Exotic Topological Types of Majorana Zero-modes and Their Universal Quantum Manipulation

Abstract

From our general index theorem that characterises faithfully the boundary-bulk correspondence of topological superconductors and insulators, we reveal rigorously that four topologically distinct types of Majorana zero-modes can emerge at the ends of superconducting wires with various symmetry classes. More intriguingly, we establish three exotic one-dimensional models that have different types of topological charge of Majorana zero-modes, and disclose exactly the corresponding topological properties, which are respectively different from those of the Kitaev model because their topological essences (i.e., the types of topological charge) are distinct. Moreover, we also address their application in universal quantum manipulation, which is very promising for realising universal topological quantum computation.

The text is refined, with new analyses and results on the three 1D models being added; 7 pages

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Anyonic interferometry without anyons: How a flux qubit can read out a topological qubit
• Inducing time reversal invariant topological superconductivity and fermion parity pumping in quantum wires
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• Majorana-Like Modes of Light in a One-Dimensional Array of Nonlinear Cavities
• Correlated spin currents generated by resonant crossed Andreev reflections in topological superconductors
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors

Cited by in corpus (19)

• Unified theory of PT and CP invariant topological metals and nodal superconductors
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice
• Universality classes of topological phase transitions with higher-order band crossing
• Universal topological marker
• Disordered Weyl semimetals and their topological family
• Unification of topological invariants in Dirac models
• Novel ${\mathbb{Z}}_2$-topological metals and semimetals
• Robust interface between flying and topological qubits
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Topological invariants for phase transition points of one-dimensional ${\mathbb{Z}}_2$ topological systems
• Topology of critical chiral phases: multiband insulators and superconductors
• Topological photonics on superconducting quantum circuits with parametric couplings
• Exotic Haldane Superfluid Phase of Soft-Core Bosons in Optical Lattices
• Charge-impurity-induced Majorana fermions in topological superconductors
• General response theory of topologically stable Fermi points and its implications for disordered cases
• Quantum simulation of topological Majorana bound states and their universal quantum operations using charge-qubit arrays
• Realizing universal quantum gates with topological bases in quantum-simulated superconducting chains
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry