Visualizing spin-dependent bulk scattering and breakdown of the linear dispersion relation in Bi2Te3

Abstract

We performed a scanning tunneling spectroscopy investigation of the electronic properties of the topological insulator Bi 2 Te 3 in the energy range between −200 and +700 meV with respect to the Fermi level. For unoccupied states, tunneling into topological surface states dominates. Analysis of Fourier-transformed (FT) dI/dU maps allowed us to obtain their energy dispersion relation and to visualize the breakdown of the linear dispersion relation typical of massless particles. For occupied states, no signature of scattering events involving surface states can be detected. FT dI/dU maps reveal in this case two scattering vectors pointing along the M and K directions. Both are identified with scattering events within bulk states. Interestingly, vectors pointing along K which correspond to bulk backscattering events have a length longer than the minimum distance necessary to match opposite pockets on a constant energy cut. Comparison with calculated spin-resolved constant-energy cuts shows that this is a direct consequence of the chiral spin texture present in bulk states when their energy and momentum are close to the resonances of the spin-polarized topological surface states. The recent discovery of topological insulators (TIs), a new class of materials insulating in the bulk but conducting on the surface, has opened a new route towards spintronic devices. 1-3Topological surface states of TIs are gapless and, contrary to the trivial surface states usually found at surfaces in metals and semiconductors, cannot be destroyed by the presence of defects and adsorbates as long as time-reversal symmetry is preserved. [4][5][6][7][8] Topological surface states are characterized by a linear energy-momentum dispersion relation, and their charge carriers can be described by a Dirac-like equation for massless particles rather than the Schrödinger equation.9 Consequently, their phase velocity is coincident with the group velocity, and carriers at different energies are all moving with same speed. Because of the Kramers degeneracy theorem, opposite spin directions are degenerate only at high-symmetry points of the surface Brillouin zone where both time-and space-reversal symmetry is preserved: the so-called Dirac points. Above and below these points the spin is perpendicularly locked to the momentum, resulting in a chiral spin texture, 10 spin currents intrinsically tied to charge currents, 11 and forbidden backscattering. 12,13 This results in an increased spin coherence time, an important quantity for spintronic devices in which the information is encoded by the spin degree of freedom.14 In addition to possible technological applications, their spin and electronic structures make these materials a platform to search for exotic phenomena like Majorana fermions 15 and magnetic monopoles. 16 However, to what extent the electronic structure of topological states resembles the one typical of massless particles has not been clearly experimentally addressed so far. The same holds true concerning the spin-related properties of thes...

Superparamagnetism-induced mesoscopic electron focusing in topological insulators

“…The scattering channel along ΓM directions (q 2 ) is routinely found on TI materials [8,14]. Its appearance is related to the strength of the warping term which allows to effectively scatter between next-nearest neighbors segments of a CEC because of their parallel spin polarization.…”

“…1(k)]. The FT-QPI map reveals the simultaneous existence of two scattering vectors which-as a result of the hexagonal surface symmetry-both appear in six equivalent directions, here represented by six (very weak) inner spots in ΓM directions and six (stronger) outer spots which can be found along ΓK directions.The scattering channel along ΓM directions (q 2 ) is routinely found on TI materials [8,14]. Its appearance is related to the strength of the warping term which allows to effectively scatter between next-nearest neighbors segments of a CEC because of their parallel spin polarization.…”

“…1(c)-(e), the scattering vectors q 1 and q 2 specific for each energy can be obtained by using the stationary phase approximation [13]. At E − E F = −70 meV The scattering channel along ΓM directions (q 2 ) is routinely found on TI materials [8,14]. Its appearance is related to the strength of the warping term which allows to effectively scatter between next-nearest neighbors segments of a CEC because of their parallel spin polarization.…”

Breaking time-reversal symmetry at the topological insulator surface by metal-organic coordination networks

“…The consequences of an incommensurate growth of MOCN/TI are also discussed. We believe that the results obtained reflect general characteristic features of the TCNE-, TCNB-, and TCNQ-based MOCNs deposited on top of tetradymite-type TIs [8,[72][73][74]. The main conclusion of this study is that the time-reversal symmetry can indeed be broken by the deposition of a MOCN on top of the TI surface.…”

“…As a consequence of the strong spin-orbit coupling, the band gap in TIs gets inverted giving rise to a special type of surface states that have linear dispersion characteristic of Dirac fermions. The uniqueness of these Dirac states lies in that the electron's spin is locked perpendicular to its momentum, forming a surface state's spin structure which protects the electrons from the elastic backscattering on defects or due to disorder [5][6][7][8][9]. This property, provided by the time-reversal symmetry, leads to a nearly dissipationless current whereby TIs possess an enormous potential for applications in spintronics and quantum computing.…”