Topological States for New Modes of Information Storage and Transfer : A Survey of the Status of the Discovery of the Majorana Modes in the Solid State

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. Contents 5 About the Authors 8 Chapter 1: Introduction 9 1.1 Seeking Majorana Particles and Modes in Superconducting Materials Systems 15 1.2 Mathematical Description of the Majorana Fermion Modes 16 1.3 Majorana Modes for Quantum Information Science (QIS) 18 1.4 Experimental Realization of the Majorana Modes in Superconductor Materials 20 1.5 The Environmental Robustness of Majorana Modes 21 Chapter 2: Practical Materials Systems, and Related Criteria, for Hosting the Majorana Modes 24 2.1 Topological Insulators (TI)—With Induced Topological Superconductivity (TSC) 25 2.2 The Spin–Orbit (S–O) Interactions in a Nanowire (NW) 25 2.3 Manifestation of Topological Superconductivity in One-Dimensional Systems 26 2.4 Probing Majorana Modes: Issues Related to Finite System Size and the Possibility of Alternative Zero-Energy Modes 29 2.5 Mid-Gap States of the Andreev, Yu–Shiba–Rusinov, and the Coulomb Kind 32 Chapter 3: Experimental Investigations of Majorana Modes and Majorana-Bound States (MBS) 34 3.1 Majorana Modes in One-Dimensional Nanowires (NWs) 35 3.1.1 Tunnel Barriers to Channel Electrons from a Contact into an MBS State in a NW 36 3.1.2 Conductance Quantization to 2e2/h (= Go) in NWs as a Metric for an MBS 36 3.2 Identifying Majorana States Through the Josephson Effects 45 3.2.1 The Phase Variation for Deducing MBS in a Topological Superconductor 48 3.2.2 Response of a Josephson Junction to AC Radiation (External): Missing Shapiro Steps 53 3.2.3 Response of a Josephson Junction to AC Radiation (Internal): Single Electron Conduction 56 3.3 Majorana Modes in Ferromagnetic Atomic Chains 59 3.3.1 Possible Artefacts in the Measurements 62 3.3.2 Possible Contributions of Magnetic Impurities and Their Resolution 63 3.3.3 Majorana Modes at Topological Insulators (TI)–Related Interfaces 66 3.4 Majorana Modes in Quantum Spin Hall/Quantum Anomalous Hall Insulators 71 3.4.1 The Quantum Anomalous Hall Effect (QAHE) and Chiral Majorana Modes 72 3.4.2 Possible Manifestation of Chiral Majorana Modes Through Experiments on Coupled SC–Quantum Anomalous Hall Insulator (QAHI) Systems 73 3.4.3 The “Absence of Evidence” of the Chiral Majorana Modes in QAHI–SC Hybrids 76 3.5 Majorana Modes in the Vortices of Superconductors 77 3.5.1 Probing the Possibility of Majorana Modes in the Vortices of Se-Based SCs 80 3.5.2 Obtaining a Mode with a Zero-Bias Peak (ZBP) Conductance ~ Go 84 3.5.3 The Influence of Defects in the Vortex Cores 86 Chapter 4: Issues Related to Determination of Majorana Fermion Related Modes 91 4.1 Sub-Gap States with Finite Zero-Bias Conductance, Confused with Majorana Modes 93 4.2 The Influence of Disorder on Conclusively Determining the Majorana States 94 4.3 The Influence of a Small Device Size in Precluding Proper Majorana Mode Localization and Identification 95 Chapter 5: Suggestions for Future Experiments 96 5.1 Identification of Suitable Superconductors for Hosting Unique TS 96 5.2 Probing the Topological States Through Alternative STM Modalities 97 5.3 Implementation of Electrode-Based Schemes for Modulation and Readout of the Topological States 98 5.4 Braiding Schemes Would Demonstrate the Utility of TS for Quantum Information 100 Chapter 6: Outlook 103 References 105 Index 114 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 author explains 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.