arXiv subjects

Frédéric Bègue

Publications and source records attributed to Frédéric Bègue.

3 recordsLinked to original sources

arXiv2016

$Z_2$ antiferromagnetic topological insulators with broken $C_4$ symmetry

A two-dimensional topological insulator may arise in a centrosymmetric commensurate Néel antiferromagnet (AF), where staggered magnetization breaks both the elementary translation and time reversal, but retains their product as a symmetry. Fang et al.[Phys. Rev. B 88, 085406 (2013)] proposed an expression for a $Z_2$ topological invariant to characterize such systems. Here, we show that this expression does not allow to detect all the existing phases if a certain lattice symmetry is lacking. We implement numerical techniques to diagnose topological phases of a toy Hamiltonian, and verify our results by computing the Chern numbers of degenerate bands, and also by explicitly constructing the edge states, thus illustrating the efficiency of the method.

cond-mat.str-el↗

arXiv2016

Identifying two-dimensional $Z_2$ antiferromagnetic topological insulators

We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate Néel antiferromagnet, where staggered magnetization breaks both the elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called $Z_2$ topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of a topological invariant has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram based on a recently proposed criterion for centrosymmetric systems [Fang et al., Phys. Rev. B 88, 085406 (2013)]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular example treated in this work, and admit straightforward generalization. We illustrate this by considering a non-centrosymmetric system, where there are no simple criteria to identify topological phases. We also present an explicit construction of edge states in an antiferromagnetic topological insulator.

cond-mat.str-el↗

arXiv2015

Diagnosing a strong topological insulator by quantum oscillations

We show how quantum oscillation measurements of surface states in an insulator may allow to diagnose a strong topological insulator and distinguish it from its weak or topologically trivial counterpart. The criterion is defined by the parity of the number of fundamental frequencies in the surface-state quantum oscillation spectrum: an even number of frequencies implies a weak or a topologically trivial insulator, whereas an odd number points to a strong topological insulator. We also discuss various aspects and issues related to applying this criterion in practice.

cond-mat.str-el↗