a Dirac semimetallic phase in a striped (π, 0) SDW order within a multi-orbital Hubbard model. By tuning the orbital splitting δ between dxz and dyz orbitals, Dirac points are brought exactly to the Fermi level, eliminating additional band crossings. Edge-state dispersions for ribbons with varying orientations and chain parity are also analyzed. v) Chapter 5 provides a detailed analysis of optical conductivity and quasiparticle excitation spectra in the semimetallic SDW phase, demonstrating that Dirac cones near the Fermi level can play a very significant role in the origin of anisotropic transport and one-dimensional QPI patterns. vi) Chapter 6 explores the semimetallic state in iron-based superconductors with the checkerboard-type antiferrromagnetic order, which emerges upon suppression of second-neighbor intraorbital hopping in the minimal two-orbital model of iron pnictides. Fermi-surface reconstruction collapses the pockets into Dirac points with equal orbital contributions but anisotropic. Analytical conditions for Dirac point formation and the evolution of edge states with interaction strength are derived. Furthermore, quasiparticle interference as well as optical conductivity are also explored. vii) Chapter 7 summarizes the principal findings and outlines potential directions for future research in the field of topological quantum materials.