Magnetoconductance, Quantum Hall Effect, and Coulomb Blockade in Topological Insulator Nanocones

Abstract

Magnetotransport through cylindrical topological insulator (TI) nanowires is governed by the interplay between quantum confinement and geometric (Aharonov-Bohm and Berry) phases. Here, we argue that the much broader class of TI nanowires with varying radius -for which a homogeneous coaxial magnetic field induces a varying Aharonov-Bohm flux that gives rise to a non-trivial masslike potential along the wire -is accessible by studying its simplest member, a TI nanocone. Such nanocones allow to observe intriguing mesoscopic transport phenomena: While the conductance in a perpendicular magnetic field is quantized due to higher-order topological hinge states, it shows resonant transmission through Dirac Landau levels in a coaxial magnetic field. Furthermore, it may act as a quantum magnetic bottle, confining surface Dirac electrons and leading to Coulomb blockade. We show numerically that the above-mentioned effects occur for experimentally accessible values of system size and magnetic field, suggesting that TI nanocone junctions may serve as building blocks for Dirac electron optics setups.Electronic transport across phase-coherent structures has been a central topic of solid state research ever since the birth of mesoscopic physics some 40 years ago. While the complexity of mesoscopic setups has steadily increased, from the simple gate-defined quantum point contacts of the '80s [1] to elaborate present-day electron optics circuits in semiconductors [2] and graphene [3,4], their structure remains in the vast majority of cases planar -i.e. transport takes place in flat two-dimensional (2D) space. Exceptions to the 2D scenario are samples based on carbon nanotubes and 3D topological insulator (3DTI) nanowires [5][6][7][8]. 3DTIs are bulk band insulators hosting protected 2D surface metallic statesà la Dirac [9]. In mesoscopic nanostructures built out of 3DTIs low-temperature phase-coherent transport takes place on a 2D Dirac metal wrapped around an insulating 3D bulk. As such, it is strongly dependent on a peculiar conjunction of structural (real space) and spectral (reciprocal space) geometrical properties. This has remarkable consequences even for the possibly simplest setup, a topological insulator nanowire (TINW) with constant circular cross section in a coaxial magnetic field, shown in Fig. 2(a). The magnetoconductance of such an object is characterized by a non-trivial interplay between two fundamentals of mesoscopic physics: quantum confinement and geometric [Aharonov-Bohm (AB) and Berry] phases [6][7][8][10][11][12].

Theory of magnetotransport in shaped topological insulator nanowires

“…[49,50] for reviews. tematic study of their magnetotransport properties, thereby extending previous work [10] on truncated TI nanocones (TINCs) [see Fig. 1(a)].…”

“…Moreover, transport takes place on a surface which is closed along the transversal direction, enclosing the (nominally) insulating three-dimensional (3D) TI bulk. This leads to the interplay between the spin Berry phase of surface states and an Aharonov-Bohm phase acquired in the presence of a coaxial magnetic field [10][11][12][13][14][15][16][17][18].…”

“…It is instructive to study each component separately. If the component perpendicular to the TINW axis is strong, i.e., the associated magnetic length l B is much smaller than the nanowire diameter, the nanowire conductance will be dominated by chiral side (hinge) states [10,[22][23][24][25][26]. These states are largely independent of the TINW shape.…”

“…circumference, generates a mass-like z-dependent potential. This potential can be used to qualitatively predict the transport characteristics of any shaped TINW, and was recently discussed for the simplest case of a single TINC [10]. In order to understand magnetotransport in shaped nanowires, an essential step will be to consider such TINCs as building blocks of more complex geometries (see Fig.…”

Confinement versus interface bound states in spin-orbit coupled nanowires

“…While early studies have focussed on the topological bound states of proximitized spinorbit coupled nanowires, more recent works have pointed out that in the presence of a superconducting coupling both topological and trivial bound states may exist [52][53][54][55][56][57][58][59][60][61][62][63]. Also, quite recently it has been realized that peculiar bound states can appear even when no superconducting coupling is present, if magnetic domains induce an inhomogeneous magnetic field on the nanowire [64], similarly to the magnetic confinement effects predicted in other materials [65][66][67].…”