Abstract
Understanding the interplay between symmetries and phases lies at the heart of characterizing states of matter. The conventional Landau's paradigm associates local ordered states with symmetry breaking. However, this paradigm fails to include gapped topological phases, which can only be distinguished by the global topological invariant and the present of gapless edge modes at open boundaries.
In this seminar, the variety of states of matter is enriched from two aspects: Firstly, a new paradigm of phases that incorporates both symmetry broken phase and topological phase is proposed. This is demonstrated in a one-dimensional lattice model of spinful fermions that has Z2 symmetry broken ground states, and each state is topological nontrivial with edge zero modes of fractional fermions. Secondly, I propose exotic topological phases realized in different degrees of freedom of the same system. Remarkably, Majorana modes and fractional fermions are shown to exist simultaneously in a spinless fermionic ladder in the charge and pseudo-spin degrees of freedom separately.
In additional, quasiparticle interferences of gapless topological systems are also investigated. A framework of generalized joint density of states (GJDOS) is constructed to address effects from the geometry of band dispersion and topological charges separately. Robust quasiparticle interference features resulting from topological charges of Fermi points of some materials are obtained both analytically and numerically.
Anyone interested is welcome to attend.