Delicate Topology of Luttinger Semimetal

TL;DR

This paper demonstrates that delicate topology naturally appears in the Luttinger-Kohn model, revealing new topological phases and surface states in semiconductors and semimetals, and highlights its potential for quantum material research.

Contribution

It uncovers the emergence of delicate topology in the Luttinger semimetal and identifies new topological insulators and semimetals with unique surface states.

Findings

Luttinger semimetal is a quantum critical point with a quantized topological invariant.

Identified new electronic phases with intertwined stable and delicate topologies.

All phases exhibit gapless surface states with anomalous rotational symmetry transformations.

Abstract

Recent advances in delicate topology have expanded the classification of topological bands, but its presence in solid-state materials remains elusive. Here we show that delicate topology naturally emerges in the Luttinger-Kohn model that describes many semiconductors and semimetals. In particular, the Luttinger semimetal is found to be a quantum critical point leading to a quantized jump of an integer-valued delicate topological invariant. Away from this criticality, we have identified new types of electronic insulators and semimetals with intertwined stable and delicate topologies. They all carry gapless surface states that transform anomalously under rotation symmetry. Our work provides a starting point for exploring delicate topological phenomena in quantum materials.