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DOE OSTI2021

Observation of a chiral wave function in the twofold-degenerate quadruple Weyl system BaPtGe

Topological states in quantum materials are defined by bulk wave functions that possess nontrivial topological invariants. While edge modes are widely presented as signatures of nontrivial topology, how bulk wave functions can manifest explicitly topological properties remains unresolved. Here, using high-resolution inelastic x-ray spectroscopy (IXS) combined with first principles calculations, we report experimental signatures of chiral wave functions in the bulk phonon spectrum of BaPtGe, which we show to host a previously undiscovered twofold-degenerate quadruple Weyl node. The chirality of the degenerate phononic wave function yields a nontrivial phonon dynamical structure factor, S(Q,ω), along high-symmetry directions, that is in excellent agreement with numerical and model calculations. Furthermore, our results establish IXS as a powerful tool to uncover topological wave functions, providing a key missing ingredient in the study of topological quantum matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Stereoconvergent Reduction of Activated Alkenes by a Nicotinamide Free Synergistic Photobiocatalytic System

There is a growing interest in developing cooperative chemoenzymatic reactions to harness the reactivity of chemical catalysts and the selectivity of enzymes for the synthesis of nonracemic chiral compounds. However, existing chemoenzymatic systems with more than one chemical reaction and one enzymatic reaction working cooperatively are rare. Moreover, the application of oxidoreductases in cooperative chemoenzymatic reactions is limited by the necessity of using expensive and unstable redox equivalents such as nicotinamide cofactors. Here we report a lightdriven cooperative chemoenzymatic system comprised of a photoinduced electron transfer reaction (PET) and a photosensitized energy transfer reaction (PEnT) with enzymatic reduction in one-pot to synthesize chiral building blocks of bioactive compounds. As a proof of concept, ene-reductase was directly regenerated by PET in the absence of external cofactors. Meanwhile, enzymatic reduction worked cooperatively with photocatalyst-catalyzed energy transfer that continuously replenished the reactive isomer from the less reactive one. The whole system stereoconvergently reduced E/Z mixtures of alkenes to the enantiopure products. Additionally, enantioselective enzymatic reduction worked competitively with photocatalyst-catalyzed racemic background reaction and side reactions to channel the overall electron flow to the single enantiopure product. As a result, such a light-driven cooperative chemoenzymatic system holds great potential for asymmetric synthesis using inexpensive petroleum or biomass derived alkenes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Data from Stereoconvergent Reduction of Activated Alkenes by a Nicotinamide Free Synergistic Photobiocatalytic System

There is a growing interest in developing cooperative chemoenzymatic reactions to harness the reactivity of chemical catalysts and the selectivity of enzymes for the synthesis of nonracemic chiral compounds. However, existing chemoenzymatic systems with more than one chemical reaction and one enzymatic reaction working cooperatively are rare. Moreover, the application of oxidoreductases in cooperative chemoenzymatic reactions is limited by the necessity of using expensive and unstable redox equivalents such as nicotinamide cofactors. Here, we report a light-driven cooperative chemoenzymatic system comprised of a photoinduced electron transfer reaction (PET) and a photosensitized energy transfer reaction (PEnT) with an enzymatic reduction in one-pot to synthesize chiral building blocks of bioactive compounds. As a proof of concept, ene-reductase was directly regenerated by PET in the absence of external cofactors. Meanwhile, enzymatic reduction worked cooperatively with photocatalyst-catalyzed energy transfer that continuously replenished the reactive isomer from the less reactive one. The whole system stereoconvergently reduced E/Z mixtures of alkenes to the enantiopure products. Additionally, enantioselective enzymatic reduction worked competitively with photocatalyst-catalyzed racemic background reaction and side reactions to channel the overall electron flow to the single enantiopure product. Such a light-driven cooperative chemoenzymatic system holds great potential for asymmetric synthesis using inexpensive petroleum or biomass-derived alkenes.

Catalysis↗

DOE OSTI2019

Molecular-Level Design of Heterogeneous Chiral Catalysts

A recent major focus of catalyst research has been on improving the selectivity or atom efficiency of catalytic processes. Perhaps the most subtle and difficult form of selectivity to control is enantioselectivity, a catalyst’s ability to preferentially yield one enantiomer of a chiral product. Since two enantiomers are identical in all respects except for their mirror reflection symmetry, both are formed in non-chiral environments at exactly equal rates; only by introducing some type of chiral modification to the system can the rate of formation of one enantiomer be favored over the other. This has been successfully achieved for homogeneous-phase, organometallic catalysts, but the empirical development of heterogeneous-phase analogs has proven elusive. The design of such heterogeneous-phase catalysts would obviate the need for inefficient purification steps to remove the heavy-metal catalysts. The goal of the proposed research by the Chiral Catalysis Group is to understand the interactions of prochiral reactants on chirally modified surfaces that lead to the preferential formation of one enantiomer over the other. There are two general concepts for designing heterogeneous-phase enantioselective catalysts. The first adopts the strategy used in homogeneous phase, by adding a chiral modifier to the surface. This approach, while conceptually simple has challenges associated with modifying an extended surface. The second concept, which is unique to extended surfaces, is the idea of creating surfaces that are themselves naturally chiral. A fundamental understanding of the interactions that control enantioselectivity will enable the Chiral Catalysis Group to develop the concepts necessary to design novel, heterogenous catalytic materials. Enantioselectivity is also central to catalytic processes that underpin the pharmaceutical and agrochemical industries. With funding from the Department of Energy, the Chiral Catalysis Group has played a leading role in developing a fundamental understanding of chiral catalysis and of the adsorbate structures, interactions and kinetic effects that control heterogenous-phase enantioselectivity. The proposed research program is organized conceptually around three types of enantiospecific interactions: interactions with naturally chiral surfaces; those with modified surfaces categorized as chirally templated surfaces; and one-to-one interactions of prochiral molecules with chiral surface modifiers. Our specific goals are to: (1) determine the structures of chiral surfaces, prochiral reactants, chiral products and chiral modifiers; (2) understand the enantiospecific interactions that occur between prochiral reactants and chiral products with chirally modified surfaces; (3) develop methods for detection of enantiospecific surface phenomena; and (4) elucidate enantioselective reaction pathways and the interactions that control them. The range of expertise within the Chiral Catalysis Group includes molecular-scale theory, surface science experiments, state-of-the-art spectroscopic, kinetic and atomic-scale imaging capabilities carried out in vacuum and under more-realistic liquid- and gas-phase environments complemented by catalytic measurements. By fully integrating such a breadth of approaches and extensive expertise, the Chiral Catalysis Group will, for the first time, be able to understand, rationally design and then control active sites for optimal enantioselectivity. In addition to having a significant impact on the field of chiral catalysis, the proposed research program will further our general understanding of the molecular-scale origins of catalytic selectivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Helical Photonic Metamaterials for Encrypted Chiral Holograms

Helical structures are among the most quintessential three-dimensional (3D) forms that exhibit mirror asymmetry, a hallmark of chirality. Various structural parameters of helices directly linked to chiroptical properties highlight their importance as essential optical metamaterials for polarization-resolved sensors, imaging, and spectroscopies. However, such function-defining properties remain incompletely understood due to fabrication challenges and the lack of a relationship between structure and optical properties. Here, helical structures are analyzed parametrically, and correlations are established that are applicable to the design of chiral helical optical metamaterials. By systematically varying independent parameters—such as from single-turn to five-turn helices and from small major radii to larger ones optimized to fit the unit cell—the underlying relationships with ellipticty are revealed. In addition to theoretical modeling, the findings are experimentally validated using 3D printing and terahertz spectroscopy. The results demonstrate that optimized helical structures are mechanically tunable and exhibit unprecedented optical properties, including broadband and high-magnitude ellipticity spectra. Being embedded in soft elastomers, helical arrays can serve as soft, stretchable optical-mechanical sensors and holograms containing encoded information, such as barcodes and quick response (QR) codes. Chiral QR codes are realized using pixelated single helices with different handedness, demonstrating their potential as advanced encryption/decryption systems for security applications and chiral metaholograms.

Encrypted QR codes↗

DOE OSTI2022

An operator-based approach to topological photonics

Abstract Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure’s topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system’s Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system’s crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice—such as (p x , p y )-wave and (d x 2 –y 2 , d xy )-wave superconductors. Such a system has two possible superconducting states: the chiral state (e.g., p + ip or d + id), which breaks time-reversal symmetry, and the nematic state (e.g., p + p or d + d), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A nonanalytic cubic term arises, as in the case of a conventional s -wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. Here, we analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Emergent biaxiality in chiral hybrid liquid crystals

Biaxial nematic liquid crystals are fascinating systems sometimes referred to as the Higgs boson of soft matter because of experimental observation challenges. Here we describe unexpected states of matter that feature biaxial orientational order of colloidal supercritical fluids and gases formed by sparse rodlike particles. Colloidal rods with perpendicular surface boundary conditions exhibit a strong biaxial symmetry breaking when doped into conventional chiral nematic fluids. Minimization of free energy prompts these particles to orient perpendicular to the local molecular director and the helical axis, thereby imparting biaxiality on the hybrid molecular-colloidal system. The ensuing phase diagram features colloidal gas and liquid and supercritical colloidal fluid states with long-range biaxial orientational symmetry, as supported by analytical and numerical modeling at all hierarchical levels of ordering. Unlike for nonchiral hybrid systems, dispersions in chiral nematic hosts display biaxial orientational order at vanishing colloid volume fractions, promising both technological and fundamental research utility.

Colloids↗

DOE OSTI2026

Hierarchical Chiral Self-Assembly of Nanocylinders Composed of Sequence-Defined Mesogenic Dimers

Chiral ensembles can arise through supramolecular curvature that resolves geometric frustrations in the packing of bent, achiral molecular or colloidal building blocks. Here, we leverage orthogonal protection−deprotection click chemistry to create sequence-defined mesogenic heterodimers exhibiting emergent chirality. We compare the hierarchical self-assembly of the synthesized asymmetric, achiral heterodimers, which differ only in the position of a methyl substituent. Both dimers form chiral spherulites composed of nanocylinders. However, the detailed arrangement of nanocylinders depends on the position of the methyl substituent and the crystallization conditions. Despite the chemical similarity, in one dimer, two crystalline forms are optically active. They form conglomerates of dextrorotatory and levorotatory spherulites. The other dimer forms more highly anisotropic spherulites that mask circular birefringence arising from the misorientation of nanocylinders, while mapping of nanocylinder directors reveals a sense at the spherulite surface. We propose that differences in nanocylinder arrangements may arise from changes in nanocylinder curvature and dimensions dictated by the methyl substituent position, inducing chirality. These results demonstrate multiscale hierarchical assembly relevant to dense systems of tubular structures and highlight the role of sequence and molecular design in directing the bottom-up hierarchical self-assembly and chirality of mesogenic systems.

Alkyls↗

DOE OSTI2021

Orbital Chern Insulator and Quantum Phase Diagram of a Kagome Electron System with Half-Filled Flat Bands

In this work, we study the quantum phase diagram of electrons on kagome lattice with half-filled lowest flat bands by considering the antiferromagnetic Heisenberg interaction J, and short-range Coulomb interaction V. In the weak J regime, we identify a fully spin-polarized phase. The presence of finite V drives a spontaneous chiral current, which makes the system an orbital Chern insulator by contributing an orbital magnetization. Such an out-of-plane orbital magnetization allows the presence of a Chern insulating phase independent of the spin orientation in contrast to the spin-orbit coupling induced Chern insulator that disappears with inplane ferromagnetism constrained by symmetry. Such a symmetry difference provides a criterion to distinguish the physical origin of topological responses in kagome systems. The orbital Chern insulator is robust against small coupling J. By further increasing J, we find that the ferromagnetic topological phase is suppressed, which first becomes partially polarized and then enters a nonmagnetic phase with spin and charge nematicity. The frustrated flat band allows the spin and Coulomb interaction to play an essential role in determining the quantum phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Chiral spin liquid with spinon Fermi surfaces in the spin-$\frac{1}{2}$ triangular Heisenberg model

Here, we study the interplay of competing interactions in spin-$\frac{1}{2}$ triangular Heisenberg model through tuning the first- ($J_1$), second- ($J_2$), and third-neighbor ($J_ 3$) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate $J_2$ and $J_ 3$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the U (1) staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the U (1) Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $J_2$ and $J_3$, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Exact Ground State of Interacting Electrons in Magic Angle Graphene

One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-θ$${\theta }$$ and Weierstrass-℘$${\wp }$$ functions.

Becker, Simon↗

NASA NTRS2000

Remote Enantioselection Transmitted by an Achiral Peptide Nucleic Acid Backbone

short homochiral segment of DNA into a PNA helix could have guaranteed that the next short segment of DNA to be incorporated would have the same handedness as the first. Once two segments of the same handedness were present, the probability that a third segment would have the same handedness would increase, and so on. Evolution could then slowly dilute out the PNA part. This scenario would ultimately allow the formation of a chiral oligonucleotide by processes that are largely resistant to enantiomeric crossinhibition. It is important to note that the ligation of homochiral dinucleotides on a nucleic acid template would probably be at least as enantiospecific as the reaction that we have studied. The disadvantage of using chiral monomers as components of a replicating system arises from the difficulty of generating a first long homochiral template from a racemic mixture of monomers, although results of experiments designed to overcome this difficulty by employing homochiral tetramers have been reported.l l The probability of obtaining a homochiral n-mer from achiral substrates is approximately 1P-I if the nontemplate-directed extension of the primer is not enantioselective. Hence, it would be very hard to get started with a homochiral 40-mer, for example. No such difficulty exists in a scenario that originates with an achiral genetic material and in which the incorporation of very few chiral monomers in this achiral background gradually progresses towards homochirality. It seems possible that some PNA sequences could act as catalysts, analogous to ribozymes, even though PNA lacks clear metal binding sites. Although such catalysts could not be enantioselective, the incorporation of as few as two chiral nucleotides could then impose chiral specificity on the system. Furthermore, such patch chimeras could help to bridge the gap in catalytic potential between PNA and RNA, while guaranteeing enantioselectivity.

Kozlov, Igor A.↗

DOE OSTI2025

Quenching through the QCD chiral phase transition

We present a detailed numerical and analytical study of the out-of-equilibrium dynamics of Model G, the dynamical universality class relevant to the chiral phase transition. We perform numerical 3D stochastic (Langevin) simulations of the 𝑂⁡(4) critical point for large lattices in the chiral limit. We quench the system from the high-temperature unbroken phase to the broken phase and study the nonequilibrium dynamics of pion fields. Strikingly, the nonequilibrium evolution of the two-point functions exhibits a regime of growth, a parametrically large enhancement, and a subsequent slow relaxation to equilibrium. We analyze our numerical results using dynamic critical scaling and mean-field theory. The growth of the two-point functions is determined by the nonlinear dynamics of an ideal non-Abelian superfluid, which is a limit of Model G that reflects the broken chiral symmetry. We also relate the nonequilibrium two-point functions to a long-lived parametric enhancement of soft pion yields relative to thermal equilibrium following a quench.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks

Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which introduce gauge fields to describe the dynamics of singularities in the original field configurations. In this work, homotopy groups are utilized to identify topologically protected singularities, and the conservation of their protected number is captured by a topological action term that unambiguously obtains from the given set of symmetries. Stable phases of these theories include quantum liquids with emergent massless Abelian and non-Abelian gauge fields, as well as topological orders with long-range quantum entanglement, fractional excitations, boundary modes, and unconventional responses to external perturbations. This paper focuses on the derivation of topological field theories and basic phenomenological characterization of topological orders associated with homotopy groups π n (S n ), n ≥ 1 . These homotopies govern monopole and hedgehog topological defects in d = n + 1 dimensions, and enable the generalization of both weakly interacting and fractional quantum Hall liquids of vortices to d > 2 . Hedgehogs have not been in the spotlight so far, but they are particularly important defects of magnetic moments because they can be stimulated in realistic systems with spin-orbit coupling, such as chiral magnets and d = 3 topological materials. We predict topological orders in systems with U(1) × Spin(d) symmetry in which fractional electric charge attaches to hedgehogs. Monopoles, the analogous defects of charge or generic U(1) currents, may bind to hedgehogs via Zeeman effect, or effectively emerge in purely magnetic systems. The latter can lead to spin liquids with different topological orders than that of the resonant valence bond spin liquid. Charge fractionalization of quarks in atomic nuclei is also seen as possibly arising from the charge-hedgehog attachment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Formation of helices with controllable chirality in gel-fiber composites

While microscale helices with specified chirality are pervasive in biological systems, driving purely synthetic materials to self-organize into such useful structures remains a significant challenge. Through theory and simulations, we model the behavior of initially flat ribbons of gel-fiber composites and show that these materials self-organize into three-dimensional helices with the application of heat. We specifically focus on thermo-responsive gels, which shrink when heated to a point near the lower critical solubility temperature (LCST). Within the composite, regions of the LCST gel that lie far from the fibers can readily shrink in response to the increased temperature; however, near the fibers the network is inhibited from undergoing the heat-induced collapse. This competition between the constrained and the unconstrained regions of the heated sample plays a vital role in the structural evolution of the material. Additionally, we find that this dynamic process can be controlled through the careful placement of the fibers on the outer surface of the gel. We specifically identify fiber arrangements that lead to the formation of helical structures with controlled chirality. Moreover, we isolate scenarios where constraining the movement of one or both the free ends of the sample promotes and stabilizes the formation of helical structures with specified handedness. Such structurally tailored composites are useful for creating mechanically robust actuators, and “appendages” for soft robots that can controllably curl and uncurl with variations in temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Giant topological longitudinal circular photo-galvanic effect in the chiral multifold semimetal CoSi

The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light’s polarization, known as the circular photo-galvanic effect, is predicted to depend only on fundamental constants. The conditions to observe quantization are non-universal, and depend on material parameters and the incident frequency. In this work, we perform terahertz emission spectroscopy with tunable photon energy from 0.2 –1.1 eV in the chiral topological semimetal CoSi. We identify a large longitudinal photocurrent peaked at 0.4 eV reaching ~550 μ A/V 2 , which is much larger than the photocurrent in any chiral crystal reported in the literature. Using first-principles calculations we establish that the peak originates only from topological band crossings, reaching 3.3 ± 0.3 in units of the quantization constant. Our calculations indicate that the quantized circular photo-galvanic effect is within reach in CoSi upon doping and increase of the hot-carrier lifetime. The large photo-conductivity suggests that topological semimetals could potentially be used as novel mid-infrared detectors.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Chiral Spectroscopy of Nanostructures

Chirality is ubiquitous in the universe and in living creatures over detectable length scales from the subatomic to the galactic, as exemplified in the two extremes by subatomic particles (neutrinos) and spiral galaxies. Between them are living creatures that display multiple levels of chirality emerging from hierarchically assembled asymmetric building blocks. Not too far from the bottom of this pyramid are the foundational building blocks with chiral atomic centers on sp 3 carbon atoms exemplified by L-amino acids and D-sugars that are self-assembled into higher-order structures with increasing dimensions forming highly complex, amazingly functional, and energy-efficient living systems. The organization and materials employed in their construction inspired scientists to replicate complex living systems via the self-assembly of chiral components. Multiple studies pointed to unexpected and unique electromagnetic properties of chiral structures with nanoscale and microscale dimensions, including giant circular dichroism and collective circularly polarized scattering that their constituent units did not possess. To address the wide variety of chiral geometries observed in continuous materials, singular particles, and their complex systems, multiple analytic techniques are needed. Simultaneously, their spectroscopic properties create a pathway to multiple applications. For example, mirror-asymmetric vibrations at chiral centers formed by sp 3 carbon atoms lead to optical activity for the infrared (IR) wavelength regions. At the same time, understanding the optical activity in, for example, the IR region enables biomedical applications because multiple modalities of biomedical imaging and vibrational optical activity (VOA) of biomolecules are known for IR range. In turn, VOA can be realized in both absorption and emission modalities due to large magnetic transition moments, as vibrational circular dichroism (VCD) or Raman optical activity (ROA) spectroscopy. In addition to the VOA, in the range of longer wavelengths, lattice vibrational mode or phononic behavior occurs in chiral crystals and nanoassemblies, which can be readily detected by terahertz circular dichroism (TCD) spectroscopy. Meanwhile, chiral self-assembly can induce circularly polarized light emission (CPLE) regardless of the existence of chirality in coassembled fluorophores. The CPLE from self-assembled chiral materials is particularly interesting because the CPLE can originate from both circularly polarized luminescence and circularly polarized scattering (CPS). Furthermore, because self-assembled nanostructures often exhibit stronger optical activity than their building blocks owing to dimension and resonance effects, the optical activity of single assembled nanostructures can be investigated by using microscopic technology combined with chiral optics. Here, we describe the state of the art for spectroscopic methods for the comprehensive analysis of chiral nanomaterials at various photon wavelengths, addressed with special attention given to new tools emerging both for materials with self-organized hierarchical chirality and single-particle spectroscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗