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Direct observation of spin-polarized surface states in the parent compound of a topological insulator using spin- and angle-resolved photoemission spectroscopy in a Mott-polarimetry mode

We report high-resolution spin-resolved photoemission spectroscopy (spin-ARPES) measurements on the parent compound Sb of the recently discovered three-dimensional topological insulator Bi1−xSbx (Hsieh et al 2008 Nature 452 970, Hsieh et al 2009 Science 323 919). By modulating the incident photon energy, we are able to map both the bulk and the (111) surface band structure, from which we directly demonstrate that the surface bands are spin polarized by the spin–orbit interaction and connect the bulk valence and conduction bands in a topologically non-trivial way. A unique asymmetric Dirac surface state gives rise to a k-splitting of its spin-polarized electronic channels. These results complement our previously published works on this class of materials and re-confirm our discovery of topological insulator states in the Bi1−xSbx series.

2 published works on this class of materials and re-confirm our discovery of topological insulator states in the Bi 1−x Sb x series.
Topological insulators are a new phase of quantum matter that are theoretically distinguished from ordinary insulators by a Z 2 topological number that describes its bulk band structure [1]- [3]. They are characterized by a bulk electronic excitation gap that is opened by spin-orbit coupling, and unusual metallic states that are localized at the boundary of the crystal. The two-dimensional (2D) version, known as the quantum spin Hall insulator [4]- [6], is commonly understood as two copies of the integer quantum Hall effect [7] where the spin-orbit coupling acts as a magnetic field that points in a spin-dependent direction, giving rise to counterpropagating spin-polarized states [8] on the 1D crystal edge. 3D topological insulators, on the other hand, have no quantum Hall analogue. Its surface states, which are necessarily spin polarized, realize a novel 2D metal that remains delocalized even in the presence of disorder [2,3], [9]- [11]. For these reasons, they have also been proposed as a route to dissipationless spin currents that, unlike current semiconductor heterostructure-based spintronics devices, do not require an externally applied electric field.
Recent photoemission [12] and theoretical results [2,10] suggest that single crystals of insulating Bi 1−x Sb x (0.07 x 0.22) alloys realize a 3D topological insulator. The non-trivial Z 2 invariant that characterizes Bi 1−x Sb x is inherited from the bulk band structure of pure Sb [2,10]; therefore, although Sb is a bulk semimetal, its non-trivial bulk band topology should be manifest in its surface state spectrum. Such a study requires a separation of the Fermi surface of the surface states of Sb from that of its bulk states over the entire surface Brillouin zone (BZ), as well as a direct measurement of the spin degeneracy of the surface states. To date, angle-resolved photoemission spectroscopy (ARPES) experiments on low-lying states have only been performed on single-crystal Sb with fixed He Iα radiation, which does not allow for separation of bulk and surface states [13]. Moreover, the aforementioned study, as well as ARPES experiments on Sb thin films [14], only maps the band dispersion near¯ , missing the band structure nearM that is critical for determining the Z 2 invariant [12]. In this paper, we have performed spin-and angle-resolved photoemission experiments on single-crystal Sb(111). Using variable photon energies, we successfully isolate the surface from bulk electronic bands over the entire BZ and map them with spin sensitivity. We show directly that the surface states are gapless and spin split and that they connect the bulk valence and conduction bands in a topologically non-trivial way.
Spin-integrated ARPES measurements were carried out with 14-30 eV photons on beamline 5-4 at the SSRL. Spin-resolved ARPES (spin-ARPES) measurements were carried out at the SIS beamline at the SLS using the COPHEE spectrometer [15] with a single 40 kV classical Mott detector and a photon energy of 20 eV. The typical energy and momentum resolution was 15 meV and 1% of the surface BZ, respectively, at beamline 5-4, and 80 meV and 3% of the surface BZ, respectively, at SIS using a pass energy of 3 eV. High-quality single crystals of Sb and Sb 0.9 Bi 0.1 were grown by methods detailed in [12]. Cleaving these samples in situ between 10 and 55 K at chamber pressures less than 5 × 10 −11 torr resulted in shiny flat surfaces, characterized by low-energy electron diffraction to be clean and well ordered with the same symmetry as the bulk (figures 1(a) and (b)). This is consistent with photoelectron diffraction measurements that show no substantial structural relaxation of the Sb(111) surface [16]. Band calculation was performed using the full potential linearized augmented plane wave method in film geometry as implemented in FLEUR program and local density approximation for a description of the exchange correlation potential [17]. Figure 1(c) shows momentum distribution curves (MDCs) of electrons emitted at E F as a function of k x ( ¯ -M) for Sb(111). The out-of-plane component of the momentum k z was calculated for different incident photon energies (hν) using the free electron final state approximation with an experimentally determined inner potential of 14.5 eV [14]. There are four peaks in the MDCs centered about¯ that show no dispersion along k z and have narrow widths of k x ≈ 0.03 Å −1 . These are attributed to surface states and are similar to those that appear in Sb(111) thin films [14]. As hν is increased beyond 20 eV, a broad peak appears at k x ≈ −0.2 Å −1 , outside the k range of the surface states near¯ , and eventually splits into two peaks. Such a strong k z dispersion, together with a broadened linewidth ( k x ≈ 0.12 Å −1 ), is indicative of bulk band behavior, and indeed these MDC peaks trace out a Fermi surface (figure 1(d)) that is similar in shape to the hole pocket calculated for bulk Sb near H [23]. Therefore, by choosing an appropriate photon energy (e.g. 20 eV), the ARPES spectrum along¯ -M will have contributions only from the surface states. The small bulk electron pocket centered at L is not accessed using the photon energy range we employed (figure 1(d)). ARPES spectra along¯ -M taken at three different photon energies are shown in figure 2. Near¯ there are two rather linearly dispersive electron-like bands that meet exactly at¯ at a binding energy E B ∼ −0.2 eV. This behavior is consistent with previous ARPES measurements along the¯ -K direction [13] and is thought to come from a pair of spin-split surface bands that becomes degenerate at the time reversal invariant momentum (TRIM)¯ due to Kramers degeneracy. The Fermi velocities of the inner and outer V-shaped bands are 4.4 ± 0.1 and 2.2 ± 0.1 eV Å, respectively, as found by fitting straight lines to their MDC peak positions. The surface origin of this pair of bands is established by their lack of dependence on hν (figures 2(a)-(c)). A strongly photon energy dispersive hole-like band is clearly seen on the negative k x side of the surface Kramers pair, which crosses E F for hν = 24 eV and gives rise to the bulk hole Fermi surface near H ( figure 1(d)). For hν 20 eV, this band shows clear back folding near E B ≈ −0.2 eV, indicating that it has completely sunk below E F . Further evidence for its bulk origin comes from its close match to band calculations (figure 2(a)). Interestingly, at photon energies such as 18 eV where the bulk bands are far below E F , there remains a uniform envelope of weak spectral intensity near the Fermi level in the shape of the bulk hole pocket 5 seen with hν = 24 eV photons, which is symmetric about¯ . This envelope does not change shape with hν, suggesting that it is of surface origin. Due to its weak intensity relative to states at higher binding energy, these features cannot be easily seen in the energy distribution curves (EDCs) in figures 2(a)-(c), but can be clearly observed in the MDCs shown in figure 1(c), especially on the positive k x side. Centered about theM point, we also observe a crescentshaped envelope of weak intensity that does not disperse with k z (figures 2(d)-(f)), pointing to its surface origin. Unlike the sharp surface states near¯ , the peaks in the EDCs of the feature nearM are much broader ( E ∼80 meV) than the spectrometer resolution (15 meV). The origin of this diffuse ARPES signal is not due to surface structural disorder because if that were the case, electrons at¯ should be even more severely scattered from defects than those atM. In fact, the occurrence of both sharp and diffuse surface states originates from a k-dependent coupling to the bulk, as discussed later.
To extract the spin polarization vector of each of the surface bands near¯ , we carried out spin-resolved MDC measurements along theM -¯ -M cut at E B = −30 meV for maximal intensity and used the two-step fitting routine developed in [24]. The Mott detector in the COPHEE instrument is mounted so that at normal emission it is sensitive to a purely outof-plane spin component (z ) and a purely in-plane (y ) spin component that is rotated by 45 • from the sample¯ -M direction ( figure 3(a)). Each of these two directions represents a normal to a scattering plane, defined by the electron incidence direction on a gold foil and two detectors mounted on either side that measure the left-right asymmetry A y ,z = [(I  [15]. Figure 3(d) shows the spin polarization for both components given by P = (1/S eff ) × A y ,z , where S eff = 0.085 is the Sherman function. Following the procedure described in [24], we take the spins to be fully polarized, assign a spin-resolved spectra for each of the fitted peaks I i shown in figure 3(c) and fit the calculated polarization spectrum to the measurement. The spin-resolved spectra for the y-component derived from the polarization fit are shown in figure 3(e), given by I ↑,↓ y = 4 i=1 I i (1 ± P i y )/6 + B/6, where B is a background and P i y is the fitted y-component of polarization. There is a clear difference in I ↑ y and I ↓ y at each of the four MDC peaks, indicating that the surface state bands are spin polarized. Each of the pairs l2/l1 and r 1/r 2 has opposite spin, consistent with the behavior of a spin-split Kramers pair, and the spin polarization of these bands is reversed on either side of¯ in accordance with time reversal symmetry (figure 3(f)). Similar to Au(111) [21] and W(110)-(1×1)H [18], the spin polarization of each band is largely in-plane consistent with a predominantly out-of-plane electric field at the surface. However, unlike the case in Au(111), where the surface band dispersion is free electron like and the magnitude of the Rashba coupling can be quantified by the momentum displacement between the spin-up and spin-down band minima [21], the surface band dispersion of Sb(111) is highly non-parabolic. A comparison of the k-separation between spin-split band minima near¯ of Sb(111) ( figure 3(b)) with those of Bi(111) [17], which are 0.03 and 0.08 Å −1 , respectively, nevertheless is consistent with the magnitude of the atomic p level splitting of Sb (0.6 eV) and Bi (1.5 eV) [25]. Figure 4(a) shows the full ARPES intensity map from¯ toM together with the calculated bulk bands of Sb projected onto the (111) surface. Although the sixfold rotational symmetry of the surface band dispersion is not known a priori due to the threefold symmetry of the bulk, we measured an identical surface band dispersion along¯ -M'. The spin-split Kramers pair near¯ lies completely within the gap of the projected bulk bands near E F attesting to their purely surface character. In contrast, the weak diffuse hole-like band centered near   In general, the spin degeneracy of surface bands on spin-orbit coupled insulators can be lifted due to the breaking of space inversion symmetry. However, the Kramers theorem requires that they remain degenerate at four special TRIM on the 2D surface BZ, which for Sb(111) are located at¯ and threeM points rotated by 60 • from one another. According to recent theory, there are a total of four Z 2 topological numbers ν 0 ;(ν 1 ν 2 ν 3 ) that characterize a 3D spin-orbitcoupled insulator's bulk band structure [3,9,11]. One in particular (ν 0 ) determines whether the spin-polarized surface bands cross E F an even or odd number of times between any pair of surface TRIM and consequently whether the insulator is trivial (ν 0 = 0) or topological (ν 0 = 1). An experimental signature of topologically non-trivial surface states in insulating Bi 1−x Sb x is that the spin-polarized surface bands traverse E F an odd number of times between¯ andM [2,12,19]. Although this method of counting cannot be applied to Sb because it is a semimetal, since there is a direct gap at every bulk k-point, it is meaningful to assume some perturbation, such as alloying with Bi [27] that does not significantly alter the spin splitting (figure 5), that pushes the bulk valence H and conduction L bands completely below and above E F , respectively, without changing its Z 2 class. Under such an operation, it is clear that the spin-polarized surface bands must traverse E F an odd number of times between¯ andM, consistent with the 1;(111) topological classification of Sb. This conclusion can also be reached by noting that the spinsplit pair of surface bands that emerge from¯ does not recombine atM, indicative of a 'partner switching' [9] characteristic of topological insulators.
In conclusion, we have mapped the spin structure of the surface bands of Sb(111) and shown that the purely surface bands located in the projected bulk gap are spin split by a combination of spin-orbit coupling and loss of inversion symmetry at the crystal surface. The spin-polarized surface states have an asymmetric Dirac-like dispersion that gives rise to its k-splitting between spin-up and spin-down bands at E F . This property of Sb, in combination with its small density of spin degenerate bulk states at the Fermi level due to its semimetallic nature, makes it a promising candidate for high-temperature spin current sources. Moreover, its topologically non-trivial surface band structure makes Sb(111) an especially appealing candidate for an unusual 2D Dirac protected free fermion system that exhibits antilocalization [9].