# Topological phases in pyrochlore thallium niobate Tl$_2$Nb$_2$O$_{6+x}$

## TL;DR

This paper predicts that by varying oxygen content in pyrochlore Tl$_2$Nb$_2$O$_{6+x}$, multiple topological phases such as insulators, Dirac semimetals, and nodal point semimetals can be realized, enabling exploration of topological phase transitions.

## Contribution

It introduces a tunable topological oxide material, Tl$_2$Nb$_2$O$_{6+x}$, capable of hosting various topological states through oxygen content variation and symmetry control, which was not previously demonstrated.

## Key findings

- Different topological phases are achievable by adjusting oxygen content.
- Topological phase transitions are driven by valence state changes of Tl.
- Solid solution approach enables continuous tuning of topological properties.

## Abstract

The discovery of new topological electronic materials brings a chance to uncover novel physics and plays a key role in observing and controlling various intriguing phenomena. Up to now, many materials have been theoretically proposed and experimentally proved to host different kinds of topological states. Unfortunately, there is little convincing experimental evidence for the existence of topological oxides. The reason is that oxidation of oxygen leads to ionic crystal in general and makes band inversion unlikely. In addition, the realization of different topological states in a single material is quite difficult, but strongly needed for exploring topological phase transitions. In this work, using first-principles calculations and symmetry analysis, we propose that the experimentally tunable continuous solid solution of oxygen in pyrochlore Tl$_2$Nb$_2$O$_{6+x}$ ($ 0\leq x \leq 1.0$) leads to various topological states. Topological insulator, Dirac semimetal and triply degenerate nodal point semimetal can be realized in it via changing the oxygen content and/or tuning the crystalline symmetries. When $x = 1$, it is a semimetal with quadratic band touching point at Fermi level. It transits into a Dirac semimetal or a topological insulator depending on the in-plane strain. When $x = 0.5$, the inversion symmetry is spontaneously broken in Tl$_2$Nb$_2$O$_{6.5}$, leading to triply degenerate nodal points. When $x = 0$, Tl$_2$Nb$_2$O$_6$ becomes a trivial insulator with a narrow band gap. These topological phase transitions driven by solid solution of oxygen are unique and physically plausible due to the variation of valence state of $Tl^{1+}$ and $Tl^{3+}$. This topological oxide will be promising for studying correlation induced topological states and potential applications.

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Source: https://tomesphere.com/paper/1903.00891