Two-dimensional terahertz spectroscopy in electronic systems: A many-body diagrammatic approach

The term “two-dimensional coherent spectroscopy” (2DCS) usually refers to experimental setups where a coherently generated electric field in a sample is recorded over many runs as a function of two time variables: the delay τ between two consequent excitation pulses and the time t over which the signal is emitted. Even if its implementation in the femtosecond time domain for investigation of vibrational molecular states was developed more than two decades ago, its experimental development in the terahertz domain with application to interacting electronic systems is still in its infancy. The present work aims at providing a theoretical framework for the description and interpretation of 2DCS by using the same many-body language based on a perturbative diagrammatic expansion that has been largely developed and applied in the literature to linear spectroscopy. By focusing on the case of centrosymmetric systems, we show how the problem of the theoretical interpretation of the 2D maps can be recast in the solution of two different but complementary problems. The first one is the evaluation of a third-order response function to the gauge field, whose derivation in the velocity gauge leads to a semianalytical expression for the computation of the 2D maps in the case of simple band dispersions and a Gaussianlike pulse envelope. This has the twofold advantage of reducing considerably the computational complexity and to guide the assignment of the spectral features to microscopic processes, as we demonstrate explicitly for a toy model of electrons in a semiconductinglike band structure. The second one is a careful description of multiwave propagation effects inside the material, that for bulk systems can completely screen the intrinsic properties of the nonlinear response, as we show for the case of soft superconducting Josephson plasmons. Our results provide a theoretical foundation prone to further extension to several interacting systems and offer a flexible method for modeling realistically the nonlinear responses across arbitrary spectral widths of the driving fields.