[Paper Review] Lightwave topology for strong-field valleytronics

Álvaro Jiménez-Galán, Rui E. F. Silva+2 more|Figshare|Oct 16, 2019

Laser-Matter Interactions and Applications4 citations

TL;DR

This paper proposes a robust, all-optical method for ultrafast, valley-selective excitation in 2D materials using tailored bicircular light fields to induce topological Floquet band structures. By controlling the Lissajous figure's orientation relative to the lattice, it enables femtosecond switching of valley polarization independent of material specifics, with experimental verification via harmonic helicity mapping and numerical evidence of light-induced topological phase transitions at specific field intensities and wavelengths.

ABSTRACT

Modern light generation technology offers extraordinary capabilities for sculpting light pulses, with full control over individual electric field oscillations within each laser cycle. These capabilities are at the core of lightwave electronics - the dream of ultrafast lightwave control over electron dynamics in solids, on a few-cycle to sub-cycle timescale, aiming at information processing at tera-Hertz to peta-Hertz rates. Here we show a robust and general approach to valley-selective electron excitations in two-dimensional solids, by controlling the sub-cycle structure of non-resonant driving fields at a few-femtosecond timescale. Bringing the frequency-domain concept of topological Floquet systems to the few-fsec time domain, we develop a transparent control mechanism in real space and an all-optical, non-element-specific method to coherently write, manipulate and read selective valley excitations using fields carried in a wide range of frequencies, on timescales that can be much shorter than the valley lifetime, crucial for implementation of valleytronic devices.

Motivation & Objective

• To achieve ultrafast, valley-selective electron excitation in 2D materials on a few-femtosecond timescale, overcoming the challenge of short valley lifetimes.
• To develop a non-resonant, all-optical method for coherently writing, manipulating, and reading valley polarization without requiring material-specific tuning or resonant excitation.
• To demonstrate that strong, non-resonant bicircular light fields can induce Haldane-type complex second-neighbor hoppings, thereby modifying the topological band structure and enabling valley control via field polarization geometry.
• To provide a real-space, transparent control mechanism for valleytronics based on sub-cycle field shaping and Berry curvature engineering.
• To experimentally verify valley polarization via all-optical harmonic probing and demonstrate a light-induced topological phase transition in hBN using gated time-dependent anomalous Hall conductivity.

Proposed method

• The method employs a bicircular light field composed of counter-rotating fundamental and second-harmonic components to generate a tunable Lissajous figure with controllable symmetry and orientation relative to the 2D lattice.
• The orientation of the Lissajous figure, controlled by the two-color phase φ, determines the relative coupling strength to the two sublattices in the hexagonal lattice, thereby inducing complex-valued second-neighbor hoppings analogous to Haldane's model.
• The cycle-averaged band structure and Berry curvature are modified by this light-induced hopping, leading to valley-dependent bandgap reduction and selective multi-photon excitation.
• Valley polarization is measured via a linearly polarized probe pulse that generates odd-harmonic radiation; the helicity of the harmonic response (h = 2(I↻ - I↺)/(I↻ + I↺)) directly maps the valley asymmetry.
• The time-dependent anomalous Hall conductivity (AHC) is computed using a gated average over laser cycles to extract the effective topological response, with σ̄xy(t) derived from instantaneous populations fₙ(k,t) and field-free Berry curvature Ω(k).
• A semi-analytical model for the effective t₂ hopping parameter is used to predict the conditions for a topological phase transition, confirmed by numerical simulations of AHC sign changes under varying intensity and wavelength.

Experimental results

Research questions

• RQ1 Can strong, non-resonant bicircular light fields induce topological band structure modifications in trivial 2D materials like hBN and MoS₂ to enable valley-selective excitation?
• RQ2 How does the orientation of the Lissajous figure of the bicircular field relative to the lattice affect the induced complex hoppings and valley polarization?
• RQ3 Can valley polarization be initialized and manipulated on a few-femtosecond timescale using only the polarization geometry of the driving field, independent of material details?
• RQ4 Can the valley pseudospin be read out all-optically via the helicity of harmonics generated by a linearly polarized probe pulse?
• RQ5 Under what conditions does non-resonant light induce a topological phase transition, and can this be detected via a sign change in the time-averaged anomalous Hall conductivity?

Key findings

• The Lissajous figure's orientation relative to the lattice controls the magnitude and phase of light-induced complex second-neighbor hoppings, enabling selective valley excitation through bandgap reduction.
• Femtosecond valley switching is achieved using strong, low-frequency circularly polarized fields, with valley polarization reversed compared to the weak-field resonant regime due to light-induced electron streaking.
• The helicity of the harmonic response from a linearly polarized probe pulse directly maps the valley pseudospin, providing a background-free, all-optical readout method.
• Numerical simulations show a sign change in the gated time-dependent anomalous Hall conductivity (σ̄xy(t)) when the bicircular field intensity and wavelength reach values predicted by the analytical model, confirming a light-induced topological phase transition.
• The method is robust across a broad range of field intensities and frequencies, with no need for resonant tuning or material-specific parameters, enabling universal valley control in 2D materials.
• In hBN, the AHC sign change occurs at I_tot = 8.4 TW/cm² and λ = 4 μm, matching the analytical prediction, and is observed near the peak of the 20-cycle pulse, confirming the emergence of a topologically nontrivial phase.