Thermal near-field energy density and LDOS in topological 1D SSH chains and 2D SSH lattices of plasmonic nanoparticles

We derive a general expression for electric and magnetic part of the near-field energy density of N dipoles of temperatures T1, . . . , TN immersed in a background field having a different temperature Tb. In contrast to former expressions this inclusion of the background field allows for determining the energy density of heated or cooled isotropic dipolar objects within an arbitrary environment which is thermalized at a different temperature. Furthermore, we show how the energy density is related to the local density of states. We use this general expression to study the near-field enhanced energy density at the edges and corners of 1D Su-Schrieffer-Heeger chains and 2D Su-Schrieffer-Heeger lattices of plasmonic InSb nanoparticles when the phase transition from a topological trivial to a topological non-trivial state is made. We discuss the robustness of these modes when adding defects and the possibility to measure the topological edge and corner modes.