Measuring Valley Polarization in Two-Dimensional Materials with Second-Harmonic Spectroscopy

Abstract

A population imbalance at different valleys of an electronic system lowers its effective rotational symmetry. We introduce a technique to measure such imbalance (a valley polarization), which exploits the unique fingerprints of this symmetry reduction in the polarization-dependent secondharmonic generation (SHG). We present 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, and provide a direct experimental demonstration using a molybdenum diselenide monolayer with 2H polytype at room temperature. We deliberately use the simplest possible setup, where a single pulsed laser beam simultaneously controls the valley imbalance and tracks the SHG process. We further developed a model of the transient population dynamics, which analytically describes the valley-induced SHG rotation in very good agreement with the experimental data. In addition to providing the first experimental demonstration of the effect, this work establishes a conceptually simple, compact, and transferable way of measuring instantaneous valley polarization, with direct applicability in the nascent field of valleytronics.

Berry curvature, orbital magnetization, and Nernst effect in biased bilayer WSe2

“…Our work highlights the role of a gate electric field on certain valley-dependent, topological properties and it is pertinent to other bilayer TMDCs. A method to measure the population imbalance at different valleys of TMDCs has been developed recently, thus making possible the realization of the findings of this work [40].…”

Probing valley population imbalance in transition metal dichalcogenides via temperature-dependent second harmonic generation imaging

“…A direct consequence of this effect is the possibility for such crystals to produce valley-induced SHG, additionally to the intrinsic second-order response. As a result, in the presence of population imbalance between the two valleys, additional elements in the second-order nonlinear optical susceptibility tensor become nonzero 32,34,35,40 . Therefore, we have: χ VPI can be either induced 10,40 or emerge spontaneously 41 and depending on the way it is created, it reflects different aspects of the electronic system.…”

“…As a result, in the presence of population imbalance between the two valleys, additional elements in the second-order nonlinear optical susceptibility tensor become nonzero 32,34,35,40 . Therefore, we have: χ VPI can be either induced 10,40 or emerge spontaneously 41 and depending on the way it is created, it reflects different aspects of the electronic system. For instance, when circularly polarized light is used for excitation, only one of the two valleys is populated and the spin-valley polarization is transferred to the detected one-or two-photon PL 15 .…”

“…vpi $ δμ 34,35,41 . Accordingly, local variations in the chemical potential affect the SHG induced by the VPI and thus can be probed by nonlinear optical experiments 40 . More importantly, and in contrast to the intrinsic nonlinear optical response of 2D TMDs, the valley-induced SHG is sensitive to temperature variations.…”

“…The linear polarization of the excitation changes to elliptical as the beam passes through the quarter-wave plate whose axis has an offset of 5°with respect to the polarization axis. Such a configuration provides the means for an asymmetric population of the two valleys 40 . An accurate description of the polarization state of the fundamental field incident to the sample and the SHG field emerging from the 2D crystal entails the use of the Jones formalism and is presented in detail in the Supplementary Eqs.…”