Topology of time-reversal invariant energy bands with adiabatic structure

On invariant sets topology

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Propagation of Adiabatic Shear Bands

“Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids”

The degrees of freedom in our microscopic models are so-called Fibonacci anyons, one of the simplest types of non-abelian anyons [1, 2]. The Fibonacci theory has two distinct particles, the trivial state 1 and the Fibonacci anyon τ , which can be thought of as a generalization (or more precisely a ‘truncated version’) of an ‘angular momentum’ when viewing the Fibonacci theory as a certain defor...

The time reversal invariant fractional Josephson effect

One of the most basic consequences of topological superconductivity is the fractional Josephson effect, which arises due to the coherent tunneling of single electrons between two superconductors, leading to an ac Josephson effect with half the usual Josephson frequency. In this paper we will review the theoretical and experimental foundations of topological superconductivity and the fractional ...

Gerbes and time-reversal-invariant topological insulators

Definition. A bundle gerbe G with unitary connection (below, gerbe for short) over manifold M is a triple (Y,B,L) s.t. Y is a manifold equipped with a surjective submersion π : Y →M B is a 2-form on Y L is a line bundle (always with hermitian structure and unitary connection) over Y [2] ≡ Y ×M Y p1 −→ −→ p2 Y with the curvature p2B − p1B L comes with a groupoid multiplication L(y1,y2) × L(y2,y3...