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Register a new userStability of topological properties of bismuth (111) bilayer
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We investigate electronic and transport properties of bismuth (111) bilayer in the context of stability of its topological properties against different perturbations. The effects of spin-orbit coupling variations, geometry relaxation and an interaction with a substrate are considered. Transport properties are studied in the presence of Anderson disorder. Band structure calculations are performed within multi-orbital tight-binding model and density functional theory methods. A band inversion process in bismuth (111) infinite bilayer and an evolution of edge states dispersion in ribbons as a function of spin-orbit coupling strength are analyzed. A significant change of orbital composition of the conduction and valence bands during a topological phase transition is observed. A topological phase is shown to be robust when the effect of geometry relaxation is taken into account. An interaction with a substrate has similar effect to an external perpendicular electric field. The robust quantized conductance is observed when the Fermi energy lies within the bulk energy gap, where only two counter-propagating edge states are present. For energies where the Fermi level crosses more in-gap states, a scattering is possible between channels lying close in $k-$space. When the energy of edge states overlaps with bulk states, no topological protection is observed.
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Structures and electronic properties of rhombohedral [111] and [110] bismuth nanowires are calculated with the use of density functional theory. The formation of an energy band gap from quantum confinement is studied and to improve estimates for the band gap the GW approximation is applied. The [111] oriented nanowires require surface bonds to be chemically saturated to avoid formation of metallic surface states whereas the surface of the [110] nanowires do not support metallic surface states. It is found that the onset of quantum confinement in the surface passivated [111] nanowires occurs at larger critical dimensions than for the [110] nanowires. For the [111] oriented nanowires it is predicted that a band gap of approximately 0.5 eV can be formed at a diameter of approximately 6 nm, whereas for the [110] oriented nanowires a diameter of approximately 3 nm is required to achieve a similar band gap energy. The GW correction is also applied to estimates of the electron affinity, ionisation potentials and work functions for both orientations of the nanowires for various diameters below 5 nm. The magnitude of the energy band gaps that arise in bismuth at critical dimensions of a few nanometers are of the same order as for conventional bulk semiconductors.
Bulk boundary correspondence in topological materials allows to study their bulk topology through the investigation of their topological boundary modes. However, for classes that share similar boundary phenomenology, the growing diversity of topological phases may lead to ambiguity in the topological classification of materials. Such is the current status of bulk bismuth. While some theoretical models indicate that bismuth possesses a trivial topological nature, other theoretical and experimental studies suggest non-trivial topological classifications such as a strong or a higher order topological insulator, both of which hosts helical modes on their boundaries. Here we use a novel approach to resolve the topological classification of bismuth by spectroscopically mapping the response of its boundary modes to a topological defect in the form of a screw dislocation (SD). We find that the edge mode extends over a wide energy range, and withstands crystallographic irregularities, without showing any signs of backscattering. It seems to bind to the bulk SD, as expected for a topological insulator (TI) with non-vanishing weak indices. We argue that the small scale of the bulk energy gap, at the time reversal symmetric momentum $L$, positions bismuth within the critical region of a topological phase transition to a strong TI with non-vanishing weak indices. We show that the observed boundary modes are approximately helical already on the $mathbb{Z}_2$ trivial side of the topological phase transition. This work opens the door for further possibilities to examine the response of topological phases to crystallographic topological defects, and to uniquely explore their associated bulk boundary phenomena.
A topological insulator is a novel quantum state, characterized by symmetry-protected non-trivial edge/surface states. Our first-principle simulations show the significant effects of the chemical decoration on edge states of topological Bi(111) bilayer nanoribbon, which remove the trivial edge state and recover the Dirac linear dispersion of topological edge state. By comparing the edge states with and without chemical decoration, the Bi(111) bilayer nanoribbon offers a simple system for assessing conductance fluctuation of edge states. The chemical decoration can also modify the penetration depth and the spin texture of edge states. A low-energy effective model is proposed to explain the distinctive spin texture of Bi(111) bilayer nanoribbon, which breaks the spin-momentum orthogonality along the armchair edge.
The long-sought Majorana fermion is expected to manifest in a topological-superconductor heterostructure as a zero bias conductance peak (ZBCP). As one promising platform for such heterostructures, we investigate the cleaved surface of the topological semimetal Sb(111) using scanning tunneling microscopy and spectroscopy. Remarkably, we find a robust ZBCP on some terraces of the cleaved surface, although no superconductor is present. Using quasiparticle interference imaging, Landau level spectroscopy and density functional theory, we show that the ZBCP originates from a van Hove singularity pushed up to the Fermi level by a sub-surface stacking fault. Amidst the sprint to stake claims on new Majorana fermion systems, our finding highlights the importance of using a local probe together with detailed modeling to check thoroughly for crystal imperfections that may give rise to a trivial ZBCP unrelated to Majorana physics.
We report on fabrication of a two-dimensional topological insulator-Bi(111) bilayer on Sb nanofilms via a sequential molecular beam epitaxy (MBE) growth technique. Our angle-resolved photoemission measurements demonstrate the evolution of the electronic band structure of the heterostructure as a function of the film thickness and reveal the existence of a two-dimensional spinful massless electron gas within the top Bi bilayer. Interestingly, Our first-principles calculation extrapolating the observed band structure shows that, by tuning down the thickness of the supporting Sb films into the quantum dimension regime, a pair of isolated topological edge states emerges in a partial energy gap at 0.32 eV above the Fermi level as a consequence of quantum confinement effect. Our results and methodology of fabricating nanoscale heterostructures establish the Bi bilayer/Sb heterostructure as a platform of great potential for both ultralow-energy-cost electronics and surface-based spintronics.
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