Measuring valley polarization in transition metal dichalcogenides with second-harmonic spectroscopy

Abstract

Inducing a population imbalance at different valleys of an electronic system lowers its effective rotational symmetry. We introduce a technique to measure such valley imbalance (a valley polarization) that directly exploits this symmetry reduction as well as the unique fingerprints it has in the polarization-dependent second-harmonic generation. We describe the principle and detection scheme in the context of hexagonal two-dimensional crystals, which include graphene-based systems and the family of transition metal dichalcogenides. The technique is demonstrated on a MoSe$_2$ monolayer at room temperature. We include a model that shows the valley polarization-induced second-harmonic susceptibility is proportional to the effective valley imbalance, and one order of magnitude larger for quasi-resonant pump conditions versus off-resonant excitation. Importantly, we deliberately keep the setup as simple as possible, where a single laser beam simultaneously creates a controllable valley imbalance and pumps the second-harmonic process. In addition to providing the first experimental demonstration of the effect, this work establishes a conceptually very simple and compact way of measuring the instantaneous valley polarization, with direct applicability in valleytronics.