Title: Thermoelectric response enhanced by surface/edge states in physical nanogaps

Abstract: We propose here a feasible and effective design of new thermoelectric systems based on physical gaps in nanoscale junctions. We show that, depending on the type of features, i.e. the character of surface/edge states, on both sides of the gap, it is possible to achieve rather high figures of merit. In particular, we show that for configurations that have localized states at the surfaces/edges, which translate into sharp resonances in the transmission, it is possible to achieve large Seebeck coefficients and figures of merit by carefully tuning their energy and their coupling to other states. We calculate the thermoelectric coefficients as a function of different parameters and find non-obvious behaviours, like the existence of a certain coupling between the localized and bulk states for which these quantities have a maximum. The highest Seebeck coefficients and figures of merit are achieved for symmetric junctions, which have the same coupling between the localized state and the bulk states on both sides of the gap. The features and trends of the thermoelectric properties and their change with various parameters that we find here cannot only be applied to systems with nanogaps, but also to many other nanoscale junctions, such as e.g. those that have surface states or states localized near the contacts between the nanoscale object and the electrodes. The model presented here can therefore be used to characterize and predict the thermoelectric properties of many different nanoscale junctions and can also serve as a guide for studying other systems. These results pave then the way for the design and fabrication of stable next-generation thermoelectric devices with robust features and improved performances.