In insulators, correlations can drive topological states, as exemplified by the fractional quantum Hall effect. Whether and how that happens in gapless matter is an outstanding and pressing question. I will describe the route we have taken from certain canonical correlation physics to electronic topology in strongly correlated metallic systems. This has been done in the context of heavy fermion metals, where there is well-defined input about the effective degrees of freedom that describe the low-energy physics. I will present the notion and salient properties of Weyl-Kondo semimetal for which there is by now compelling experimental evidence [1,2]. They set the stage for a general approach of utilizing the cooperation between interactions and crystalline symmetry to produce correlated topological phases [3], and the identification of an electronic topological state without any free-electron counterpart [4]. Some general implications about topology and correlation physics will be discussed.
[1] H.-H. Lai, S. E. Grefe et al., PNAS 115, 93 (2018).
[2] S. Dzsaber et al., PNAS 118, e2013386118 (2021).
[3] L. Chen et al, arXiv:2107.10837 ( https://arxiv.org/abs/2107.10837 )
[4] H. Hu, L. Chen, C. Setty et al., arXiv:2110.06182 ( https://arxiv.org/abs/2110.06182 )