Electronic structure and transport in exotic nanostructures

This thesis explores the physics of nanostructures involving nanowires, quantum dots, superconductors, and topological insulators. These systems serve as excellent platforms for fundamental physics studies and quantum technology applications.The introduction contains information on the band structures of crystalline materials and transport phenomena in quantum dots. It is followed by discussions on nanostructures involving superconductors. One-dimensional topological superconductors and Majorana bound states, as well as two-dimensional topological insulators and relevant material systems, are also presented. The theoretical tools used for modeling the various nanostructures are discussed.The thesis includes six research articles. The first two articles theoretically investigate the possibility of creating high-quality Majorana bound states in a system with two quantum dots coupled via a third quantum dot that is proximitized by a superconductor. The study not only confirms the possibility of creating these states, but also offers a roadmap for their detection, quality assessment, and the demonstration of their nonabelian properties. The third and fourth articles experimentally and theoretically study a parallel-coupled double quantum dot system epitaxially defined in an InAs nanowire. It was found that certain orbital crossings lead to the formation of ring-like states associated with giant g-factors. The same system was studied at higher magnetic fields. The main finding was that, for an increasing magnetic flux through the structure, crossings with ring-like states periodically turn to crossings without ring-like states and vice versa, with a period equal to one flux quantum. The fifth article focused on a similar double quantum dot system coupled to superconducting leads to form a Josephson junction. We found that, control over the hybridization between the quantum dot orbitals can induce a π-0 transition in the current-phase relation. In the sixth article, a core/shell/shell InAs/GaSb nanowire was theoretically studied. The study revealed that the structure exhibits a finite hybridization gap and hosts highly-localized end states,which are only partially protected against disorder

Odd-frequency superconducting pairing in Kitaev-based junctions

We investigate odd-frequency superconducting correlations in normal-superconductor (NS) and short superconductor-normal-superconductor (SNS) junctions with the S region described by the Kitaev model of spinless fermions in one dimension. We demonstrate that, in both the trivial and topological phases, Andreev reflection is responsible for the coexistence of even- and odd-frequency pair amplitudes at interfaces, while normal reflections solely contribute to odd-frequency pairing. At NS interfaces we find that the odd-frequency pair amplitude exhibits large, but finite, values in the topological phase at low frequencies. This enhancement is due to the emergence of a Majorana zero mode at the interface, but notably there is no divergence and a finite odd-frequency pair amplitude also exists outside the topological phase. We also show that the local density of states and local odd-frequency pairing can be characterized solely by Andreev reflections deep in the topological phase. Moreover, in the topological phase of short SNS junctions, we find that both even- and odd-frequency amplitudes capture the emergence of topological Andreev bound states. For a superconducting phase difference $0<\phi<\pi$ the odd-frequency magnitude exhibits a linear frequency ($\sim |\omega|$) dependence at low-frequencies, while at $\phi=\pi$ it develops a resonance peak ($\sim 1/|\omega|$) due to the protected Majorana zero modes.Comment: 12 pages, 7 figures + 7 pages of supplemental material. Published versio

Creating and detecting poor man's Majorana bound states in interacting quantum dots

We propose and theoretically investigate an alternative way to create the poor man's Majorana bound states (MBSs) introduced in Phys. Rev. B 86, 134528 (2012). Our proposal is based on two quantum dots (QDs) with strong electron-electron interactions that couple via a central QD with proximity-induced superconductivity. In the presence of spin-orbit coupling and a magnetic field, gate control of all three QDs allows tuning the system into sweet spots with one MBS localized on each outer dot. We quantify the quality of these MBSs and show how it depends on the Zeeman energy and interaction strength. We also show how nonlocal transport spectroscopy can be used to identify sweet spots with high MBS quality. Our results provide a path for investigating MBS physics in a setting that is free of many of the doubts and uncertainties that plague other platforms.Comment: 10 pages, 8 figure

Band structure and end states in InAs/GaSb core-shell-shell nanowires

Quantum wells in InAs/GaSb heterostructures can be tuned to a topological regime associated with the quantum spin Hall effect, which arises due to an inverted band gap and hybridized electron and hole states. Here, we investigate electron-hole hybridization and the fate of the quantum spin Hall effect in a quasi one-dimensional geometry, realized in a core-shell-shell nanowire with an insulator core and InAs and GaSb shells. We calculate the band structure for an infinitely long nanowire using $\mathbf{k \cdot p}$ theory within the Kane model and the envelope function approximation, then map the result onto a BHZ model which is used to investigate finite-length wires. Clearly, quantum spin Hall edge states cannot appear in the core-shell-shell nanowires which lack one-dimensional edges, but in the inverted band-gap regime we find that the finite-length wires instead host localized states at the wire ends. These end states are not topologically protected, they are four-fold degenerate and split into two Kramers pairs in the presence of potential disorder along the axial direction. However, there is some remnant of the topological protection of the quantum spin Hall edge states in the sense that the end states are fully robust to (time-reversal preserving) angular disorder, as long as the bulk band gap is not closed.Comment: 7 pages, 6 figure

Electrical control of spins and giant g-factors in ring-like coupled quantum dots

Emerging theoretical concepts for quantum technologies have driven a continuous search for structures where a quantum state, such as spin, can be manipulated efficiently. Central to many concepts is the ability to control a system by electric and magnetic fields, relying on strong spin-orbit interaction and a large g-factor. Here, we present a new mechanism for spin and orbital manipulation using small electric and magnetic fields. By hybridizing specific quantum dot states at two points inside InAs nanowires, nearly perfect quantum rings form. Large and highly anisotropic effective g-factors are observed, explained by a strong orbital contribution. Importantly, we find that the orbital and spin-orbital contributions can be efficiently quenched by simply detuning the individual quantum dot levels with an electric field. In this way, we demonstrate not only control of the effective g-factor from 80 to almost 0 for the same charge state, but also electrostatic change of the ground state spin

Probing Majorana localization in minimal Kitaev chains through a quantum dot

Artificial Kitaev chains, formed by quantum dots coupled via superconductors, have emerged as a promising platform for realizing Majorana bound states. Even a minimal Kitaev chain (a quantum dot--superconductor--quantum dot setup) can host Majorana states at discrete sweet spots. However, unambiguously identifying Majorana sweet spots in such a system is still challenging. In this work, we propose an additional dot coupled to one side of the chain as a tool to identify good sweet spots in minimal Kitaev chains. When the two Majorana states in the chain overlap, the extra dot couples to both and thus splits an even--odd ground-state degeneracy when its level is on resonance. In contrast, a ground-state degeneracy will persist for well-separated Majorana states. This difference can be used to identify points in parameter space with spatially separated Majorana states, using tunneling spectroscopy measurements. We perform a systematic analysis of different relevant situations. We show that the additional dot can help distinguishing between Majorana sweet spots and other trivial zero-energy crossings. We also characterize the different conductance patterns, which can serve as a guide for future experiments aiming to study Majorana states in minimal Kitaev chains