Time-reversal symmetry breaking driven topological phase transition in EuB$_6$

TL;DR

This study visualizes a topological phase transition in EuB$_6$ driven by time-reversal symmetry breaking, revealing a shift from an ordinary insulator to a magnetic topological semimetal with ideal electronic structure.

Contribution

First direct observation of a TRS-breaking induced topological phase transition in EuB$_6$ using angle-resolved photoemission spectroscopy.

Findings

Band inversion at TRI points upon ferromagnetic order

Transition from trivial insulator to magnetic topological semimetal

Band crossings at the Fermi level without interference

Abstract

The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads to nontrivial topological states, such as topological insulators and Dirac semimetals. When the TRS is broken, the exchange field induces spin splitting of the bands. The inversion of a pair of spin-splitting subbands can generate more exotic topological states, such as quantum anomalous Hall insulators and magnetic Weyl semimetals. So far, such topological phase transitions driven by the TRS breaking have not been visualized. In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spin-splitting subbands at the TRI points of Brillouin zone in EuB$_6$, when a long-range ferromagnetic order is developed. The dramatic changes in the electronic structure result in a topological phase transition from a TRI ordinary insulator state to a TRS-broken topological semimetal (TSM) state. Remarkably, the magnetic TSM state has an ideal electronic structure, in which the band crossings are located at the Fermi level without any interference from other bands. Our findings not only reveal the topological phase transition driven by the TRS breaking, but also provide an excellent platform to explore novel physical behavior in the magnetic topological states of quantum matter.