RT Journal Article
T1 Density-matrix Chern insulators: finite-temperature generalization of topological insulators
A1 Rivas Vargas, Ángel
A1 Viyuela García, Óscar
A1 Martín-Delgado Alcántara, Miguel Ángel
AB Thermal noise can destroy topological insulators (TI). However, we demonstrate how TIs can be made stable in dissipative systems. To that aim, we introduce the notion of band Liouvillian as the dissipative counterpart of band Hamiltonian, and show a method to evaluate the topological order of its steady state. This is based on a generalization of the Chern number valid for general mixed states (referred to as density-matrix Chern value), which witnesses topological order in a system coupled to external noise. Additionally, we study its relation with the electrical conductivity at finite temperature, which is not a topological property. Nonetheless, the density-matrix Chern value represents the part of the conductivity which is topological due to the presence of quantum mixed edge states at finite temperature. To make our formalism concrete, we apply these concepts to the two-dimensional Haldane model in the presence of thermal dissipation, but our results hold for arbitrary dimensions and density matrices.
PB American Physical Society
SN 1098-0121
YR 2013
FD 2013-10-31
LK https://hdl.handle.net/20.500.14352/35608
UL https://hdl.handle.net/20.500.14352/35608
LA eng
NO © 2013 American Physical Society. We thank A. Dauphin for fruitful discussions. This work has been supported by the Spanish MINECO Grant No. FIS2012-33152, CAM research consortium QUITEMAD S2009-ESP1594, European Commission PICC: FP7 2007-2013, Grant No. 249958, UCM-BS Grant No. GICC-910758.
NO Unión Europea. FP7
NO Ministerio de Economía y Competitividad (MINECO)
NO Comunidad de Madrid
NO Universidad Complutense de Madrid/Banco de Santander
DS Docta Complutense
RD 6 abr 2025