Topological router induced via long-range hopping in a Su-Schrieffer-Heeger chain

We show how to implement the various kinds of topological routers via introducing the specific long-range hopping in the one-dimensional modulated Su-Schrieffer-Heeger chain. We find that the long-range hopping with hopping amplitudes identical to those of the intercell hopping between the first site and other odd sites holds a distinctive topological channel (gap state), by which the particle initially prepared at the last site can appear at the first site and all of the even sites with approximately equal probabilities. This extraordinary performance indicates that, from the perspective of treating the last site as the input port and treating the first site and other even sites as output ports, the present system can be naturally equivalent to a distribution device with multiple output ports, i.e., the topological router. We show that the number of the output ports for the present topological router can be flexibly tuned via reducing the long-range hopping terms. Especially, the system experiences a phase transition with the increasing of the long-range hopping amplitudes, in which the original gap state becomes a topological channel to implement the topological router with the output ports only at all even sites. We stress that both the two kinds of topological routers are protected by the energy gap and hence are robust to the mild disorder added into the system. Moreover, together with the construction of the topological interface, we find that the topological routers can own the output ports in a symmetrical way about the interface site. The topological routers may play the pivotal role in the large-scale entanglement distributions, which significantly expands and supplies the potential applications of the topological materials in quantum information processing.

Automated summary

By introducing specific long-range hopping, various kinds of topological routers can be implemented with flexible control over the number of output ports by adjusting the long-range hopping terms. These topological routers are protected by the energy gap, robust to mild disorder, and have output ports symmetrically around the topological interface.