Measuring valley polarization in two-dimensional materials with second-harmonic spectroscopy

TL;DR

This paper introduces a simple, effective method using second-harmonic generation to measure valley polarization in two-dimensional materials, demonstrated experimentally on a monolayer of 2H-MoSe2 at room temperature.

Contribution

It presents the first experimental demonstration of valley polarization measurement via SHG and develops a model describing the valley-induced SHG rotation.

Findings

Successful detection of valley polarization in 2H-MoSe2 monolayer

Model accurately describes valley-induced SHG rotation

Method is simple, compact, and applicable to valleytronics

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 - that exploits the unique fingerprints of this symmetry reduction in the polarization-dependent second-harmonic 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 2H-MoSe$_{2}$ monolayer 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 experiment. In addition to providing the first experimental demonstration of the effect, this work establishes a conceptually simple, com-pact and transferable way of measuring instantaneous valley polarization, with direct applicability in the nascent field of valleytronics.