Non-equilibrium quantum physics

The theoretical investigation of out-of-equilibrium quantum systems has recently generated a tremendous interest, mostly in consequence of the development of time-resolved spectroscopy. My initial contribution to this field was to develop a novel method which extends the dynamical mean-field theory to the out-of-equilibrium regime, including a quantum dissipation channel in the non-equilibrium dynamics of correlated materials. This novel approach revealed as a fundamental ingredient to study the dynamics of driven strongly correlated systems. Using this method I demonstrated that coupling to external thermostat is a necessary and sufficient condition to dynamically access the non-equilibrium stationary state and, more in general, to capture the relaxation of a driven correlated system  (see fig. 3). Beyond this, we investigated the stationary properties and the non-linear response. We pointed out the existence of the “analogue” of the Pomeranchuk effect and characterized the presence of a “optimal” dissipation regime via a suitable entropy function. 

Real-time evolution of the current in a driven strongly correlated electronic system with/without quantum dissipation.

Phase-diagram of a stationary non-equilibrium superconductor

More recently, I focued on the non-equilibrium properties in strongly correlated heterostructures, as paradigmatic realizations of non-linear transport effects. Using Nambu-Keldysh stationary DMFT I studied the bulk properties of non-equilibrium superconductors in a simplified model. The system is driven out-of-equilibrium by a voltage bias. We show that the superconducting state is destabilized by voltage biases of the order of the energy gap. We demonstrate that the transition to the normal state occurs through an intermediate bad superconducting state, which is characterized by a smaller value of the order parameter and incoherent excitations. We discuss the energetic balance behind the stabilization of such exotic superconducting state. 

Next, using of the Time-Dependent Gutzwiller approximation we investigated the transport properties of a strongly-correlated slab contacted to two metal leads in presence of voltage bias. We studied the real-time evolution of the electronic properties in both metallic and insulating regime. When the strongly-correlated slab is metallic, a steady-state is established that sustains a finite current. Specif- ically, we have shown that the zero-bias conductance is finite and independent of the degree of correlations within the slab. On the contrary, when the slab is Mott insulating we found currents that are exponentially activated by charge tunneling across the Mott-Hubbard gap, consistent with the Landau- Zener dielectric breakdown scenario. 

Moving from this result we investigated a novel approach to the resistive switch in Mott insulators. Indeed, recent experiments on a class of narrow Mott insulators have pointed out how the formation of a conductive state in these systems takes place through a large discontinuity, which on its side as been phenomenologically interpreted as a field-driven Mott transition. A genuine microscopic understanding on such a novel mechanism to drive the sudden formation of a robust conductive state is expected to be of large importance in the realization of novel Mott-based microelectronic devices. 

In this work we explicitly unveil how the unlocking of the conductive state in Mott insulators happens, using a simple, yet generic, toy model that shows coexistence of a stable Mott insulator and a metastable metal. Specifically, we consider such model in a slab geometry subject to a linear potential drop across the slab, and study its phase diagram by means of dynamical mean-field theory. In the coexistence region, we find that the electric breakdown of the Mott insulator occurs via a first-order insulator-to-metal transition characterized by an abrupt gap-collapse in sharp contrast to the standard Zener breakdown. The switch-on of charge conduction is due to the field-driven stabilization of the more polarisable metallic phase that preexists as metastable state and is disconnected from the stable insulator. Outside insulator-metal coexistence, the electric breakdown seems instead to occur more conventionally through quantum tunnelling across the Hubbard bands tilted by the field. Our findings rationalize recent experimental observations and may offer a guideline for future technological research.

Non-equilibrium statistical-mechanics

The construction of a statistical theory of the non-equilibrium phenomena is a fascinating problem in classical physics. One route used in the construction of non-equilibrium statistical ensembles is to generalize the ergodic hypothesis by assuming that the phase-space motion of a stationary many- particles system is described by a paradigmatic chaotic dynamics. This admit a stationary distribution which can be used to evaluate expectation value of observables. In collaboration with Dr.P.Falco e Prof.F.Bonetto I studied the statistical properties of a class of such chaotic dynamical systems, including the dissipative case. I have constructed the corresponding asymptotic distributions by means of explicit construction at all orders in perturbation theory using exact Renormalization Group methods and non-commutative Fourier analysis.