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Novel fermionic quasiparticles with integer pseudospins in some energy bands, such as pseudospin-1 triple-point fermions, recently attract increasing interest since they are beyond the conventional spin-$1/2$ Dirac and Weyl counterparts. In…
Recently Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here we present a theory of real Dirac points that can be understood as…
A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The…
Recent discovery of both gapped and gapless topological phases in weakly correlated electron systems has introduced various relativistic particles and a number of exotic phenomena in condensed matter physics. The Weyl fermion is a prominent…
The fermion doubling theorem plays a pivotal role in Hermitian topological materials. It states, for example, that Weyl points must come in pairs in three-dimensional semimetals. Here, we present an extension of the doubling theorem to…
Dirac semimetals, the materials featured with discrete linearly crossing points (called Dirac points) between four bands, are critical states of topologically distinct phases. Such gapless topological states have been accomplished by a…
We compare the critical multipoint correlation functions for two-dimensional (massless) Dirac fermions in the presence of a random su(N) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous…
Recently a generic class of three-dimensional band structures was identified that host two-fold line degeneracies meeting at three-fold or triple point degeneracies, which resist the usual topological characterization of isolated point…
We propose a new concept of two-dimensional (2D) Dirac semiconductor which is characterized by the emergence of fourfold degenerate band crossings near the band edge and provide a generic approach to realize this novel semiconductor in the…
Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality.…
Topological band theory predicts a $\mathbb{Z}$ classification of three-dimensional (3D) Dirac semimetals (DSMs) at the single-particle level. Namely, an arbitrary number of identical bulk Dirac nodes will always remain locally stable and…
Three dimensional (3D) Dirac semimetal is a novel state of quantum matter, characterized by the gapless bulk four-fold degeneracy near Fermi energy. Soon after its discovery, the classification of stable 3D Dirac semimetals with inversion…
Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich topological properties result from the interplay of symmetries and dimensionality. Their topological properties have been extensively studied…
Massive Dirac fermions, which are essential for realizing novel topological phenomena, are expected to be generated from massless Dirac fermions by breaking the related symmetry, such as time-reversal symmetry (TRS) in topological…
Crystalline symmetries can generate exotic band-crossing features, which can lead to unconventional fermionic excitations with interesting physical properties. We show how a cubic Dirac point---a four-fold-degenerate band-crossing point…
In most Dirac semimetals, time-reversal and inversion symmetries are believed to play a crucial role in their stability. We demonstrate that these symmetries are broken in Dirac fermions in the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$…
Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary…
Dirac semimetal (DSM) hosts four-fold degenerate isolated band-crossing points with linear dispersion, around which the quasiparticles resemble the relativistic Dirac Fermions. It can be described by a 4 * 4 massless Dirac Hamiltonian which…
Magnetic topological materials have recently drawn significant importance and interest, due to their topologically nontrivial electronic structure within spontaneous magnetic moments and band inversion. Based on first-principles…
Recent developments in topological semimetals open a way to realize relativistic dispersions in condensed matter systems. One recently studied type of topological feature is the "triple nodal point" where three bands become degenerate. In…