Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator

Abstract

The three-dimensional (3D) topological insulator is a novel quantum state of matter where an insulating bulk hosts a linearly dispersing surface state, which can be viewed as a sea of massless Dirac fermions protected by the time-reversal symmetry (TRS). Breaking the TRS by a magnetic order leads to the opening of a gap in the surface state 1 , and consequently the Dirac fermions become massive. It has been proposed theoretically that such a mass acquisition is necessary to realize novel topological phenomena 2,3 , but achieving a sufficiently large mass is an experimental challenge. Here we report an unexpected discovery that the surface Dirac fermions in a solid-solution system TlBi(S 1−x Se x ) 2 acquire a mass without explicitly breaking the TRS. We found that this system goes through a quantum phase transition from the topological to the non-topological phase, and, by tracing the evolution of the electronic states using the angle-resolved photoemission, we observed that the massless Dirac state in TlBiSe 2 switches to a massive state before it disappears in the non-topological phase. This result suggests the existence of a condensedmatter version of the 'Higgs mechanism' where particles acquire a mass through spontaneous symmetry breaking.Whether a band insulator is topological or not is determined by the parity of the valence-band wave function, which is described by the Z 2 topological invariant. Strong spin-orbit coupling can lead to an inversion of the character of valence-and conduction-band wave functions, resulting in an odd Z 2 invariant that characterizes the topological insulator 4,5 . All known topological insulators 6-14 are based on this band-inversion mechanism 4,5,[15][16][17][18] , but the successive evolution of the electronic state across the quantum phase transition (QPT) from trivial to topological has not been well studied in 3D topological insulators owing to the lack of suitable materials. TlBi(S 1−x Se x ) 2 is therefore the first system where one can investigate the 3D topological QPT (ref. 19). The advantage of this system is that it always maintains the same crystal structure (Fig. 1a), irrespective of the S/Se ratio. Low-energy, ultrahigh-resolution angle-resolved photoemission spectroscopy (ARPES), which has recently become available, is particularly suited to trace such a QPT in great detail.The bulk band structures of the two end members, TlBiSe 2 and TlBiS 2 , are shown in Fig. 1b, where one can see several common features, such as the prominent hole-like band at the binding energy E B of 0.5-1 eV and a weaker intensity at the Fermi level (E F ), both being centred at the point (Brillouin-zone centre). These features

Topological Insulator Materials

“…115) The non-topological nature of TlBiS 2 naturally points to a topological phase transition, accompanied by a closing of the bulk band gap, occurring in the solid solution TlBi(S 1Àx Se x ) 2 . Such a transition was studied independently by Xu et al 116) and by Sato et al 117) and was found to be located at x ¼ 0:5. Intriguingly, Sato et al found an unexpected gap opening at the Dirac point when the composition is on the topological side and is close to the transition.…”

“…Intriguingly, Sato et al found an unexpected gap opening at the Dirac point when the composition is on the topological side and is close to the transition. 117) This is surprising, because such a gap opening points to a lifting of the Kramers degeneracy, but in this system TRS is not explicitly broken. While the origin of this ''Dirac gap'' is not clear and its existence has been a matter of debate, a recent follow-up experiment substantiated its unique properties.…”

Topological Floquet spectrum in three dimensions via a two-photon resonance

“…By Eq. (14), 29 , where a gap of ∼ 10K can be achieved using microwave fields of intensity ≤ 1 W mm 2 . As opposed to the its 2D counterpart 10 , the surface modes emerging in the 3D driven system, allow direct probing of the driven topological state using a multitude of all-optical means.…”

Classification of stable three-dimensional Dirac semimetals with nontrivial topology

“…However, the recent progress in the field of topological insulators has shown that stable 2D Dirac fermions exist ubiquitously on the surface of 3D topological insulators 1,2 . Moreover, through the careful studies on the topological phase transition between a 3D topological insulator and a normal insulator [4][5][6][7][8] , it is demonstrated that even the 3D Dirac fermions with the linear dispersion in all three momentum directions can be observed in the same material if we can reach the quantum critical point. As the 3D Dirac point (DP) with fourfold degeneracy does not carry a Chern number, the degeneracy at the gap-closing point can be easily lifted by small external perturbations, hence, the 3D Dirac fermions can be observed only at the single quantum critical point.…”