Interaction-enhanced magnetically ordered insulating state at the edge of a two-dimensional topological insulator

• Published in: arXiv.org
• Main Author: Kharitonov, Maxim
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.12.2012
• Subjects: Current carriers; Dependence; Excitation spectra; Ferromagnetism; Parameters; Physics - Strongly Correlated Electrons; Resistance; Scaling; Topological insulators
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1004.0194

We develop a theory of the correlated magnetically ordered insulating state at the edge of a two-dimensional topological insulator. We demonstrate that the gapped spin-polarized state, induced by the application of the magnetic field \(B\), is naturally facilitated by electron interactions, which drive the critical easy-plane ferromagnetic correlations in the helical liquid. As the key manifestation, the gap \(\De\) in the spectrum of collective excitations, which carry both spin and charge, is enhanced and exhibits a scaling dependence \(\De \propto B^{1/(2-K)}\), controlled by the Luttinger liquid parameter \(K\). This scaling dependence could be probed through the activation behavior \(G \sim (e^2/h) \exp(- \De/T)\) of the longitudinal conductance of a Hall-bar device at lower temperatures, providing a straightforward way to extract the parameter \(K\) experimentally. Our findings thus suggest that the signatures of the interaction-driven quantum criticality of the helical liquid could be revealed already in a standard Hall-bar measurement.