Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

TKM Institutsseminar

Vortragender:

Nikolaos Kainaris

Datum:

28.05.2015 12:30

Ort:

Raum 10.01, Geb. 30.23 (Physikhochhaus), Campus Süd

Zugehörigkeit:

TKM

Gastgeber:

Prof. A. Mirlin

Abstract

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology.
While topological properties of materials with weakly interacting quasiparticles are well understood, the interplay of strong interaction and topology remains a subject of active research.

In many materials topological properties are often realized when strong spin-orbit coupling is present. Quantum wires are a particularly promising class of materials in this context since they naturally display both (i) spin-orbit coupling effects as a consequence of structural assymetry inherent in their manufacturing process and (ii) strong electronic correlations due to their reduced dimensionality.

Here we present analysis of a single channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low energy theory is then a two band model with a difference of Fermi velocities $\delta v$.
Using bosonization and a two-loop RG procedure we show that electron-electron interactions can open a gap in the spin sector of the theory when the interaction strength $U$ is smaller than $\delta v$ in appropriate units. For repulsive interactions the resulting strong coupling phase is of the spin-density wave type. We show that this phase has peculiar emergent topological properties. The gapped spin sector behaves as a topological insulator, with zero-energy edge modes with fractional spin. On the other hand, the charge sector remains critical, meaning the entire system is metallic. However this bulk electron liquid as a whole exhibits properties commonly associated with the one-dimensional edge states of two-dimensional spin-Hall insulators, in particular the conduction of $2e^2/h$ is robust against nonmagnetic impurities.