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.
Highlights
Since the discovery of the integer quantum Hall effect, time-reversal symmetry (TRS) has been a key issue in the study of topological states of quantum matter [1,2,3]
In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spinsplitting subbands at the TRI points of Brillouin zone in EuB6, when a long-range ferromagnetic order is developed
While it is believed that the quantum anomalous Hall (QAH) insulator state in magnetically doped Bi2Te3 [10,11,12,13,14,15] and MnBi2Te4 [16,17,18,19] and the magnetic Weyl semimetal state in Co3Sn2S2 [20,21,22,23] arise from the mechanism illustrated in Fig. 1(a), the topological phase transitions driven by the TRS breaking have not been observed
Summary
Since the discovery of the integer quantum Hall effect, time-reversal symmetry (TRS) has been a key issue in the study of topological states of quantum matter [1,2,3]. The QAH insulator and magnetic Weyl semimetal states are closely related to the band inversion under the TRS breaking. In two-dimensional (2D) systems, the band inversion opens an energy gap characterized by a nonzero Chern number, forming the QAH insulators [10]. While it is believed that the QAH insulator state in magnetically doped Bi2Te3 [10,11,12,13,14,15] and MnBi2Te4 [16,17,18,19] and the magnetic Weyl semimetal state in Co3Sn2S2 [20,21,22,23] arise from the mechanism illustrated, the topological phase transitions driven by the TRS breaking have not been observed. The band crossings are the only feature at the Fermi level (EF) without the existence of other Fermi surfaces (FSs), which is favorable to the emergence of exotic physics associated with the topological nodes
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