Parafermion chain with2π/kFloquet edge modes

Abstract

We study parafermion chains with Z k symmetry subject to a periodic binary drive. We focus on the case k = 3. We find that the chains support different Floquet edge modes at nontrivial quasienergies, distinct from those for the static system. We map out the corresponding phase diagram by a combination of analytics and numerics, and provide the location of 2π/3 modes in parameter space. We also show that the modes are robust to weak disorder. While the previously studied Z2-invariant Majorana systems posesses a transparent weakly interacting case where the existence of a π-Majorana mode is manifest, our intrinsically strongly interacting generalization demonstrates that the existence of such a limit is not necessary.

Almost strong ( 0,π ) edge modes in clean interacting one-dimensional Floquet systems

“…In Ref. 14 it was shown that edge modes lead to approximate degeneracies in the Floquet spectrum of a particular clean, interacting system. However the implications of this for the dynamics of the modes and their robustness to heating was not investigated.…”

Topological Phases of Parafermions: A Model with Exactly Solvable Ground States

“…After the experimental clarification that two zero-energy Majorana modes can be localized at the edges of a one-dimensional fermionic wire [6,7], the possibility of localizing parafermionic modes, and letting them interact, is currently under deep investigation. These excitations cannot appear in strictly one-dimensional spinless fermionic systems [8,9], but may emerge at the edge of a two-dimensional fractional topological insulator coupled to alternating ferromagnetic and superconducting materials [5,[10][11][12][13][14][15], as well as in other nanostructures or models [16][17][18][19][20][21][22][23][24].In these setups, one-dimensional chains of interacting parafermions arise, which, in certain circumstances, display TO and edge Z N parafermionic modes [5,[25][26][27][28][29][30][31][32][33][34]. Such edge modes are called strong when they commute with the Hamiltonian [35] and thereby generate a N -fold degeneracy in the entire spectrum, and weak when the commutation property and associated degeneracy are restricted to the ground state manifold.…”

“…In these setups, one-dimensional chains of interacting parafermions arise, which, in certain circumstances, display TO and edge Z N parafermionic modes [5,[25][26][27][28][29][30][31][32][33][34]. Such edge modes are called strong when they commute with the Hamiltonian [35] and thereby generate a N -fold degeneracy in the entire spectrum, and weak when the commutation property and associated degeneracy are restricted to the ground state manifold.…”

Emergent Weyl nodes and Fermi arcs in a Floquet Weyl semimetal

“…Recently, time periodic modulations of topologically trivial systems, often realized via light-matter interaction, have emerged as an interesting way of obtaining topological phases, often richer than their static counterparts [33][34][35][36][37][38][39][40][41][42][43][44][45] and effects of interaction and disorder have also been explored [46][47][48][49][50][51]. Such protocols have also been complemented with their experimental realizations.…”