Generalized Wilson Loop Method for Nonlinear Light-Matter Interaction

Abstract

Nonlinear light-matter interaction, as the core of ultrafast optics, bulk photovoltaics, nonlinear optical sensing and imaging, and efficient generation of entangled photons, has been traditionally studied by first-principles theoretical methods with the sum-over-states approach. However, this indirect method often suffers from the divergence at band degeneracy and optical zeros as well as convergence issues and high computation costs when summing over the states. Here, using shift vector and shift current conductivity tensor as an example, we present a gauge-invariant generalized approach for efficient and direct calculations of nonlinear optical responses by representing interband Berry curvature, quantum metric, and shift vector in a generalized Wilson loop. This generalized Wilson loop method avoids the above cumbersome challenges and allows for easy implementation and efficient calculations. More importantly, the Wilson loop representation provides a succinct geometric interpretation of nonlinear optical processes and responses based on quantum geometric tensors and quantum geometric potentials and can be readily applied to studying other excited-state responses.

arXiv comment20 pages, 10 figures

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Cited by in corpus (9)

• Photocurrent as a multi-physics diagnostic of quantum materials
• The Berry dipole photovoltaic demon and the thermodynamics of photo-current generation within the optical gap of metals
• Anomalous shift and optical vorticity in the steady photovoltaic current
• Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals
• Quantum Fluctuation of the Quantum Geometric Tensor and its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems
• Electric quadrupole second harmonic generation revealing dual magnetic orders in a magnetic Weyl semimetal
• The multi-state geometry of shift current and polarization
• Berry curvature and shift vector effects at high-order wave mixing in biased bilayer graphene
• Scattering of relativistic electrons and analogies with optical phenomena: A study of longitudinal and transverse shifts at step potentials