Topological phases of topological-insulator thin films

Abstract

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi2Se3 and Bi2Te3. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi2Se3, making Bi2Te3, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators. arXiv:1801.02084v1 [cond-mat.mes-hall]

Surface step states and Majorana end states in profiled topological insulator thin films

“…However, when the film thickness is reduced (below a few quintuple layers) the T,B surface states overlap and a hybridisation of equal spin (and therefore equal helicity) eigenstates develops. This problem has been fundamentally treated and analyzed in great generality in the work of Asmar et al [19] and also in Ref. 29.…”

“…The thickness dependent effective hybridisation t(d) may be obtained from the solution of a subtle boundary value problem for the thin film [19], starting form the k • p Hamiltonian of the bulk bands. It may be represented by the phenomenological form [19,21]…”

“…Here the energy t 0 and thickness d 0 , d 0 scales are determined by the parameters of bulk bands [19,21]. As an example we give the theoretical values for Bi 2 Te 3 in terms of natural units E * = 0.25 meV and 1QL = 10.16 Å, respectively as (t 0 , d 0 , d 0 ) = (0.80, 1.79, 0.3).…”

“…This has indeed been verified directly by photoemission [16,17] but also by a sudden breakdown of weak anti-localisation in magnetotransport [1,2] as function of film thickness when the latter falls below about five quintuple layers (QL). The effective hybridisation between the surface states has been calculated [18][19][20] solving the thin film boundary value problem for an effective k • p Hamiltonian of the bulk. Due to the constrained film geometry the effective inter-surface hybridisation t(d) not only decreases exponentially with film thickness d but also generally oscillates as function of thickness d with an oscillation period depending on the material parameters.…”

Spectroscopic signature of surface states and bunching of bulk subbands in topological insulator ( Bi0.4Sb0.6)2TeMulder1, Castenmiller2, Witmans3 et al. 2022Phys. Rev. B0000View full textAdd to dashboardCite

“…Due to the spatial extent of the surface state in the z -direction, it has been predicted that ultrathin slabs of 3D TIs provide a route to a hybridization gap around the DP [6,7], thereby gapping out the topological surface states and paving the way to topologically protected one-dimensional (1D) edge state transport, very comparable to the quantum spin Hall (QSH) effect in HgTe quantum wells [8][9][10]. Even though Bi 2 Se 3 presents the largest bulk bandgap, Bi 2 Te 3 and Sb 2 Te 3 are predicted to be more appealing candidates to exhibit 1D transport due to their relatively short edge state decay length in the ultrathin film limit [7,11,12]. While stoichiometric slabs have been well-investigated spectroscopically [13][14][15], even in the limit of hybridized surface states [16], the electronic structure of ultrathin films of off-stoichiometric (Bi 1−x Sb x ) 2 Te 3 is still relatively unexplored.…”