Majorana edge modes in Kitaev model on honeycomb lattice

Manisha Thakurathi, K. Sengupta, Diptiman Sen

We study the Majorana modes, both equilibrium and Floquet, which can appear at the edges of the Kitaev model on the honeycomb lattice. We first present the analytical solutions known for the equilibrium Majorana edge modes for both zigzag and armchair edges of a semi-infinite Kitaev model and chart the parameter regimes in which they appear. We then examine how edge modes can be generated if the Kitaev coupling on the bonds perpendicular to the edge is varied periodically in time as periodic $\ensuremath{\delta}$-function kicks. We derive a general condition for the appearance and disappearance of the Floquet edge modes as a function of the drive frequency for a generic $d$-dimensional integrable system. We confirm this general condition for the Kitaev model with a finite width by mapping it to a one-dimensional model. Our numerical and analytical study of this problem shows that Floquet Majorana modes can appear on some edges in the kicked system even when the corresponding equilibrium Hamiltonian has no Majorana mode solutions on those edges. We support our analytical studies by numerics for a finite sized system which show that periodic kicks can generate modes at the edges and the corners of the lattice.

Seung-Hwan Do, Sang‐Youn Park, Junki Yoshitake +8 more

Paolo Molignini, Albert Gasull, R. Chitra +1 more

The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts crossdimensional universality classes: although the static Kitaev model is defined on a two-dimensional (2D) honeycomb lattice, its criticality falls into the universality class of one-dimensional (1D) linear Dirac models. For the periodically driven Kitaev model, in addition to the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states.

Ville Lahtinen, Graham Kells, Angelo C. M. Carollo +3 more

Arkadiusz Bochniak, Błażej Ruba

We briefly summarize the main results from [25] which extend the ones from [17,18]. The bosonization method based on the properties of Clifford algebras is presented, together with the illustrating examples: system of Majorana fermions on honeycomb lattice and its relation to Kitaev's model, and the Hubbard model on rectangular lattices. The role of bundaries together with the presence of Majorana edge modes are discussed.

Ville Lahtinen, Graham Kells, Angelo Carollo +3 more