This book reviews evidence for the existence of information storing states present in specific materials systems called Topological Materials. It discusses how quantum computation, a possible technology for the future, demands unique paradigms where the information storing states are just not disturbed by classical forces. They are protected from environmental disturbance, suggesting that whatever information is stored in such states would could be safe forever. The authors explain how the topological aspect arises from the configuration or the shape of energy space. He further explains that the existence of related topological states has not been conclusively established in spite of significant experimental effort over the past decade. And The book as such illustrates the necessity for such investigations as well as application of the topological states for new computational technologies. The scope of coverage includes all the necessary mathematical and physics preliminaries (starting at the undergraduate level) enabling researchers to quickly understand the state of the art literature.
Author(s): Prabhakar Bandaru, Shreyam Natani
Publisher: Springer
Year: 2022
Language: English
Pages: 115
City: Cham
Contents
About the Authors
Chapter 1: Introduction
1.1 Seeking Majorana Particles and Modes in Superconducting Materials Systems
1.2 Mathematical Description of the Majorana Fermion Modes
1.3 Majorana Modes for Quantum Information Science (QIS)
1.4 Experimental Realization of the Majorana Modes in Superconductor Materials
1.5 The Environmental Robustness of Majorana Modes
Chapter 2: Practical Materials Systems, and Related Criteria, for Hosting the Majorana Modes
2.1 Topological Insulators (TI)—With Induced Topological Superconductivity (TSC)
2.2 The Spin–Orbit (S–O) Interactions in a Nanowire (NW)
2.3 Manifestation of Topological Superconductivity in One-Dimensional Systems
2.4 Probing Majorana Modes: Issues Related to Finite System Size and the Possibility of Alternative Zero-Energy Modes
2.5 Mid-Gap States of the Andreev, Yu–Shiba–Rusinov, and the Coulomb Kind
Chapter 3: Experimental Investigations of Majorana Modes and Majorana-Bound States (MBS)
3.1 Majorana Modes in One-Dimensional Nanowires (NWs)
3.1.1 Tunnel Barriers to Channel Electrons from a Contact into an MBS State in a NW
3.1.2 Conductance Quantization to 2e2/h (= Go) in NWs as a Metric for an MBS
3.2 Identifying Majorana States Through the Josephson Effects
3.2.1 The Phase Variation for Deducing MBS in a Topological Superconductor
3.2.2 Response of a Josephson Junction to AC Radiation (External): Missing Shapiro Steps
3.2.3 Response of a Josephson Junction to AC Radiation (Internal): Single Electron Conduction
3.3 Majorana Modes in Ferromagnetic Atomic Chains
3.3.1 Possible Artefacts in the Measurements
3.3.2 Possible Contributions of Magnetic Impurities and Their Resolution
3.3.3 Majorana Modes at Topological Insulators (TI)–Related Interfaces
3.4 Majorana Modes in Quantum Spin Hall/Quantum Anomalous Hall Insulators
3.4.1 The Quantum Anomalous Hall Effect (QAHE) and Chiral Majorana Modes
3.4.2 Possible Manifestation of Chiral Majorana Modes Through Experiments on Coupled SC–Quantum Anomalous Hall Insulator (QAHI) Systems
3.4.3 The “Absence of Evidence” of the Chiral Majorana Modes in QAHI–SC Hybrids
3.5 Majorana Modes in the Vortices of Superconductors
3.5.1 Probing the Possibility of Majorana Modes in the Vortices of Se-Based SCs
3.5.2 Obtaining a Mode with a Zero-Bias Peak (ZBP) Conductance ~ Go
3.5.3 The Influence of Defects in the Vortex Cores
Chapter 4: Issues Related to Determination of Majorana Fermion Related Modes
4.1 Sub-Gap States with Finite Zero-Bias Conductance, Confused with Majorana Modes
4.2 The Influence of Disorder on Conclusively Determining the Majorana States
4.3 The Influence of a Small Device Size in Precluding Proper Majorana Mode Localization and Identification
Chapter 5: Suggestions for Future Experiments
5.1 Identification of Suitable Superconductors for Hosting Unique TS
5.2 Probing the Topological States Through Alternative STM Modalities
5.3 Implementation of Electrode-Based Schemes for Modulation and Readout of the Topological States
5.4 Braiding Schemes Would Demonstrate the Utility of TS for Quantum Information
Chapter 6: Outlook
References
Index
