Strain tuned topology in the Haldane and the modified Haldane models

Abstract

We study the interplay between a uniaxial strain and the topology of the Haldane and the modified Haldane models which, respectively, exhibit chiral and antichiral edge modes. The latter were, recently, predicted by Colomés and Franz (Phys. Rev. Lett. 120, 086603 (2018)) and expected to take place in the transition metal dichalcogenides. Using the continuum approximation and a tight-binding approach, we investigate the effect of the strain on the topological phases and the corresponding edge modes. We show that the strain could induce transitions between topological phases with opposite Chern numbers or tune a topological phase into a trivial one. As a consequence, the dispersions of the chiral and antichiral edge modes are found to be strain dependent. The strain may reverse the direction of propagation of these modes and eventually destroy them. This effect may be used for strain-tunable edge currents in topological insulators and two-dimensional transition metal dichalcogenides.

Modulation of antichiral edge states in zigzag graphene nanoribbons by side potential

“…For example, Hang et al [20] construct an electrical circuit to realize a modi ed Haldane lattice with the antichiral edge states, which is of practical signi cance for theoretical applications. Based on the modi ed Haldane model, researchers propose the unipolar-bipolar lters [22], valley polarization [23], and topological phase transitions under uniaxial strain [24] in a honeycomb lattice. Besides, although the antichiral edge states are bulk gapless, which is robust against disorder [16] like the behavior of the QSH edge states.…”

Observation of antichiral edge states in a circuit lattice

“…Moreover, the bulk spectrum is ungapped, so on a finite rectangular strip the transmission in one direction is edge-dominated whereas transmission in the opposite direction must occur via the bulk [20]. To our knowledge, there is thus far no experimental demonstration of this effect, despite proposals to realize it using strained materials [21], ferromagnetic materials with Dzyaloshinskii-Moriya interactions [22], exciton polaritons [23], gyromagnetic photonic crystals [24], graphene [25,26], and other systems [27].…”

Anti-chiral edge states and hinge states based on the Haldane model

“…However, the antichiral edge states on the opposite edges can propagate in the same direction instead. This interesting phenomenon has also been theoretically investigated in many other physical systems, for example, an exciton-polariton honeycomb lattice with strip geometry [36], a Heisenberg ferromagnet on the honeycomb lattice [37], and a graphene nanoribbon with zigzag edges under a uniform uniaxial strain [38], etc [39][40][41][42]. More importantly, the existence of antichiral edge states based on this modified Haldane model has been experimentally demonstrated in gyromagnetic photonic crystal system [43] and classical circuit lattice [44].…”