Elsevier

Physica B: Condensed Matter

Volume 516, 1 July 2017, Pages 100-104
Physica B: Condensed Matter

Surface state of the dual topological insulator Bi0.91Sb0.09(112¯)

https://doi.org/10.1016/j.physb.2017.04.031Get rights and content

Abstract

The electronic structure of a Bi0.91Sb0.09 single crystal was elucidated at a bisectrix (112¯) surface by angle-resolved photoemission spectroscopy using microbeam synchrotron radiation. A Dirac-cone-like dispersion of the surface state was observed at the Γ¯ point. The detected surface-state band likely corresponds to the one observed in previous quantum transport research (Taskin and Ando, 2009) [14].

Introduction

Topological insulators are currently an intriguing topic in condensed matter physics. Theoretical frameworks of the topology of such materials have characterized their properties like spin currents and explained new quantum phenomena that have been observed in various experiments [1], [2], [3]. The first reported three-dimensional (3D) topological insulator was a crystal of the Bi1xSbx alloy (x=0.070.22) [4], [5], [6], [7]. In the classification of a topological invariant of Z2 index, this material has a nontrivial Z2 topology of the bulk state that gives rise to spin-polarized gapless surface states at any surface, so it is classified as a strong topological insulator. Moreover, crystals of the Bi1xSbx alloy (x=0.070.22) have been predicted to be a dual topological insulator [8], [9], possessing two non-trivial topological invariants of the Z2 index and the mirror Chern number [10].

Fig. 1 shows a 3D Brillouin zone (BZ) and set of two-dimensional (2D) BZs for surfaces of the trigonal, tetragonal and bisectrix axes. The symmetry points in the 2D BZs are projected from those in the 3D BZ. The symbols in the 2D BZs for the trigonal axis, i.e. (111) surface, and tetragonal axis, i.e. (110) surface, were adopted from the literature [4], [5], [6], [7], [11], [12], [13]. Concerning the surface of the bisectrix axis, i.e. (112¯), which is studied in this research, we define symbols of the symmetry points in the 2D BZ with respect to the 3D BZ as in Table 1 [2].

Edge- or surface-states of 3D topological insulators have been directly observed by angle-resolved photoemission spectroscopy (ARPES). For the case of the trigonal axis of a Bi1xSbx surface, dispersion curves of the spin-polarized surface-state bands have been determined by spin-resolved photoemission spectroscopy, ARPES [4], [5], [6], [7], [12] and quasiparticle interference measurements on a cleaved surface [11]. Concerning a bisectrix (112¯) surface, a Fermi surface of the surface state has been detected only through measurement of the quantum magnetic oscillation [14]; no ARPES measurement has been carried out yet. The (110) surface state has been measured by ARPES of a surface of a Bi1xSbx film grown on a regulated template of Bi(110) [13]. However, it has recently been pointed out in the researches of a bismuth crystal that the band dispersion of a surface state of the film is not necessarily identical to that of the bulk crystal, which has lead to a long controversy in determining topology of Bi [15], [16]. Thus, experimental examination of electronic states on different crystal surfaces of the same bulk sample is a significant step for a proper understanding of topology in condensed matter physics.

On the other hand, it has been theoretically predicted that a single Dirac cone can be constructed in Bi1xSbx films with a thickness of several hundred nanometers grown along the bisectrix axis [17], [18], [19]. The Dirac cones are composed of bulk L bands and their number depends on the crystal axis of film growth. While novel physical phenomena associated with massless and massive Dirac fermions are expected in these Bi1xSbx nanofilms, it is also important to examine the surface states of the bisectrix surface for the comprehensive arguments.

In the present research, we perform high-resolution ARPES measurements of a cleaved (112¯) bisectrix surface of a Bi0.91Sb0.09 crystal [17], [18], [19]. A single Dirac-like band of the surface state is observed at the Γ¯ point, that agrees with that observed in magnetotransport measurements [14].

Section snippets

Experimental methods

High-resolution momentum-resolved photoemission spectroscopy experiments were performed at the Cassiopée beamline (SOLEIL, France). ARPES measurements were performed with a hemispherical photoelectron spectrometer (VG Scienta R4000) at an energy resolution of <15meV and angular resolution of 0.1°. Linearly and circularly polarized light at photon energies ranging from 17 to 60 eV were used. Spectra were detected under ultrahigh vacuum (UHV) conditions of 10−9 Pa at 5 K, as measured with a Si-diode

Results and discussion

Figs. 3(a) and (b) display kyEB diagrams of the Bi0.91Sb0.09(112¯) surface depicted as ARPES intensity map and corresponding derivative plot, respectively [21]. Here, lines of kx and ky are defined along Γ¯Y¯ and Γ¯X¯ directions, respectively. A Dirac cone-like band, labeled S, is observed near the Fermi level (EF) at the Γ¯ point. To assign the band, the photoemission kyEB diagram was determined at various photon energies (hν=1724eV), as depicted in Fig. 4. Dispersion curves of the S band

Summary

We performed high-resolution ARPES measurements on a cleaved (112¯) bisectrix surface of a Bi0.91Sb0.09 crystal. A single Dirac-like band was observed for the surface state at the Γ¯ point and its band velocity agreed with that determined from magnetotransport measurements. Consistent existence of the surface state in the ARPES and transport experiment confirms that Bi1xSbx alloy (x=0.070.22) is a strong topological insulator. The present result is likely to be the first direct evidence to

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