In this paper we study the topology of the bands of a plasmonic crystal composed of graphene and of a metallic grating. Firstly, we derive a Kronig-Penney type of equation for the plasmonic bands as function of the Bloch wavevector and discuss the propagation of the surface plasmon polaritons on the polaritonic crystal using a transfer-matrix approach considering a finite relaxation time. Second, we reformulate the problem as a tight-binding model that resembles the Su-Schrieffer-Heeger (SSH) Hamiltonian, one difference being that the hopping amplitudes are, in this case, energy dependent. In possession of the tight-binding equations it is a simple task to determine the topology (value of the winding number) of the bands. This allows to determine the existense or absence of topological end modes in the system. Similarly to the SSH model, we show that there is a tunable parameter that induces topological phase transitions from trivial to non-trivial. In our case, it is the distance d between the graphene sheet and the metallic grating. We note that d is a parameter that can be easily tuned experimentally simply by controlling the thickness of the spacer between the grating and the graphene sheet. It is then experimentally feasible to engineer devices with the required topological properties. Finally, we suggest a scattering experiment allowing the observation of the topological states.

We show that hexagonal boron nitride (hBN), a two-dimensional insulator, when subjected to an external superlattice potential forms a paradigm for electrostatically tunable excitons in the near- and mid-ultraviolet (UV). With a combination of analytical and numerical methods, we see that the imposed potential has three consequences: (i) It renormalizes the effective mass tensor, leading to anisotropic effective masses. (ii) It renormalizes the band gap, eventually reducing it. (iii) It reduces the exciton binding energies. All these consequences depend on a single dimensionless parameter, which includes the product of strength of the external potential with its period. In addition to the excitonic energy levels, we compute the optical conductivity along two orthogonal directions and from it the absorption spectrum. The results for the latter show that our system is able to mimic a grid polarizer. These characteristics make one-dimensional hBN superlattices a viable and meaningful platform for fine-tuned polaritonics in the UV to visible spectral range.

We argue that strain engineering is a powerful tool that may facilitate the experimental realization and control of topological phases in laser-driven two-dimensional (2D) ferromagnetic systems. To this extent, we show that by applying a circularly polarized laser field to a 2D honeycomb ferromagnet that is uniaxially strained in either the zigzag or armchair direction, it is possible to generate a synthetic Dzyaloshinskii-Moriya interaction tunable by the intensity of the applied electric field, as well as by the magnitude of applied strain. Such deformations enable transitions to phases with the opposite sign of the Chern number, or to trivial phases. These are basic results that could pave the way for the development of a new field of strain-engineered topological spintronics.

We construct a one-dimensional (1D) topological SSH-like model with chiral symmetry and a superimposed hopping modulation, which we call the chiral Aubry-André model. We show that its topological properties can be described in terms of a pair (C,W) of a two-dimensional (2D) Chern number C, stemming from a superspace description of the model, and a 1D winding number W, originating in its chiral symmetric nature. Thus, we showcase the explicit coexistence of 1D and 2D topology in a model composed of a single 1D chain. We detail the superspace description by showcasing how our model can be mapped to a Harper-Hofstadter model, familiar from the description of the integer quantum Hall effect, and analyze the vanishing field limit analytically. An extension of the method used for vanishing fields is provided in order to handle any finite fields, corresponding to hopping modulations both commensurate and incommensurate with the lattice. In addition, this formalism allows us to obtain certain features of the 2D superspace model, such as its number of massless Dirac nodes, purely in terms of topological quantities, computed without the need to go into momentum space.