Topological States for New Modes of Information Storage and Transfer by Prabhakar Bandaru & Shreyam Natani

Author:Prabhakar Bandaru & Shreyam Natani
Language: eng
Format: epub
ISBN: 9783030933401
Publisher: Springer International Publishing

3.3.3 Majorana Modes at Topological Insulators (TI)–Related Interfaces

A fundamental property of a d-dimensional TI is the existence of lower-dimensional gapless states at the boundary [118]. Ordinary TIs possess d−1-dimensional gapless states. Recently discovered higher-order TIs, that is, HOTIs, such as Bi, possess related states of dimension d−2 or lower [119–123]. These gapless states (hinge states) are protected by certain global symmetries, for example, time reversal symmetry (TRS), inversion symmetry, or chiral symmetry (comprised of particle–hole symmetry and TRS)—inducing immunity of particle-like zero-dimensional states to magnetic forces [124]. Each dimension reducing step may be characterized by its own global symmetry. The gapless states may be manipulated by explicitly breaking symmetries. For example, the TRS may be broken by applying magnetic fields or polarized optical pumping.

The interface between the related one-dimensional helical hinge modes and Fe atom chains—again on top of a SC substrate (Nb) were posited to host the Majorana modes [125]. The related study was complementary to much of the earlier work related to the identification of the Majorana modes conducted in topological SCs synthesized through proximity-induced superconductivity in (a) materials systems with a large S–O coupling and related internal magnetic fields for inducing spinless/p-wave character, and involving (b) Tis, where the intrinsic gap is modulated by the SC gap, so as to induce band gap closing and reopening and concomitant zero-energy states, at the crossover. As one essence of a TI is the presence of edge modes, it was sought to investigate whether such states may host the Majorana modes [125]. A dimensional reduction from one (characteristic of the edge states) to zero (for the point like Majorana modes) is implicit.

There is then again the possibility of inducing SC in such topologically protected edge and related lower-dimensional states. Such states exhibit ballistic transport and may be probed to yield quantized conductance (Go). As TRS is preserved, the edge states intrinsically manifest extremely large (“essentially infinite” [125]) values of an intrinsic BSO. The zero-energy states related to the Majorana modes may be identified at the intersection of edge states or through the specific interaction of edge states, say with Fe clusters. Such an aspect was probed in [125] where Bi hinge states were placed in proximity of a Nb-based SC to create one-dimensional topological SC systems. As indicated in Sect. 2.​1, the ingredients, related to (i) the breaking of spin symmetry through an internal magnetic field from the Fe clusters, and (ii) the particle–hole symmetry, are both achieved at the interface. Here, 3D Bismuth as a HOTI would be the host of the topologically protected hinge states [126].

The Bi films were synthesized through deposition on a cooled Nb single crystal (110) surface. The one-dimensional hinge modes are manifested in Bi bilayer constituted islands on top of a Bi (111) thin film surface. The bilayer Bi (with trivial gapped surface states but topologically protected gapless hinge states) embodies topologically protected edge states on every other edge of the hexagon in the bilayer, classified as an A edge: Fig. 3.10a, depending on whether the surface atoms are proximate to the vacuum [127].

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