Abstract
We have designed honeycomb lattices for microwave photons with a frequency imbalance between the two sites in the unit cell. This imbalance is the equivalent of a mass term that breaks the lattice inversion symmetry. At the interface between two lattices with opposite imbalance, we observe topological valley edge states. By imaging the spatial dependence of the modes along the interface, we obtain their dispersion relation that we compare to the predictions of an ab initio tight-binding model describing our microwave photonic lattices.
Highlights
Even though static lattices for spinless particles that do not break time reversal symmetry have band structures that only contain bands with zero Chern number, topological effects can still be observed in such systems, with topological valley hall edge (TVHE) states being a prominent example [1,2,3]
In a honeycomb lattice with an on-site energy imbalance μ between the nonequivalents A and B sites in the unit cell, the inversion symmetry is broken and a gap opens at the Dirac points, giving rise to an insulator [4, 5]
The states are spatially localized along the boundary and their direction of propagation is correlated to the valley index, in a way similar to the quantum spin Hall effect, where the direction of propagation is correlated to the spin [9]
Summary
Even though static lattices for spinless particles that do not break time reversal symmetry have band structures that only contain bands with zero Chern number, topological effects can still be observed in such systems, with topological valley hall edge (TVHE) states being a prominent example [1,2,3]. We have designed two samples with different boundaries, zigzag and armchair, between two lattices with an imbalance μ, whose absolute value is equal to half the hopping amplitude between neighbouring sites This results in the apparition of well localized TVHE states at the boundary that we image using a laser scanning technique [21]. This allows us to reconstruct the dispersion relation of the states and to show that it is approximately linear, with a slope which is close to the Fermi velocity, independently of the type of boundary. The model parameters are obtained from an ab initio model of the lattice and its predictions are in good agreement with our experimental data
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
