Quantum spin Hall effect in a transition metal oxide Na2IrO3

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Abstract

We study theoretically the electronic states in a \(5d\) transition metal oxide Na\(_2\)IrO\(_3\), in which both the spin-orbit interaction and the electron correlation play crucial roles. Tight-binding model analysis together with the fisrt-principles band structure calculation predicts that this material is a layered quantum spin Hall system. Due to the electron correlation, an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures.

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\(Z_2\) Topological Order and the Quantum Spin Hall Effect

C. L. Kane, E. Mele (2005)

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel \(Z_2\) topological invariant, which distinguishes it from an ordinary insulator. The \(Z_2\) classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the \(Z_2\) order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multi band and interacting systems.

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Helical Metal Inside a Topological Band Insulator

Yi Zhang, Ying Ran, Ashvin Vishwanath (2008)

Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems like the B-phase of superfluid helium He\(_3\), where vortices are associated with low energy excitations in the cores. Similarly, cosmic strings may be tied to propagating fermion modes. Can analogous phenomena occur in crystalline solids that host a plethora of topological defects? Here we show that indeed dislocation lines are associated with one dimensional fermionic excitations in a `topological insulator', a novel band insulator believed to be realized in the bulk material Bi\(_{0.9}\)Sb\(_{0.1}\). In contrast to fermionic excitations in a regular quantum wire, these modes are topologically protected like the helical edge states of the quantum spin-Hall insulator, and not scattered by disorder. Since dislocations are ubiquitous in real materials, these excitations could dominate spin and charge transport in topological insulators. Our results provide a novel route to creating a potentially ideal quantum wire in a bulk solid.

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Spin, Orbital and Charge Order at the Interface between Correlated Oxides

G Khaliullin, G Jackeli (2008)

The collective behavior of correlated electrons in the VO\(_2-\)interface layer of LaVO\(_3\)/SrTiO\(_3\) heterostructure is studied within a quarter-filled \(t_{2g}\)-orbital Hubbard model on a square lattice. We argue that the ground state is ferromagnetic driven by the double exchange mechanism, and is orbitally and charge ordered due to a confined geometry and electron correlations. The orbital and charge density waves open gaps on the entire Fermi surfaces of all orbitals. The theory explains the observed insulating behavior of the \(p\)-type interface between LaVO\(_3\) and SrTiO\(_3\).