Line nodes and surface Majorana flat bands in static and kicked p-wave superconducting Harper model

Abstract

We investigate the effect of introducing nearest-neighbor $p$-wave superconducting pairing to both the static and kicked extended Harper model with two periodic phase parameters acting as artificial dimensions to simulate three-dimensional systems. It is found that in both the static model and the kicked model, by varying the $p$-wave pairing order parameter, the system can switch between a fully gapped phase and a gapless phase with point nodes or line nodes. The topological property of both the static and kicked model is revealed by calculating corresponding topological invariants defined in the one-dimensional lattice dimension. Under open boundary conditions along the physical dimension, Majorana flat bands at energy zero (quasienergy zero and $\pi$) emerge in the static (kicked) model at the two-dimensional surface Brillouin zone. For certain values of pairing order parameter, (Floquet) Su-Schrieffer-Heeger-like edge modes appear in the form of arcs connecting different (Floquet) Majorana flat bands. Finally, we find that in the kicked model, it is possible to generate two controllable Floquet Majorana modes, one at quasienergy zero and the other at quasienergy $\pi$, at the same parameter values.

12 pages, 5 figures. Published version, with some changes

References in corpus (19)

• Classification of topological insulators and superconductors in three spatial dimensions
• Photovoltaic Hall effect in graphene
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Topological characterization of periodically-driven quantum systems
• Photo-Induced Topological Phase Transition and a Single Dirac-Cone State in Silicene
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Superconductivity of doped Weyl semimetals: finite-momentum pairing and electronic analogues of the 3He-A phase
• Tunable Line Node Semimetals
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Quantized Adiabatic Transport in Momentum Space
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Floquet Semimetal with Floquet-band Holonomy
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Interband Coherence Induced Correction to Adiabatic Pumping in Periodically Driven Systems

Cited by in corpus (5)

• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Dynamics of a quantum phase transition in the Aubry-André-Harper model with $p$-wave superconductivity
• Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons
• $Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain
• Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons