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

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${}_2$ 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.

arXiv commentUpdating with published version, including typesetting corrections to eqs 3 and 4; 7 pages, 5 figures

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Cited by in corpus (13)

• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride
• Resonant photovoltaic effect in doped magnetic semiconductors
• Nonlinear optical selection rules of excitons in monolayer transition metal dichalcogenides
• Measuring valley polarization in two-dimensional materials with second-harmonic spectroscopy
• Nonlinear optical response of doped mono- and bilayer graphene: length gauge tight-binding model
• Nonlinear optics in 2D materials: from classical to quantum
• Valley Polarization-Electric Dipole Interference and Nonlinear Chiral Selection Rules in Monolayer WSe${}_2$
• Optical third harmonic generation in black phosphorus
• Valley-polarised tunnelling currents in bilayer graphene tunnelling transistors
• Nonlinear spectroscopy of excitonic states in transition metal dichalcogenides
• Non-linear anomalous Hall effect of two-dimensional spin-3/2 heavy holes
• Iterative approach to arbitrary nonlinear optical response functions of graphene