Reentrant Resistive Behavior and Dimensional Crossover in Disordered Superconducting TiN Films.

A reentrant temperature dependence of the normal state resistance often referred to as the N-shaped temperature dependence, is omnipresent in disordered superconductors - ranging from high-temperature cuprates to ultrathin superconducting films - that experience superconductor-to-insulator transition. Yet, despite the ubiquity of this phenomenon its origin still remains a subject of debate. Here we investigate strongly disordered superconducting TiN films and demonstrate universality of the reentrant behavior. We offer a quantitative description of the N-shaped resistance curve. We show that upon cooling down the resistance first decreases linearly with temperature and then passes through the minimum that marks the 3D-2D crossover in the system. In the 2D temperature range the resistance first grows with decreasing temperature due to quantum contributions and eventually drops to zero as the system falls into a superconducting state. Our findings demonstrate the prime importance of disorder in dimensional crossover effects.