-0.6 -0.4 -0.2 0.0 0.2 GLYPH<c71> M M’ 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 Deg 1.0 0.5 0.0 -0.5 kGLYPH<.notdef>GLYPH<.notdef>(ÅGLYPH<.notdef>GLYPH<.notdef>) x -1 kGLYPH<.notdef>GLYPH<.notdef>(ÅGLYPH<.notdef>GLYPH<.notdef>) y -1 EGLYPH<.notdef>GLYPH<.notdef>(eV) B (a) (b) (d) SurfaceGLYPH<.notdef>stateGLYPH<.notdef>FS SurfaceGLYPH<.notdef>resonanceGLYPH<.notdef>FS GLYPH<c71> M GLYPH<c71> M (c) M GLYPH<s45>GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s45>GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s45>GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s32> 0 -1 1 0 1 -1 0 1 -1 0 1 P$_{x}$ P$_{y}$ P$_{z}$ P$_{inGLYPH<.notdef>plane}$ -0.2 0.0 0.2 0.1 -0.1 0.0 -0.1 -0.2 GLYPH<c172>GLYPH<c32>GLYPH<c77> GLYPH<c71>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c32>GLYPH<c77>GLYPH<c174> ’ EGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>(eV) B (b) (a) ||GLYPH<.notdef><111> GLYPH<c113> 45 GLYPH<c176> y’ x’ z ’ x y z l 2 l 1 r 1 r 2 IntensityGLYPH<.notdef>(arb.GLYPH<.notdef>units) Polarization (f) GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s32> GLYPH<s32> GLYPH<s32>GLYPH<s112> GLYPH<s121> GLYPH<s112> GLYPH<s114> GLYPH<s105>GLYPH<s109> GLYPH<s101> GLYPH<s32>GLYPH<s112> GLYPH<s122> 0.0 -0.2 -0.4 0.2 0.4 P P$^{y}$$^{’}$ z ’ GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s51> GLYPH<s48> GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s49>GLYPH<s53> GLYPH<s50>GLYPH<s48> GLYPH<s50>GLYPH<s53> GLYPH<s32> GLYPH<s32> GLYPH<s108>GLYPH<s50> GLYPH<s32> GLYPH<s108>GLYPH<s49> GLYPH<s32> GLYPH<s114>GLYPH<s49> GLYPH<s32> GLYPH<s114>GLYPH<s50> GLYPH<s32> GLYPH<s32> GLYPH<s73>GLYPH<s110>GLYPH<s116>GLYPH<s101>GLYPH<s110>GLYPH<s115>GLYPH<s105>GLYPH<s116>GLYPH<s121>GLYPH<s32>GLYPH<s40>GLYPH<s97>GLYPH<s114>GLYPH<s98>GLYPH<s46>GLYPH<s32>GLYPH<s117>GLYPH<s110>GLYPH<s105>GLYPH<s116>GLYPH<s115>GLYPH<s41> GLYPH<s73> GLYPH<s116>GLYPH<s111>GLYPH<s116> -0.2 0.0 0.2 0.1 -0.1 IntensityGLYPH<.notdef>(arb.GLYPH<.notdef>units) 0.3 EGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>=GLYPH<.notdef>-30GLYPH<.notdef>meV B r 2 r 1 l 1 l 2 0 10 20 GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s51> GLYPH<s52> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s32>GLYPH<s32>GLYPH<s117> GLYPH<s112> GLYPH<s32>GLYPH<s32>GLYPH<s100> GLYPH<s110> k (ÅGLYPH<.notdef>GLYPH<.notdef>) x IntensityGLYPH<.notdef>(arb.GLYPH<.notdef>units) -0.2 0.0 0.2 0.1 -0.1 -1 EGLYPH<.notdef>GLYPH<.notdef>GLYPH<.notdef>=GLYPH<.notdef>-30GLYPH<.notdef>meV B 0 2 4 I I$^{y}$ y (e) (d) kGLYPH<.notdef>GLYPH<.notdef>(ÅGLYPH<.notdef>GLYPH<.notdef>) x -1 -1 kGLYPH<.notdef>GLYPH<.notdef>(ÅGLYPH<.notdef>GLYPH<.notdef>) x (c) FIG. 4: Topologically non-trivial surface states of Sb(111). (a) Calculated surface state band structure for freestanding 20 bilayer Sb(111) slabs together with an ARPES intensity map of Sb(111) along the ¯ Γ- ¯ M direction taken with hν = 22 eV photons. Green curves show the calculated bulk bands along the k$_{x}$ direction projected onto the (111) plane. (b) ARPES intensity map at E$_{F}$ in the k$_{x}$ - k$_{y}$ plane taken with hν = 20 eV photons. (c) Schematic picture showing that the gapless spin polarized surface bands (red and blue lines) con- nect the projected bulk valence and conduction bands (shaded regions) and are thus topologically non-trivial. The surface resonances (dashed green lines) do not connect the bulk va- lence and conduction bands and are thus topologically trivial. (d) Schematic of the surface Fermi surface topology of Sb(111) showing the pockets formed by the pure surface states (un- filled) and the surface resonances (filled green). The purely surface state Fermi contours enclose only the one surface TRIM located at ¯ Γ. FIG. 3: Large spin splitting of surface states on Sb(111). (a) Experimental geometry of the spin resolved ARPES study. At normal emission ( θ =0 $^{◦}$), the sensitive y $^{′}$-axis of the Mott detector is rotated by 45 ◦ from the sample ¯ Γ- ¯ M ( ‖ x) direc- tion, and the sensitive z $^{′}$-axis of the Mott detector is parallel to the sample normal. Spin up and down are measured with respect to these two quantization axes. (b) Spin integrated ARPES spectra along the ¯ M’- ¯ Γ- ¯ M direction taken using a photon energy hν = 22 eV. The momentum splitting between the band minima is indicated by the black bar and is approx- imately 0.03 ˚ A − $^{1}$. (c) Momentum distribution curve of the spin integrated spectra at E$_{B}$ = -30 meV (shown in (b) by white line) using a photon energy hν = 20 eV, together with the Lorentzian peaks of the fit. (d) Measured spin polariza- tion curves (symbols) for the y ′ and z ′ components together with the fitted lines using the two-step fitting routine. Even though the measured polarization only reaches a magnitude of around ± 0.4, similar to what is observed in thin film Bi(111) [20], this is due to a non-polarized background and overlap of adjacent peaks with different spin polarization. The fitted parameters are in fact with consistent with 100% polarized spins. (e) Spin resolved spectra for the y component based on the fitted spin polarization curves shown in (d). (f) The in-plane and out-of-plane spin polarization components in the sample coordinate frame obtained from the spin polarization fit. The symbols refer to those in (c). sity near the Fermi level in the shape of the bulk hole pocket seen with hν = 24 eV photons, which is symmet- ric about ¯ Γ. 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 Fig. 2(a)-(c), but can be clearly ob- served in the MDCs shown in Fig. 1(c) especially on the positive k$_{x}$ side. Centered about the ¯ M point, we also observe a crescent shaped envelope of weak intensity that does not disperse with k$_{z}$ [Fig. 2(d)-(f)], point- ing to its surface origin. Unlike the sharp surface states near ¯ Γ, the peaks in the EDCs of the feature near ¯ M are much broader (Δ 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 ¯ Γ should be even more severely scattered from defects than those at ¯ M. 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 ¯ Γ, we performed spin resolved MDC measurements along the ¯ M’- ¯ Γ- ¯ M cut at E$_{B}$ = -30 meV for maximal intensity, and used the two-step fit- ting routine developed in [24]. The Mott detector in the COPHEE instrument is mounted so that at nor- mal emission it is sensitive to a purely out-of-plane spin component ( z $^{′}$) and a purely in-plane ( y $^{′}$) spin compo- nent that is rotated by 45 ◦ from the sample ¯ Γ- ¯ M di- rection [Fig. 3(a)]. Each of these two directions rep- 3