# Second harmonic spectroscopy to optically detect valley polarization in 2D materials

## TL;DR

This paper proposes a theoretical method using second harmonic spectroscopy to detect and quantify valley polarization in 2D materials, enabling contactless valley transport monitoring.

## Contribution

It introduces a theoretical framework for using second harmonic generation to measure valley polarization in inversion-symmetric 2D materials, distinguishing intrinsic and valley contributions.

## Key findings

- SH response depends on valley polarization, polarization, temperature, and electron density.
- Proposed experimental setup allows direct quantitative measurement of valley polarization.
- Method enables remote, contactless valley polarization mapping.

## Abstract

Valley polarization (VP), an induced imbalance in the populations of a multi-valley electronic system, allows emission of second harmonic (SH) light even in centrosymmetric crystals such as graphene. Whereas in systems such as MoS$\mathrm{_2}$ or BN this adds to their intrinsic quadratic response, SH generation in a multi-valley inversion-symmetric crystal can provide a direct measure of valley polarization. By computing the nonlinear response and characterizing theoretically the respective SH as a function of polarization, temperature, electron density, and degree of VP, we demonstrate the possibility of disentangling and individually quantifying the intrinsic and valley contributions to the SH. A specific experimental setup is proposed to obtain direct quantitative information about the degree of VP and allow its remote mapping. This approach could prove useful for direct, contactless, real-space monitoring of valley injection and other applications of valley transport and valleytronics.