PTPT Symmetric Real Dirac Fermions and Semimetals

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 real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the $PT$ symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, $2$D sub topological insulators and Fermi arcs, are studied in the $PT$ symmetric Dirac semimetals, and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about $PT$ symmetric Dirac nodal line semimetals.Comment: 7.5 pages, 5 figures. Accepted by Phys. Rev. Let

General response theory of topologically stable Fermi points and its implications for disordered cases

We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete coefficients proportional to the corresponding topological charges. Applying the theory to the effective non-linear sigma models for topological Fermi points with disorders in the framework of replica approach, we derive rigorously the Wess-Zumino terms with the topological charges being their levels in the two complex symmetry classes of A and AIII. Intriguingly, two nontrivial examples of quadratic Fermi points with the topological charge `2' are respectively illustrated for the classes A and AIII. We also address a qualitative connection of topological charges of Fermi points in the real symmetry classes to the topological terms in the non-linear sigma models, based on the one-to-one classification correspondence.Comment: 8 pages and 2 figures, revised version with appendi

Topological Classification and Stability of Fermi Surfaces

In the framework of the Cartan classification of Hamiltonians, a kind of topological classification of Fermi surfaces is established in terms of topological charges. The topological charge of a Fermi surface depends on its codimension and the class to which its Hamiltonian belongs. It is revealed that six types of topological charges exist, and they form two groups with respect to the chiral symmetry, with each group consisting of one original charge and two descendants. It is these nontrivial topological charges which lead to the robust topological protection of the corresponding Fermi surfaces against perturbations that preserve discrete symmetries.Comment: 5 pages, published version in PR