Abstract
Condensed matter systems provide a playground for exploring quasiparti-cles in solids. Many of these quasiparticles are analogues of the elementary par-ticles in the standard model. For example, the low-energy electrons in graphene resemble Dirac fermions, marking a start point for discovering fermionic quasi-particles in topological states. The following are the Majorana fermions found in superconducting heterostructures. Recently, the discovery of Weyl and Dirac semimetal phases has been the subject of intense research for exploring the Weyl and Dirac fermions in three dimensional materials. However, electrons in con-densed matter physics are much different from those in high-energy physics. In high energy physics, electrons are constrained by Poincare´ symmetry. But in condensed matter physics, the Poincare´ symmetry is broken. Thus, the elec-trons in solids are less constrained. As a result, other types of fermions that do not have a counterpart in relativistic high energy theories may exist in con-densed matter systems. Until now, the search for unconventional fermions is still at the primitive stage. Unlike the fermions predicted in relativistic quan-tum field theory, which only have three types, the unconventional fermions may take many other forms. To date, the discovered unconventional fermions are still limited. Furthermore, the search for material candidates which host un-conventional fermions near the Fermi level remains a challenge, as the bands in materials have complicated dispersions. In this thesis, we mainly focus on the theoretical prediction of unconven-tional fermions in three dimensions (3D) and two dimensions (2D). Besides the new fermions, we also predict material candidates that host the unconventional fermions close to the Fermi level. Chapter 1 provides a brief introduction of the concepts of Weyl, Dirac and Majorana fermions and the unconventional fermions discovered in condensed matter systems. Chapter 2 introduces the ab-initio methods and effective models used for exploring new fermions. Chap-ter 3 presents a proposal of a previously unrecognized hourglass Dirac chain ermions. The fermions trace out a chain of connected nodal loops in momen-tum space. We also predict a realistic material ReO2 that host such hourglass Dirac chain fermions. In chapter 4, we predict a quantum phase transition from metal to semimetal to semiconductor driven by moderate biaxial strain in 2D material Mg2C. Accompanying the phase transition, several types of 2D novel fermions emerge, including the anisotropic Dirac fermions around 12 tilted Dirac points in the metallic phase, the 2D double Weyl fermions in the semimetal phase and the 2D pseudospin-1 fermions at the critical point of the semimetal to semiconductor phase transition. In chapter 5, we report that ro-bust 2D nodal loop fermions against spin-orbit coupling can be found in mag-netic monolayer MnN. The crossings between three low-energy bands form two nodal loops centred around the G point. We also find a uniaxial strain can in-duce a loop transformation from localized single loop circling around G to a pair of extended loops penetrating the Brillouin zone boundaries. The works in this thesis not only reveals fundamental physics of unconventional fermions, but also suggest their great potential for applications.