Zero modes in a system of Aharonov–Bohm solenoids on the Lobachevsky plane

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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Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode

National Science Review ◽

10.1093/nsr/nwz189 ◽

2019 ◽

Vol 7 (3) ◽

pp. 572-578 ◽

Cited By ~ 2

Author(s):

Yijia Wu ◽

Haiwen Liu ◽

Jie Liu ◽

Hua Jiang ◽

X C Xie

Keyword(s):

Zero Mode ◽

Fusion Rule ◽

Quantum Spin ◽

Zero Energy ◽

Double Frequency ◽

Zero Modes ◽

Charge Fractionalization ◽

Bohm Effect ◽

Aharonov Bohm ◽

Special Case

Abstract Ever since its first proposal in 1976, Jackiw-Rebbi zero-mode has been drawing extensive attention for its charming properties including charge fractionalization, topologically protected zero-energy and possible non-Abelian statistics. We investigate these properties through the Jackiw-Rebbi zero-modes in quantum spin Hall insulators. Though charge fractionalization is not manifested, Jackiw-Rebbi zero-mode's zero-energy nature leads to a double-frequency Aharonov-Bohm effect, implying that it can be viewed as a special case of Majorana zero-mode without particle-hole symmetry. Such relation is strengthened for Jackiw-Rebbi zero-modes also exhibiting non-Abelian properties in the absence of superconductivity. Furthermore, in the condition that the degeneracy of Jackiw-Rebbi zero-modes is lifted, we demonstrate a novel non-Abelian braiding with continuously tunable fusion rule, which is a generalization of Majorana zero-modes’ braiding properties.

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ZERO MODES IN A SYSTEM OF AHARONOV–BOHM FLUXES

Reviews in Mathematical Physics ◽

10.1142/s0129055x04002199 ◽

2004 ◽

Vol 16 (07) ◽

pp. 851-907 ◽

Cited By ~ 8

Author(s):

V. A. GEYLER ◽

P. ŠŤOVÍČEK

Keyword(s):

Periodic Structures ◽

Periodic Systems ◽

Two Dimensional ◽

Zero Modes ◽

Aharonov Bohm

We study zero modes of two-dimensional Pauli operators with Aharonov–Bohm fluxes in the case when the solenoids are arranged in periodic structures like chains or lattices. We also consider perturbations to such periodic systems which may be infinite and irregular but they are always supposed to be sufficiently scarce.

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Zero modes in a periodic system of Aharonov-Bohm solenoids

JETP Letters ◽

10.1134/1.1485266 ◽

2002 ◽

Vol 75 (7) ◽

pp. 354-356 ◽

Cited By ~ 12

Author(s):

V. A. Geyler ◽

E. N. Grishanov

Keyword(s):

Periodic System ◽

Zero Modes ◽

Aharonov Bohm

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FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND

Modern Physics Letters A ◽

10.1142/s0217732305018037 ◽

2005 ◽

Vol 20 (39) ◽

pp. 3045-3053 ◽

Cited By ~ 29

Author(s):

YONGQIANG WANG ◽

TIEYAN SI ◽

YUXIAO LIU ◽

YISHI DUAN

Keyword(s):

Phase Shift ◽

Zero Mode ◽

Two Dimensions ◽

Two Dimensional ◽

Yang Mills ◽

Zero Modes ◽

Extra Space ◽

Bohm Effect ◽

Aharonov Bohm ◽

Unified Description

We study fermionic zero modes in the background of self-dual vortex on a two-dimensional non-compact extra space in 5+1 dimensions. In the Abelian Higgs model, we present a unified description of the topological and non-topological self-dual vortex on the extra two dimensions. Based on it, we study the localization of bulk fermions on a brane with the inclusion of Yang–Mills and gravity backgrounds in six dimensions. Through two simple cases, it is shown that the vortex background contributes a phase shift to the fermionic zero mode, this phase is actually origin from the Aharonov–Bohm effect.

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Phenomena and devices at the quantum scale and the mesoscale

10.1093/oso/9780198759874.003.0003 ◽

2017 ◽

Author(s):

Sandip Tiwari

Keyword(s):

Coulomb Blockade ◽

Secure Communication ◽

Quantum Hall ◽

Nanoscale Device ◽

Self Energy ◽

Stability Diagrams ◽

Charge Stability ◽

Bohm Effect ◽

Aharonov Bohm ◽

Non Locality

Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.

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