Quantum Transport in Topological Mesoscopic Systems

Chakraborty, Subhadeep (2026) Quantum Transport in Topological Mesoscopic Systems. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Subhadeep Chakraborty (20RS001)) 20RS001.pdf - Submitted Version Restricted to Repository staff only Download (9MB)

Abstract

This thesis focuses on quantum transport in topological mesoscopic systems. The edge state of a two-dimensional topological insulator, governed by the one-dimensional Dirac equation, when subjected to a sign-inverted mass domain wall, can host topologically protected bound state at zero energy known as the Jackiw–Rebbi zero mode. We show that applying a smoothly varying, sign-changing in-plane exchange potential leads to the formation of bound states at zero and non-zero energies, each associated with a real-space spin texture whose winding number equals its energy quantum number. These spin textures are electrically manipulable and can be read-off via tunnel magnetoresistance response of a spin-polarized lead, akin to the Datta–Das spin transistor. On the other hand, if the superconducting pair potential plays the role of inverting Dirac mass, Majorana bound state can appear, as is the case for local superconductivity proximitized helical edge. The transport signature of the presence of Majorana bound state is signalled by 2e2 /h zero-bias conductance peak, which often gets smeared due to pronounced backscattering of helical edge state in presence of time-reversal symmetry breaking disorder. Our study shows when a two-dimensional topological insulator is subjected to simultaneous domain walls in the exchange field and spin–orbit coupling, an emergent helical edge state can arise. In the presence of proximity-induced superconductivity, this state can host Majorana bound states that remain exceptionally robust against onsite and magnetic disorder, owing tothe simultaneous orthogonality in spin and pseudospin degrees of freedom. Beyond topology defined in momentum space, there has been a surge of interest in synthetic topology, which offers greater experimental tunability. A multiterminal Josephson junction can act as a synthetic quantum system, where the Andreev bound state (ABS) bands and the continuum of the Bogoliubov–de Gennes (BdG) spectrum exhibit nontrivial topology defined over the independent superconducting phase manifold. We demonstrate a hierarchy of topological phases, in which the continuum, exhibiting monopolar topology with quantized monopole charge ±1, enables phase-fluctuation-insensitive quantized transport reminiscent of a quantum Hall response. In this regime, the ABS bands become flat and exhibit quantized dipole polarization. These ABS bands provide a platform for phase-fluctuation or junction-asymmetry-insensitive Andreev qubit operation, transcending the conventional “sweet spot” to a broader “sweet plateau.” Synthetic superlattices are a versatile platform for engineering robust, tunable zero modes essential for topological quantum information processing. By applying a periodic sign-changing in-plane exchange field to a quantum spin Hall (QSH) insulator, we form a superlattice of Jackiw-Rebbi zero modes. Application of a uniform field controllably hybridizes the zero modes, inducing a hierarchical topological transition that creates fractionalized zero modes localized at the corners of the Quantum spin-Hall insulator. In addition, we show the presence of a robust unpaired boundary mode in a class of one-dimensional tight-binding chains, which are connected to a one-dimensional Su–Schrieffer–Heeger (SSH) chain in the topological phase via a supersymmetric transformation. We propose several quench protocols to realize single-qubit gate operations exploiting these zero modes. Finally, we demonstrate the presence of such modes in a quantum dot array, providing a viable platform for robust qubit operations in two- dimensional architectures, even in the absence of spin–orbit coupling.

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