Unconventional band structure for a periodically gated surface of a three-dimensional topological insulator

Abstract

The surface states of the three dimensional (3D) Topological Insulators are described by twodimensional (2D) massless dirac equation. A gate voltage induced one dimensional potential barrier on such surface creates a discrete bound state in the forbidden region outside the dirac cone. Even for a single barrier it is shown such bound state can create electrostatic analogue of Shubnikov de Haas oscillation which can be experimentally observed for relatively smaller size samples. However when these surface states are exposed to a periodic arrangement of such gate voltage induced potential barriers, the band structure of the same got nontrivially modified. This is expected to significantly alters the properties of macroscopic system. We also suggest that in suitable limit the system may offer ways to control electron spin electrostatically which may be practically useful.PACS numbers: 73.23.-b, 72.25.-b, 73.43.-f,71.20.-b The discovery of two-dimensional quantum spin Hall insulator commonly known as two dimensional topological insulators (2DTI) 1-3 and the subsequent discovery of their three dimensional generalization dubbed as three dimensional topological insulators (3DTI)4-6 led to a large amount of experimental and theoretical work in this direction 7,8 . The surface electronic states of the 3DTI are described by the two dimensional massless dirac equation and this has been demonstrated by spin and angle resolved photoemission spectroscopy 6,9 . Such massless dirac fermions (MDF) with ultra relativistic dispersion relation have fundamentally different transport properties from in comparison to the non-relativistic electron gas (NREG) in ordinary metal or semiconductor.One such peculiar properties of these surface MDF is the formation of bound states in a one dimensional potential barrier 10,11 created through a gate voltage outside the dirac cone, namely in the forbidden region. This situation should be contrasted with the prototype bound state and quasi-bound states formation in presence of quantum well in non-relativistic quantum mechanics ( for example see 12 ) as well as for the case of MDF in Graphene [13][14][15] . Particularly in the later case ( for example see 15 ) these bound states formed by the quantum wells are within the dirac cone which are in proximity with scattering states having linear dispersion.In this paper, we report such bound state induced significant modification of band structure for surface MDF in presence of a periodic array of such barriers. This modification of band structure occurs outside the dirac cone which is otherwise a forbidden zone and in a nontrivial manner changes the band structure of such surface states. We start by showing in presence of such bound states in a potential barrier the DOS of MDF in the surface of a 3DTI oscillates purely through electrostatic means creating electrostatic analogue of Shubnikov de Haas (SdH)oscillation of NREG in a magnetic field 16 . Such DOS oscillation leads to sharp oscillation in the conductance in the linear response regime. Howev...

THz photodetector using sideband-modulated transport through surface states of a 3D topological insulator

“…The device we propose is a gated structure on the surface of a 3DTI in the form of a double barrier potential [23] sketched in Fig. 1 (a).…”

“…The device we propose is a gated structure on the surface of a 3DTI in the form of a double barrier potential [27] sketched in figure 1(a). Our model contains three regions: one central region tuned by the back gate voltage, two gated areas (yellow areas) tuned by both back and top gate and ohmic contacts (source and drain).…”