Measuring Chern numbers above the Fermi level in the Type II Weyl semimetal Mo$_x$W$_{1-x}$Te$_2$

Ilya Belopolski, Su-Yang Xu, Yukiaki Ishida, Xingchen Pan, Peng Yu, Daniel S. Sanchez, Madhab Neupane, Nasser Alidoust, Guoqing Chang, Tay-Rong Chang, Yun Wu, Guang Bian, Hao Zheng, Shin-Ming Huang, Chi-Cheng Lee, Daixiang Mou, Lunan Huang, You Song, Baigeng Wang, Guanghou Wang, Yao-Wen Yeh, Nan Yao, Julien E. Rault, Patrick Le Fèvre, François Bertran, Horng-Tay Jeng, Takeshi Kondo, Adam Kaminski, Hsin Lin, Zheng Liu, Fengqi Song, Shik Shin, M. Zahid Hasan

Published 2016-04-24Version 1

It has recently been proposed that electronic band structures in crystals give rise to a previously overlooked type of Weyl fermion, which violates Lorentz invariance and, consequently, is forbidden in particle physics. It was further predicted that Mo$_x$W$_{1-x}$Te$_2$ may realize such a Type II Weyl fermion. One crucial challenge is that the Weyl points in Mo$_x$W$_{1-x}$Te$_2$ are predicted to lie above the Fermi level. Here, by studying a simple model for a Type II Weyl cone, we clarify the importance of accessing the unoccupied band structure to demonstrate that Mo$_x$W$_{1-x}$Te$_2$ is a Weyl semimetal. Then, we use pump-probe angle-resolved photoemission spectroscopy (pump-probe ARPES) to directly observe the unoccupied band structure of Mo$_x$W$_{1-x}$Te$_2$. For the first time, we directly access states $> 0.2$ eV above the Fermi level. By comparing our results with $\textit{ab initio}$ calculations, we conclude that we directly observe the surface state containing the topological Fermi arc. Our work opens the way to studying the unoccupied band structure as well as the time-domain relaxation dynamics of Mo$_x$W$_{1-x}$Te$_2$ and related transition metal dichalcogenides.