Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators

Abstract

The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe which directly couples to an exotic property of these surface states, namely the spin-momentum locking. We show that the information regarding the spin textures, so extracted, for different surfaces can be put together to reconstruct the parameters characterizing the bulk band structure of the material, hence acting as a hologram. For specific TI materials like, Bi2Se3, Bi2Te3 and Sb2Te3, the planar surface states are distinct from one another with regard to their spectrum and the associated spin texture for each angle (θ), which the normal to the surface makes with the crystal growth axis. We develop a tunnel Hamiltonian between such arbitrary surfaces and a spin polarized STM which provides a unique fingerprint of the dispersion and the associated spin texture corresponding to each θ. Additionally, the theory presented in this article can be used to extract value of θ for a given arbitrary planar surface from the STM spectra itself hence effectively mimicking X-ray spectroscopy.

Transport signatures of surface potentials on three-dimensional topological insulators

“…Note that this is the well known tunnel magnetoresistance response form for transport between two spinpolarized materials 29 . The total current turns out to be a sum of the momentumresolved current values over the available momentum modes in the bias window 27,28 . This fact is extremely crucial as the decomposition of the total current into momentum-resolved currents enables us to divide the current that flows in each half of the TI surface to each of the contacts shown in Fig.1(c) by simply summing the current over the momentum modes which go towards each contact from the spatial point r = 0.…”

Pseudospin-valve effect on transport in junctions of three-dimensional topological insulator surfaces

“…We sketch the derivations of the surface state spinors and their properties, setting up consistent notations used throughout the rest of the paper. For details refer to [5,13,14,16].…”

“…Obviously, the coefficients in the linear combinations can differ only by phase which we denote by f R . This phase is fixed by demanding the state to be an eigenstate of q T x [13,16] with eigenvalue ±1 (for the surface state of θ and p q + respectively) where q T represents the pseudospin degree of freedom given by…”

“…It is interesting to note that the polarization of the frozen degree of freedom is exactly opposite on the opposite surfaces for any angle θ [13,16] that the surfaces make with the crystal growth axis, hence leading to distinction between the top and bottom surfaces which is very similar to the distinction of north and south poles of a bar magnet. It can be understood from the observation that, when a bar magnet is broken into two halves, it exposes two new ends with opposite polarity such that each new bar magnet has opposite polarity at its two ends.…”

Transport theory for electrical detection of the spin-momentum locking of topological surface states

“…Though such spin helicity has been experimentally observed by spin-resolved angle resolved photoemission spectroscopy (ARPES) 9-12 or polarized optical spectroscopic techniques 13 , it in present becomes extremely desirable to all-electrically detect the unique SML nature and resulting spin texture from electron transports. Theoretically, two-terminal spin valve 14,15 and three-terminal asymmetric structure [16][17][18] have been suggested to extract the information of SML by probing the spin-polarized currents along TI surface. In realistic experiments 19-22 , however, it remains great challenging due to unavoidable disturbance from bulk states 23 .Alternatively, the imaging of scanning tunneling microscopy (STM) serves as a powerful tool to probe the nature of topological surface states by analyzing the quasi-particle interference (QPI) in Fourier-transform scanning-tunneling spectroscopy 4,23-29 , caused by scattering off impurities on the TI surface.…”