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DOE OSTI2025

Multistate Geometry of Shift Current and Polarization

The quantum metric and Berry curvature capture essential properties of nontrivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state geometry is necessary to explain properties involving Bloch states of multiple bands, such as optical transitions. To this end, we employ quantum state projectors to develop an explicitly gauge-invariant formalism and demonstrate its power with applications to nonlinear optics and the theory of electronic polarization. We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization, clarifies the treatment of band degeneracies, and reveals its decomposition into the sum of the skewness of the occupied states and intrinsically multistate geometry. The projector approach is applied to calculate nonlinear optical properties of transition metal dichalcogenides (TMDs) layers, using previously calculated minimal tight-binding models, and demonstrated analytically on a three-band generalization of the Rice-Mele chain to elucidate the different contributions. We close with comments on further applications of the projector operator approach to multistate geometry.

electric polarization↗

DOE OSTI2024

Chiral, Topological, and Knotted Colloids in Liquid Crystals

The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low symmetry and nontrivial topology of surface confinement are of particular interest, including surfaces shaped as handlebodies, spirals, knots, multi-component links, and so on. These types of colloidal surfaces induce topologically nontrivial three-dimensional director field configurations and topological defects. Director switching by electric fields, laser tweezing of defects, and local photo-thermal melting of the liquid crystal host medium promote transformations among many stable and metastable particle-induced director configurations that can be revealed by means of direct label-free three-dimensional nonlinear optical imaging. The interplay between topologies of colloidal surfaces, director fields, and defects is found to show a number of unexpected features, such as knotting and linking of line defects, often uniquely arising from the nonpolar nature of the nematic director field. This review article highlights fascinating examples of new physical behavior arising from the interplay of nematic molecular order and both chiral symmetry and topology of colloidal inclusions within the nematic host. Furthermore, the article concludes with a brief discussion of how these findings may lay the groundwork for new types of topology-dictated self-assembly in soft condensed matter leading to novel mesostructured composite materials, as well as for experimental insights into the pure-math aspects of low-dimensional topology.

chirality↗

DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗

DOE OSTI2024

Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

An inclusive framework for joined Hamiltonian and dissipative dynamical systems that are thermodynamically consistent, i.e., preserve energy and produce entropy, is given. The dissipative dynamics of the framework is based on the metriplectic 4-bracket , a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generated using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Many examples of both finite and infinite dimensions are given.

Physics↗

DOE OSTI2025

Geometric control of hyperbolic exciton-polariton condensate dimers

Coupled many-body quantum systems exhibit rich emergent physics with diverse stationary and dynamical behaviours. By engineering platforms with tunable and distinct coupling mechanisms, new insights emerge into the collective behaviour of coupled many body systems. Particles can be exchanged via evanescent or ballistic coupling: the former, based on proximity, yields large spectral splitting, while the latter requires strict phase-matching, analogous to phase-coupled harmonic oscillators and has a smaller impact on the energy landscape. We demonstrate an all-optically tunable quantum fluid dimer based on exciton-polariton condensates in a photonic crystal waveguide with hyperbolic (saddle-like) dispersion. Varying the dimer’s angle relative to the grating tunes the coupling from evanescent to ballistic. We directly observe spectral features and mass flow shaped by the saddle dispersion. This work highlights photonic crystals as powerful platforms to explore condensed matter phenomena lying at the interface between delay-coupled nonlinear oscillators and tight binding physics.

Georgakilas, Ioannis [IBM Research-Zurich, Rüschli↗

DOE OSTI2024

Opto-twistronic Hall effect in a three-dimensional spiral lattice

Studies of moire systems have elucidated the exquisite effect of quantum geometry on the electronic bands and their properties, leading to the discovery of new correlated phases. However, most experimental studies have been confined to a few layers in the 2D limit. The extension of twistronics to its 3D limit, where the twist is extended into the third dimension between adjacent layers, remains underexplored due to the challenges in precisely stacking layers. Here, in this study, we focus on 3D twistronics on a platform of self-assembled spiral superlattice of multilayered WS 2 . Our findings reveal an opto-twistronic Hall effect in the spiral superlattice. This mesoscopic response is an experimental manifestation of the noncommutative geometry that arises when translational symmetry is replaced by a non-symmorphic screw operation. We also discover signatures of altered laws of optical excitation, manifested as an unconventional photon momentum-lattice interaction owing to moire of moire modulations in the 3D twistronic system. Crucially, our findings mark the initial identification of higher-order quantum geometrical tensors in light-matter interactions. This breakthrough opens new avenues for designing quantum materials-based optical lattices with large nonlinearities, paving the way for the development of advanced quantum nanophotonic devices.

Ji, Zhurun↗

DOE OSTI2021

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s -1 , agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.

43 PARTICLE ACCELERATORS↗