2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229083We study the stability of spinless Fermions with power law hopping $H_{ij} \propto |i - j|^{-α}$. It is shown that at precisely $α_c =2$, the dispersive inflection point coalesces with the band minimum and the charge carriers exhibit a transition into negative effective mass regime, $m_α^* < 0$ characterized by retarded transport in the presence of an electric field. Moreover, bands with $α< 2$ must be accompanied by counter-carriers with $m_α^* > 0$, having a positive band curvature, thus stabilizing the system in order to maintain equilibrium conditions and a proper electrical response. We further examine the semi-classical transport and response properties, finding an infrared divergent conductivity for 1/r hopping($α=1$). The analysis is generalized to regular lattices in dimensions $d$ = 1, 2, and 3.6 pages. 2 figuresMesoscale and Nanoscale Physicstext