Tight binding simulation of laser-assisted ultrafast field-emission from correlated metal

The study of nonequilibrium phenomena in correlated lattice systems is an increasingly active research field in condensed matter physics. Indeed, electronic correlations induce interesting phenomena, such as Hubbard-Mott metal-to-insulator transitions [1], whose understanding is a crucial step for the exploitation of novel properties of such systems in future applications. Therefore, it is intriguing to design and possibly implement an experimental set-up capable of detecting and measuring effects induced by interactions. Field-emission can be considered a good starting point, as it is a powerful and well- known spectroscopic technique used to investigate the energy distribution of the emitted electrons. Adding a strong and ultrashort laser pulse [2], [3] can periodically modify the potential barrier for electron tunnelling and, thus, the far- field electron energy distribution, which is representative of the interactions inside of the material. In this work, we provide a theoretical-numerical tool able to analyze how interaction effects, as well as decoherence, manifest in such an energy distribution. According to the cold field-emission protocol, we consider a metallic tip which is initially at equilibrium at room temperature. Electrons in it cannot leave the solid because of a high-step potential barrier given by the metal work function W. Then, the barrier potential profile is bended by applying a voltage Vpot between an electrode and the metallic tip, opening a tunneling channel between solid and vacuum. Cold-emitted electrons are then perturbed by an electromagnetic pulse in proximity of the solid-vacuum interface and, finally, the field-emitted current, i.e., electron energy distribution, is measured by a detector placed sufficiently far from that interface. Both the solid and the vacuum are modeled using one-band Hubbard-chains with nearest-neighbour hopping. this inhomogeneous system is described using the Keldysh Green's function formalism [1], [4] which, in this case, allows to solve the equations of motion considering the two chains as they were disentangled. While the vacuum-chain problem is solved by means of the Runge-Kutta method, we choose to solve the solid-chain problem by means of the second order Born approximation within a DMFT framework [1], [4], [5] and of the implementation of the NESSi simulation package [6]. Finally, we determine the far-field electron energy distribution by considering an uncorrelated Hubbard-chain dispersion in k-space for the vacuum region. We then analyze these results by exploring various pulse parameters and different values of the correlation term U.