scholarly journals Characterizations of topological superconductors: Chern numbers, edge states and Majorana zero modes

2017 ◽  
Vol 19 (9) ◽  
pp. 093018 ◽  
Author(s):  
Xiao-Ping Liu ◽  
Yuan Zhou ◽  
Yi-Fei Wang ◽  
Chang-De Gong
Keyword(s):  
Edge States ◽  
Zero Modes ◽  
Topological Superconductors ◽  
Chern Numbers

scholarly journals Topological gaps by twisting

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Matheus I. N. Rosa ◽  
Massimo Ruzzene ◽  
Emil Prodan
Keyword(s):  
Magnetic Field ◽  
Quantum Hall Effect ◽  
Twist Angle ◽  
Quantum Hall ◽  
Topological Phases ◽  
Edge States ◽  
Layered Systems ◽  
Virtual Laboratories ◽  
Higher Dimensional ◽  
Chern Numbers

AbstractTwisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twisted n-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.

scholarly journals Search for non-Abelian Majorana braiding statistics in superconductors

2020 ◽  
Author(s):  
Carlo Beenakker
Keyword(s):  
Quantum Information ◽  
Parameter Space ◽  
Quantum Information Processing ◽  
Fusion Rule ◽  
Real Space ◽  
Edge Mode ◽  
Zero Modes ◽  
Topological Superconductors ◽  
Topological Quantum ◽  
Basic Concepts

This is a tutorial review of methods to braid non-Abelian anyons (Majorana zero-modes) in topological superconductors. That ``Holy Grail'' of topological quantum information processing has not yet been reached in the laboratory, but there now exists a variety of platforms in which one can search for the Majorana braiding statistics. After an introduction to the basic concepts of braiding we discuss how one might be able to braid immobile Majorana zero-modes, bound to the end points of a nanowire, by performing the exchange in parameter space, rather than in real space. We explain how Coulomb interaction can be used to both control and read out the braiding operation, even though Majorana zero-modes are charge neutral. We ask whether the fusion rule might provide for an easier pathway towards the demonstration of non-Abelian statistics. In the final part we discuss an approach to braiding in real space, rather than parameter space, using vortices injected into a chiral Majorana edge mode as ``flying qubits''.

scholarly journals Zero modes and edge states of the honeycomb lattice

2007 ◽  
Vol 76 (20) ◽  
Author(s):  
Mahito Kohmoto ◽  
Yasumasa Hasegawa
Keyword(s):  
Honeycomb Lattice ◽  
Edge States ◽  
Zero Modes

scholarly journals Suppression of2πphase slip due to hidden zero modes in one-dimensional topological superconductors

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
David Pekker ◽  
Chang-Yu Hou ◽  
Doron L. Bergman ◽  
Sam Goldberg ◽  
İnanç Adagideli ◽  
...  
Keyword(s):  
One Dimensional ◽  
Zero Modes ◽  
Topological Superconductors

scholarly journals Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field

2009 ◽  
Vol 80 (12) ◽  
Author(s):  
Kenta Esaki ◽  
Masatoshi Sato ◽  
Mahito Kohmoto ◽  
Bertrand I. Halperin
Keyword(s):  
Magnetic Field ◽  
Energy Gap ◽  
Honeycomb Lattice ◽  
Edge States ◽  
Zero Modes

scholarly journals ON EXOTIC SPHERE FIBRATIONS, TOPOLOGICAL PHASES, AND EDGE STATES IN PHYSICAL SYSTEMS

2013 ◽  
Vol 27 (19) ◽  
pp. 1350107 ◽  
Author(s):  
HAI LIN ◽  
SHING-TUNG YAU
Keyword(s):  
Topological Insulators ◽  
Condensed Matter ◽  
Topological Phases ◽  
Edge States ◽  
Geometric Phases ◽  
Magnetoelectric Effects ◽  
Physical Systems ◽  
Chern Numbers ◽  
Weyl Semimetals ◽  
Exotic Sphere

We suggest that exotic sphere fibrations can be mapped to band topologies in condensed matter systems. These fibrations can correspond to geometric phases of two double bands or state vector bases with second Chern numbers m+n and -n, respectively. They can be related to topological insulators, magnetoelectric effects, and photonic crystals with special edge states. We also consider time-reversal symmetry breaking perturbations of topological insulator, and heterostructures of topological insulators with normal insulators and with superconductors. We consider periodic TI/NI/TI/NI′ heterostructures, and periodic TI/SC/TI/SC′ heterostructures. They also give rise to models of Weyl semimetals which have thermal and electrical transports.

scholarly journals Topological Edge States of a Majorana BBH Model

2021 ◽  
Vol 6 (2) ◽  
pp. 15
Author(s):  
Alfonso Maiellaro ◽  
Roberta Citro
Keyword(s):  
2D Materials ◽  
Finite Size ◽  
Majorana Fermions ◽  
Topological Phase ◽  
Two Dimensional ◽  
Edge States ◽  
Finite Size Scaling ◽  
Topological Properties ◽  
Berry Curvature ◽  
Topological Superconductors

We investigate a Majorana Benalcazar–Bernevig–Hughes (BBH) model showing the emergence of topological corner states. The model, consisting of a two-dimensional Su–Schrieffer–Heeger (SSH) system of Majorana fermions with π flux, exhibits a non-trivial topological phase in the absence of Berry curvature, while the Berry connection leads to a non-trivial topology. Indeed, the system belongs to the class of second-order topological superconductors (HOTSC2), exhibiting corner Majorana states protected by C4 symmetry and reflection symmetries. By calculating the 2D Zak phase, we derive the topological phase diagram of the system and demonstrate the bulk-edge correspondence. Finally, we analyze the finite size scaling behavior of the topological properties. Our results can serve to design new 2D materials with non-zero Zak phase and robust edge states.

scholarly journals Tunable zero modes and quantum interferences in flat-band topological insulators

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 591
Author(s):  
Juan Zurita ◽  
Charles Creffield ◽  
Gloria Platero
Keyword(s):  
Topological Insulators ◽  
Flat Band ◽  
Topological Phase ◽  
Edge States ◽  
One Dimensional ◽  
Zero Modes ◽  
Symmetry Classes ◽  
Boundary Correspondence ◽  
High Degree ◽  
Aharonov Bohm

We investigate the interplay between Aharonov-Bohm (AB) caging and topological protection in a family of quasi-one-dimensional topological insulators, which we term CSSH ladders. Hybrids of the Creutz ladder and the SSH chain, they present a regime with completely flat bands, and a rich topological phase diagram, with several kinds of protected zero modes. These are reminiscent of the Creutz ladder edge states in some cases, and of the SSH chain edge states in others. Furthermore, their high degree of tunability, and the fact that they remain topologically protected even in small systems in the rungless case, due to AB caging, make them suitable for quantum information purposes. One of the ladders can belong to the BDI, AIII and D symmetry classes depending on its parameters, the latter being unusual in a non-superconducting model. Two of the models can also harbor topological end modes which do not follow the usual bulk-boundary correspondence, and are instead related to a Chern number. Finally, we propose some experimental setups to implement the CSSH ladders with current technology, focusing on the photonic lattice case.

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