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# 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.

### Most cited references3

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### $$Z_2$$ Topological Order and the Quantum Spin Hall Effect

(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

(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

(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$$_3$$.
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### Author and article information

###### Journal
08 September 2008
2009-06-25
###### Article
10.1103/PhysRevLett.102.256403
0809.1317