Chiral to helical Majorana fermion transition in a $p$-wave superconductor

Abstract

Chiral and helical Majorana edge modes are two archetypal gapless excitations of two-dimensional topological superconductors. They belong to superconductors from two different Altland-Zirnbauer symmetry classes characterized by $\mathbb{Z}$ and ${\mathbb{Z}}_2$ topological invariant respectively. It seems improbable to tune a pair of co-propagating chiral edge modes to counter-propagate without symmetry breaking. Here we show that such a direct topological transition is in fact possible, provided the system possesses an additional symmetry $\mathcal{O}$ which changes the bulk topological invariant to $\mathbb{Z}\oplus \mathbb{Z}$ type. A simple model describing the proximity structure of a Chern insulator and a $p_x$-wave superconductor is proposed and solved analytically to illustrate the transition between two topologically nontrivial phases. The weak pairing phase has two chiral Majorana edge modes, while the strong pairing phase is characterized by $\mathcal{O}$-graded Chern number and hosts a pair of counter-propagating Majorana fermions. The bulk topological invariants and edge theory are worked out in detail. Implications of these results to topological quantum computing based on Majorana fermions are discussed.

5 pages, 2 figures

References in corpus (15)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Topology of crystalline insulators and superconductors
• Quantum degenerate dipolar Fermi gas
• Observation of half-integer thermal Hall conductance
• Topological Quantum Computation Based on Chiral Majorana Fermions
• A Fermi Degenerate Gas of Polar Molecules
• High Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Engineering Superfluidity in Bose-Fermi Mixtures of Ultracold Atoms
• Electrically tunable topological superconductivity and Majorana fermions in two dimensions
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids

Cited by in corpus (5)

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• Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model