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Topological Materials in Low Dimensions

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A special issue of Nanomaterials (ISSN 2079-4991). This special issue belongs to the section "Synthesis, Interfaces and Nanostructures".

Deadline for manuscript submissions: closed (15 November 2023) | Viewed by 12593

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Prof. Dr. Detlev Grützmacher

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Guest Editor

Forschungszentrum Jülich (FZJ), Peter Grünberg Institute (PGI-6) and JARA-FIT, 52425 Jülich, Germany
Interests: semiconductor physics; nanoelectronics; nanotechnology

Special Issue Information

Dear Colleagues,

Topological materials possess exciting properties for fundamental research and functionalization in quantum computing and spintronics. Topological materials have particular topological arrangements in the geometry of their electronic band structures, resulting in robust surface states and unconventional electromagnetic activity. Following their experimental verification in 2007, topological insulators have rendered a new and fascinating class of materials, opening up an internationally flourishing research field. The properties of topological materials indicate the existence of Majorana, Weyl and Dirac fermions. Consequently, intense research has been devoted to developing codes to compute the geometry of electronic band structures, in order to predict future topological materials and optimize them in terms of the robustness of their topological phenomena. This search has led to the potential identification of a vast amount of topological materials.

To functionalize topological materials for quantum computing, they must be combined with superconductors and magnetic semiconductors in hybrid nanostructures. This is a challenging task since the materials and interfaces between them must be realized in a controlled and clean way. Topological quantum computing is a young research field with many open questions regarding experiments and theory; therefore, it is still at an exploratory stage. The promise of fault-tolerant topological quantum computing has yet to be unraveled. Here, an overarching approach to conceptually novel theoretical methodology and advanced experimental capabilities for the most promising topological materials is required. Networks of Quasi-1D nanowires of topological materials, in proximity to superconductive islands, are predicted to host non-Abelian Majorana modes at the ends and crossing points of the networks. The braiding of these elusive modes, by exchanging the position of Majorana modes in a 2D plane, resembles topologically protected quantum operations in the Majorana platform. Recent proposals for using circuit quantum electrodynamics (cQED) to detect topological superconductivity motivates the exploration of novel topological materials in such circuits.

This Special Issue will present comprehensive research outlining the latest advances in the theory and experimental verification of the fascinating physics of nanostructures assembled from topological materials. This Special Issue will also focus on the fabrication and applications of nanostructures to unravel the potential use of topological materials in quantum devices.

Prof. Dr. Detlev Grützmacher
Guest Editor

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Keywords

topological materials
topological insulators
quantum computing
spintronics
electronic band structures
superconductors
magnetic semiconductors
quantum devices

Published Papers (7 papers)

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Research

Jump to: Review

23 pages, 9294 KiB

Open AccessEditor’s ChoiceArticle

Phase-Selective Epitaxy of Trigonal and Orthorhombic Bismuth Thin Films on Si (111)

by Abdur Rehman Jalil, Xiao Hou, Peter Schüffelgen, Jin Hee Bae, Elmar Neumann, Gregor Mussler, Lukasz Plucinski and Detlev Grützmacher

Nanomaterials 2023, 13(14), 2143; https://doi.org/10.3390/nano13142143 - 24 Jul 2023

Viewed by 1300

Abstract

Over the past three decades, the growth of Bi thin films has been extensively explored due to their potential applications in various fields such as thermoelectrics, ferroelectrics, and recently for topological and neuromorphic applications, too. Despite significant research efforts in these areas, achieving reliable and controllable growth of high-quality Bi thin-film allotropes has remained a challenge. Previous studies have reported the growth of trigonal and orthorhombic phases on various substrates yielding low-quality epilayers characterized by surface morphology. In this study, we present a systematic growth investigation, enabling the high-quality growth of Bi epilayers on Bi-terminated Si (111) 1 × 1 surfaces using molecular beam epitaxy. Our work yields a phase map that demonstrates the realization of trigonal, orthorhombic, and pseudocubic thin-film allotropes of Bi. In-depth characterization through X-ray diffraction (XRD) techniques and scanning transmission electron microscopy (STEM) analysis provides a comprehensive understanding of phase segregation, phase stability, phase transformation, and phase-dependent thickness limitations in various Bi thin-film allotropes. Our study provides recipes for the realization of high-quality Bi thin films with desired phases, offering opportunities for the scalable refinement of Bi into quantum and neuromorphic devices and for revisiting technological proposals for this versatile material platform from the past 30 years. Full article

(This article belongs to the Special Issue Topological Materials in Low Dimensions)

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15 pages, 2115 KiB

Open AccessArticle

Robust and Fragile Majorana Bound States in Proximitized Topological Insulator Nanoribbons

by Dennis Heffels, Declan Burke, Malcolm R. Connolly, Peter Schüffelgen, Detlev Grützmacher and Kristof Moors

Nanomaterials 2023, 13(4), 723; https://doi.org/10.3390/nano13040723 - 14 Feb 2023

Cited by 3 | Viewed by 1754

Abstract

Topological insulator (TI) nanoribbons with proximity-induced superconductivity are a promising platform for Majorana bound states (MBSs). In this work, we consider a detailed modeling approach for a TI nanoribbon in contact with a superconductor via its top surface, which induces a superconducting gap in its surface-state spectrum. The system displays a rich phase diagram with different numbers of end-localized MBSs as a function of chemical potential and magnetic flux piercing the cross section of the ribbon. These MBSs can be robust or fragile upon consideration of electrostatic disorder. We simulate a tunneling spectroscopy setup to probe the different topological phases of top-proximitized TI nanoribbons. Our simulation results indicate that a top-proximitized TI nanoribbon is ideally suited for realizing fully gapped topological superconductivity, in particular when the Fermi level is pinned near the Dirac point. In this regime, the setup yields a single pair of MBSs, well separated at opposite ends of the proximitized ribbon, which gives rise to a robust quantized zero-bias conductance peak. Full article

(This article belongs to the Special Issue Topological Materials in Low Dimensions)

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11 pages, 659 KiB

Open AccessArticle

Effects of the Spatial Extension of the Edge Channels on the Interference Pattern of a Helical Josephson Junction

by Lucia Vigliotti, Alessio Calzona, Niccolò Traverso Ziani, F. Sebastian Bergeret, Maura Sassetti and Björn Trauzettel

Nanomaterials 2023, 13(3), 569; https://doi.org/10.3390/nano13030569 - 31 Jan 2023

Cited by 2 | Viewed by 1505

Abstract

Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either [...] Read more.

ϕ_{0}

(where

ϕ_{0} = h / 2 e

) as a fundamental period. If CPs’ splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches

2 ϕ_{0}

. Full article

(This article belongs to the Special Issue Topological Materials in Low Dimensions)

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16 pages, 5381 KiB

Open AccessArticle

Selective Area Epitaxy of Quasi-1-Dimensional Topological Nanostructures and Networks

by Abdur Rehman Jalil, Peter Schüffelgen, Helen Valencia, Michael Schleenvoigt, Christoph Ringkamp, Gregor Mussler, Martina Luysberg, Joachim Mayer and Detlev Grützmacher

Nanomaterials 2023, 13(2), 354; https://doi.org/10.3390/nano13020354 - 15 Jan 2023

Cited by 6 | Viewed by 2015

Abstract

Quasi-one-dimensional (1D) topological insulators hold the potential of forming the basis of novel devices in spintronics and quantum computing. While exposure to ambient conditions and conventional fabrication processes are an obstacle to their technological integration, ultra-high vacuum lithography techniques, such as selective area epitaxy (SAE), provide all the necessary ingredients for their refinement into scalable device architectures. In this work, high-quality SAE of quasi-1D topological insulators on templated Si substrates is demonstrated. After identifying the narrow temperature window for selectivity, the flexibility and scalability of this approach is revealed. Compared to planar growth of macroscopic thin films, selectively grown regions are observed to experience enhanced growth rates in the nanostructured templates. Based on these results, a growth model is deduced, which relates device geometry to effective growth rates. After validating the model experimentally for various three-dimensional topological insulators (3D TIs), the crystal quality of selectively grown nanostructures is optimized by tuning the effective growth rates to 5 nm/h. The high quality of selectively grown nanostructures is confirmed through detailed structural characterization via atomically resolved scanning transmission electron microscopy (STEM). Full article

(This article belongs to the Special Issue Topological Materials in Low Dimensions)

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12 pages, 9453 KiB

Open AccessEditor’s ChoiceArticle

Supercurrent in Bi₄Te₃ Topological Material-Based Three-Terminal Junctions

by Jonas Kölzer, Abdur Rehman Jalil, Daniel Rosenbach, Lisa Arndt, Gregor Mussler, Peter Schüffelgen, Detlev Grützmacher, Hans Lüth and Thomas Schäpers

Nanomaterials 2023, 13(2), 293; https://doi.org/10.3390/nano13020293 - 10 Jan 2023

Cited by 3 | Viewed by 1930

Abstract

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi

_{4}

_{3}

and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas [...] Read more.

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi

_{4}

_{3}

and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent, including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the device behaves similar to prior experiments with single Josephson junctions comprising topological insulators’ weak links. Irradiating radio frequencies to the junction, we find a spectrum of integer Shapiro steps and an additional fractional step, which is interpreted with a skewed current–phase relationship. In a perpendicular magnetic field, we observe Fraunhofer-like interference patterns in the switching currents. Full article

(This article belongs to the Special Issue Topological Materials in Low Dimensions)

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11 pages, 4680 KiB

Open AccessArticle

Edge States and Strain-Driven Topological Phase Transitions in Quantum Dots in Topological Insulators

by Benjamin Puzantian, Yasser Saleem, Marek Korkusinski and Pawel Hawrylak

Nanomaterials 2022, 12(23), 4283; https://doi.org/10.3390/nano12234283 - 01 Dec 2022

Cited by 1 | Viewed by 1404

Abstract

We present here a theory of the electronic properties of quasi two-dimensional quantum dots made of topological insulators. The topological insulator is described by either eight band

\vec{k} \cdot \vec{p}

Hamiltonian or by a four-band

\vec{k} \cdot \vec{p}

Bernevig–Hughes–Zhang [...] Read more.

We present here a theory of the electronic properties of quasi two-dimensional quantum dots made of topological insulators. The topological insulator is described by either eight band

\vec{k} \cdot \vec{p}

Hamiltonian or by a four-band

\vec{k} \cdot \vec{p}

Bernevig–Hughes–Zhang (BHZ) Hamiltonian. The trivial versus topological properties of the BHZ Hamiltonian are characterized by the different topologies that arise when mapping the in-plane wavevectors through the BHZ Hamiltonian onto a Bloch sphere. In the topologically nontrivial case, edge states are formed in the disc and square geometries of the quantum dot. We account for the effects of compressive strain in topological insulator quantum dots by means of the Bir–Pikus Hamiltonian. Tuning strain allows topological phase transitions between topological and trivial phases, which results in the vanishing of edge states from the energy gap. This may enable the design of a quantum strain sensor based on strain-driven transitions in HgTe topological insulator square quantum dots. Full article

(This article belongs to the Special Issue Topological Materials in Low Dimensions)

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Review

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18 pages, 3665 KiB

Open AccessReview

Manipulating Topological Phases in Magnetic Topological Insulators

by Gang Qiu, Hung-Yu Yang, Su Kong Chong, Yang Cheng, Lixuan Tai and Kang L. Wang

Nanomaterials 2023, 13(19), 2655; https://doi.org/10.3390/nano13192655 - 27 Sep 2023

Viewed by 1800

Abstract

Magnetic topological insulators (MTIs) are a group of materials that feature topological band structures with concurrent magnetism, which can offer new opportunities for technological advancements in various applications, such as spintronics and quantum computing. The combination of topology and magnetism introduces a rich spectrum of topological phases in MTIs, which can be controllably manipulated by tuning material parameters such as doping profiles, interfacial proximity effect, or external conditions such as pressure and electric field. In this paper, we first review the mainstream MTI material platforms where the quantum anomalous Hall effect can be achieved, along with other exotic topological phases in MTIs. We then focus on highlighting recent developments in modulating topological properties in MTI with finite-size limit, pressure, electric field, and magnetic proximity effect. The manipulation of topological phases in MTIs provides an exciting avenue for advancing both fundamental research and practical applications. As this field continues to develop, further investigations into the interplay between topology and magnetism in MTIs will undoubtedly pave the way for innovative breakthroughs in the fundamental understanding of topological physics as well as practical applications. Full article

(This article belongs to the Special Issue Topological Materials in Low Dimensions)

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