Anisotropic effect of warping on the lifetime broadening of topological surface states in angle-resolved photoemission fromBi2Te3

Abstract

We analyze the strong hexagonal warping of the Dirac cone of Bi2Te3 by angle-resolved photoemission. Along ΓM, the dispersion deviates from a linear behavior meaning that the Dirac cone is warped outwards and not inwards. We show that this introduces an anisotropy in the lifetime broadening of the topological surface state which is larger along ΓK. The result is not consistent with nesting. Based on the theoretically predicted behavior of the ground-state spin texture of a strongly warped Dirac cone, we propose spin-dependent scattering processes as explanation for the anisotropic scattering rates. These results could help paving the way for optimizing future spintronic devices using topological insulators and controlling surface-scattering processes via external gate voltages.Topological insulators (TIs) are characterized by an insulating bulk energy gap and gapless spin-polarized Dirac-cone surface states with electron spins locked perpendicular to their linear momenta. 1,2 This peculiar spin texture is believed to play a central role in inducing exotic quantum phenomena 2,3 , novel magnetic-spin physics, 4,5 as well as in the development of future spin-based lowpower transistors among a variety of applications. Such perpendicular locking can be realized if spins of electrons occupying the Dirac cone move around in ideally circular constant-energy contours between the Dirac point and the Fermi level. 6 Owing to the spin-momentum locking, electrons on the surfaces of TIs are protected from backscattering, 7 an effect that might be of crucial importance in the generation of spin currents with reduced dissipation, 8 coherent spin rotation, 9 spin-orbit qubits, 10 as well as in other applications such as manipulation of photon-polarization driven spin currents in real devices. 11 The spin texture of the Dirac cone can be affected by the presence of hexagonal warping, 12 i.e., the Dirac cone is deformed in such a way that from the Dirac point to the energy of the Fermi level the constantenergy contours develop from an ideally circular shape to a hexagon, and subsequently to a snowflake-like Fermi surface. This strong distortion of the Dirac cone might open up new possibilities for observing other interesting phenomena, such as the breaking of time-reversal symmetry and the surface quantum Hall effect under applied magnetic fields parallel to the surface, 12 enhanced surface scattering or the formation of surface spin-density waves. 12,13 In the context of exploring these possibilities, the observation and importance of hexagonal warping in the band dispersions of the topological surface states (TSSs), 14-16 as well as its theoretical description, 12,17,18 has stimulated a manifold of theoretical and experimental investigations on TIs. The strong influence of warping on the spin texture of TSSs giving rise to a finite outof-plane spin orientation was theoretically predicted, 12 and by means of spin-resolved angle-resolved photoemission (SR-ARPES) experimentally observed. 19 That in the presence of warping the electro...

Interband absorption edge in the topological insulators Bi2(Te1−xSex)3

“…The difference in the reported values is presumably caused by differences in the doping level and related MB shift and/or by a difference in the definition of the onset energy. Regardless of these relatively small differences, as noted by Chapler et al 15 , the onset of absorption at 10 K (≈ 200 meV in our data) is significantly smaller than the 290 meV value of the direct bandgap at the Γ point observed in ARPES 6,50 . Note that in our data, the value of ε 2 at 290 meV is about 25, which corresponds to a very strong absorption due to direct interband transitions.…”

“…The conduction band in Bi 2 Te 3 has a strong hexagonal warping 6,50 . The ARPES intensity related to the conduction band is centred at the Γ point, however, it has a snowflake-like shape with protrusions extending into the Γ-M direction.…”

Lifetime and surface-to-bulk scattering off vacancies of the topological surface state in the three-dimensional strong topological insulators Bi2Te3 and Bi2Se3

“…As we see in Figure 2(a), τ −1 k (E) is highly anisotropic on the TSS, with higher values at the valleys (ΓK directions) and strongly reduced values by almost an order of magnitude (factor 6.8) at the tips of the constant energy contour (ΓM direction). The anisotropy was also seen in angular-resolved photoemission experiments 26 where the line-width of the spectral density can be related to the scattering rate of the states. The effect is consistent with the fact that the states at the tips of the warped contour are more delocalized, projecting into the bulk, as compared with the states in the valleys that have a larger amplitude in the surface layer.…”

Spatially resolved Landau level spectroscopy of the topological Dirac cone of bulk-typeSb2Te3(0001): Potential fluctuations and quasiparticle lifetime

“…The fact that time-resolved ARPES data at B = 0 T find relaxation times of about τ = 1 ps at E D − E F = 0 − 100 meV [76,77], which would correspond to ∆E = /τ = 0.7 meV indicates that either the B field and the related localization of electrons or the presence of the STM tip might change the scattering rates significantly. Notice that the lifetimes observed by the fit of the line widths of ARPES data [78,79] are typically even shorter than the ones observed by LL spectroscopy [41,43] and, thus, in stronger discrepancy to the time-resolved data [80,81]. This is most likely due to disorder averaging, i.e.…”