Fractional Charge Research Articles

Does the Sign of Charge Affect the Surface Affinity of Simple Ions?

The role the charge sign of simple ions plays in determining their surface affinity in aqueous solutions is investigated by computer simulation methods. For this purpose, the free surface of aqueous solutions of fictitious salts is simulated at finite concentration both with nonpolarizable point-charge and polarizable Gaussian-charge potential models. The salts consist of monovalent cations and anions that are, apart from the sign of their charge, identical to each other. In particular, we consider the small Na+ and the large I- ions together with their charge-inverted counterparts. In an attempt to avoid the interference even between the behavior of cations and anions, we also simulate systems containing only one of the above ions, and determine the free energy profile of these ions across the liquid-vapor interface of water at infinite dilution by potential of mean force (PMF) calculations. The obtained results reveal that, in the case of small ions, the anion is hydrated considerably stronger than the cation due to the close approach of water H atoms, bearing a positive fractional charge. As a consequence, the surface affinity of a small anion is even smaller than that of its cationic counterpart. However, considering that small ions are effectively repelled from the water surface, the importance of this difference is negligible. Further, a change in the hydration energy trends of the two oppositely charged ions is observed with their increasing size. This change is largely attributed to the fact that, with increasing ion size, the factor of 2 in the magnitude of the fractional charge of the closely approaching water atoms (i.e., O around cations and H around anions) outweighs the closer approach of the H than the O atom in the hydration energy. Thus, for large ions, being already surface active themselves, the surface affinity of the anion is larger than that of its positively charged counterpart. Further, such a difference is seen even in the case when the sign of the surface potential favors the adsorption of cations.

Coexistence of magnetic and phononic second-order topological phases in two-dimensional NiZrCl6

Second-order topological phases (SOTPs) in two-dimensional (2D) magnetic and phononic systems are rarely reported. In this Letter, using first-principles calculations, we propose that the NiZrCl6 monolayer with space group P312 (No. 149) is a 2D ferromagnetic material with rich SOTPs: (i) magnetic SOTPs can be found in the band structures of both spin channels in NiZrCl6. NiZrCl6 hosts topologically protected corner states that have a quantized fractional charge (e/3) and are spin-polarized and pinned at the corners of the sample in real space. The SOTP nature in the NiZrCl6 monolayer is resistant to the spin–orbit coupling effect. (ii) Phononic SOTPs can be found in the phonon curves of NiZrCl6. The corner vibrational modes appear inside the frequency gap around 7.98 THz of the NiZrCl6 monolayer, and the secondary topological index can verify the nontrivial phase. The proposed 2D NiZrCl6 material can be a starting point for exploring higher-order topological phases in 2D magnetic and phononic systems.

Magnetic high-order topological insulator in 2D layered CrOCl

High-order topological insulators (HOTIs) have garnered significant interest in recent years due to their unique properties, but their material realization has thus far been limited to those protected by Cn (n = 3,4,6) rotation symmetry and to nonmagnetic crystals. In this study, we propose a HOTI in a recently synthesized two-dimensional (2D) magnetic material, CrOCl. Our findings reveal that the material's ground state, which has ferromagnetic ordering, features corner states carrying a quantized fractional charge. These states are enabled by a twofold rotation symmetry (C2z) and are robust against spin-orbital coupling (SOC). The corner states in CrOCl are distinct from those in nonmagnetic examples and even in magnetic examples, as they can achieve 100% spin polarization in the presence or absence of SOC. Remarkably, the corner states in CrOCl are also robust against layer stacking, symmetry breaking, and even magnetization. Furthermore, under a vertical electric field, the material undergoes a phase transition from HOTI to “hidden high-order topological insulator” phase, with the corner states submerged into edge or bulk states. Our study not only highlights the HOTI properties of 2D CrOCl, but also promotes it as a concrete material platform for exploring the intriguing physics of magnetic HOTIs. We also discuss possible experimental detections and applications of this material, which may pave the way for new advancements in materials sciences and condensed-matter physics.

Transport measurement of fractional charges in topological models

The static topological fractional charge (TFC) in condensed matter systems is related to the band topology and thus has potential applications in topological quantum computation. However, the experimental measurement of these TFCs in electronic systems is quite challenging. We propose an electronic transport measurement scheme in which both the charge amount and the spatial distribution of the TFC can be extracted from the differential conductance through a quantum dot coupled to the topological system being measured. For one-dimensional Su–Schrieffer–Heeger (SSH) model, both the e/2 charge of the TFC and its distribution can be verified. As for the disorder effect, it is shown that the Anderson disorder, which breaks certain symmetry related to the TFC, is significant in higher-dimensional systems while having little effect on the one-dimensional SSH chain. Nonetheless, our measurement scheme can still work well for specific higher-order topological insulator materials, for instance, the 2e/3 TFC in the breathing kagome model could be confirmed even in the presence of disorder effect. These conclusions about spatial dimension and disorder effect are quite universal, which also applies to other topological systems such as topological classic wave system.

Floquet Gauge Anomaly Inflow and Arbitrary Fractional Charge in Periodically Driven Topological-Normal Insulator Heterostructures.

Usually, when coupling in a background gauge field, topological zero modes would yield an anomalous current at the interface, culminating in the zero-mode anomaly inflow, which is ultimately conserved by extra contributions from the topological bulk. However, the anomaly inflow mechanism for guiding Floquet steady states is rarely explored in periodically driven systems. Here we synthesize a driven topological-normal insulator heterostructure and propose a Floquet gauge anomaly inflow, associated with the occurrence of arbitrary fractional charge. Through our photonic modeling, we experimentally observed a Floquet gauge anomaly as the system was driven into anomalous topological phases. Prospectively, we believe our findings could pave a novel avenue on exploring Floquet gauge anomalies in driven systems of condensed matter, photonics, and ultracold atoms.

Topological field theories of three-dimensional rotation symmetric insulators: Coupling curvature and electromagnetism

Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation symmetry along a fixed axis, in addition to either mirror symmetry or particle-hole symmetry. These insulators can realize quantized mixed geometry-charge responses. When the surface of these insulators is gapped, disclinations on the surface carry a fractional charge that is half the minimal amount that can occur in purely $2$D systems. Similarly, disclination lines in the bulk carry a fractionally quantized electric polarization. These effects, and other related phenomena, are captured by a $3$D topological response term that couples the lattice curvature to the electromagnetic field strength. Additionally, mirror symmetric insulators with this response can be smoothly deformed into a higher-order octopole insulator with quantized corner charges. We also construct a symmetry indicator form for the topological invariant that describes the quantized response of the mirror symmetric topological crystalline insulators, and discuss an unusual response quantization in time-reversal breaking systems.

Rotational symmetry protected edge and corner states in Abelian topological phases

Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In this paper, we study the edge physics of systems with a non-trivial shift invariant, which is protected by either a continuous $\text{U}(1)_r$ or discrete $\text{C}_n$ rotation symmetry, along with internal $\text{U}(1)_c$ charge conservation. Specifically, we construct an interface between two systems which have the same Chern number but are distinguished by their Wen-Zee shift and, through analytic arguments supported by numerics, show that the interface hosts counter-propagating gapless edge modes which cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian sub-algebra framework for gapped boundaries while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and compute them in the case where the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Our work paves the way for studying the edge physics associated with spatial symmetries in symmetry enriched topological phases.

Size-tunable graphitized carbon spheres for water defluoridation

We fabricated non-catalytic carbon spheres with controllable dimensions (diameter 0.3–1.5 µm) by chemical vapour deposition at 1273 K using C2H2 (carbon source) and N2 (dilutant) gas precursors. By varying the flow rates of precursor gases, spherical or pseudo-spherical morphologies with chain-like hierarchical structures are discerned. The X-ray diffraction data show hexagonally graphitized networks. The mechanism of carbon sphere formation is not yet fully resolved largely due to the ambiguity associated with the nucleation step, viz. pentagon or heptagon route. According to molecular dynamics calculations, the formation of carbon pentagons is energetically more favorable than heptagons. Pentagon structures seem to form by closing Fjord regions of the graphitized network as evidenced in IR bands at 635 cm−1 and 796 cm−1. The X-ray photon spectroscopic (XPS) measurements show adventitious oxygen on the carbon sphere’s surface sites with -COOH and -C-CO groups. The -COOH and -C-CO groups are polar; hence, the carbon spheres’ surface sites readily hydroxylate (where ≡GOHδ represents surface sites with a fractional charge). The carbon sphere synthesized under C2H2N2 = 56 gas flow ratio (viz., CS3) shows the highest fluoride removal capacity, viz., 0.095 ± 0.01 mmol.m2-. The comparable zeta potential values observed between the carbon spheres and fluoride laden carbon spheres point to an anion exchange of surface hydroxyl ions for F- sorption. In agreement with the XPS data, the broad IR band at 3440 cm−1 due to H-bonded surface hydroxyl stretching vibrations has resolved into three discrete bands, e.g., 3640, 3752, and 3738 cm−1, which evidenced fluoride adsorption. Compared to activated carbon, the retention of fluoride on carbon spheres is over 60 times higher, which shows its potential in water treatment in removing fluoride.

Fractional mode charge of higher-order topological acoustic transport

The local density of states (LDOS), which describes the space-resolved density of states, has been studied in the context of exploring topological materials. Here, we report the observation of the fractional mode charge of topological states in a four-dimensional synthetic acoustic system, which is based on coupled acoustic cavities. We experimentally measured the LDOS of topological boundary states and corner states of this system and observed one-half and one-quarter fractional mode charges. In addition, we also obtained the LDOS in a three-dimensional acoustic system by simulation and observed the one-eighth fractional mode charge of the system. The results show that the appearance of topological states can correspond to the fractional charges, which is useful for the understanding of topology in acoustic systems and provides a new method for the characterization of topological states in topological acoustic systems.

Studying chemistry in cyberspace

Jun-Hyeong earned his BS degree in physics and chemistry from Ulsan National Institute of Science and Technology (UNIST). He later moved to Korea Advanced Institute of Science and Technology (KAIST) to obtain a PhD degree in chemistry under the guidance of Prof. Mu-Hyun (Mookie) Baik. During his PhD studies, he focused on gaining a quantitative understanding of the electronic structure of redox non-innocent ligands using multiconfigurational methods. He is now expanding his research area to developing density functional methods for the electro-inductive effect, namely fractional charge density functional theory (DFT). Jun-Hyeong earned his BS degree in physics and chemistry from Ulsan National Institute of Science and Technology (UNIST). He later moved to Korea Advanced Institute of Science and Technology (KAIST) to obtain a PhD degree in chemistry under the guidance of Prof. Mu-Hyun (Mookie) Baik. During his PhD studies, he focused on gaining a quantitative understanding of the electronic structure of redox non-innocent ligands using multiconfigurational methods. He is now expanding his research area to developing density functional methods for the electro-inductive effect, namely fractional charge density functional theory (DFT). Photodynamic treatment of acute vascular occlusion by using an iron–nitrosyl complexChoe et al.ChemMarch 15, 2023In BriefSpatiotemporally controllable nitric oxide transporter, iron–nitrosyl complex, was synthesized and precisely characterized by various physicochemical methods, including X-ray crystallography, together with quantum chemical calculations. Normal retinal blood vessels were expanded by the photoreactive iron–nitrosyl complex. Occluded retinal vessels were effectively reperfused by nitric oxide released from the iron–nitrosyl complex via photoreaction in animal disease models. Our strategy demonstrates potential in the treatment option for acute vascular occlusive diseases. Full-Text PDF Open Access

Measurement of the integer and fractional topological charge of optical vortex beams by using crossed blades.

Measurement of the topological charge (TC) of vortex beams, including integer and fractional orbital angular momentum, is of great importance in diverse fields. Here we first investigate the diffraction patterns of a vortex beam from crossed blades with different opening angles and positionings on the beam by a simulation and experiment. Then the positions and opening angles of the crossed blades that are sensitive to the variation of TC are selected and characterized. We show that for a specific position of the crossed blades on the vortex beam, the integer TC can be measured directly by counting the bright spots in the diffraction pattern. Moreover, we show experimentally that for other positions of the crossed blades, by calculating the first-order moment of the intensity of the diffraction pattern, the integer TC between -10 and 10 can be obtained. In addition, this method is used to measure the fractional TC and, as an example, the TC measurement is demonstrated for a range between 1 and 2 with 0.1 steps. The result of the simulation and experiment shows good agreement.

Optically polarized selective transmission of a fractional vector vortex beam by the polarized atoms with external magnetic fields.

We investigate the role of external magnetic fields and linearly polarized pump light, especially when their directions are parallel or vertical, on the propagation of the fractional vector vortex beams (FVVBs) through a polarized atomic system. Herein, the different configurations of external magnetic fields lead to various optically polarized selective transmissions of FVVBs with different fractional topological charge α caused by the polarized atoms, which is theoretically demonstrated by the atomic density matrix visualization analysis and experimentally explored by Cesium atom vapor. Meanwhile, we find that the FVVBs-atom interaction is a vectorial process due to the different optical vector polarized states. In this interaction process, the atomic optically polarized selection property provides potential for the realization of the magnetic compass based on warm atoms. For the FVVBs, due to the rotational asymmetry of the intensity distribution, we can observe some transmitted light spots with unequal energy. Compared with the integer vector vortex beam, it is possible to obtain a more precise magnetic field direction by fitting the different "petal" spots of the FVVBs.

Z_{3} Parafermion in the Double Charge Kondo Model.

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [W. Pouse et al., Nat. Phys. (2023)NPAHAX1745-247310.1038/s41567-022-01905-4] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here, we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a Z_{3} parafermion emerges at the critical point, characterized by a fractional 1/2ln(3) residual entropy, and scattering fractional charges e/3. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.

Theory for Heterogeneous Electron Transfer Kinetics on Nanocorrugated Atomic Stepped Metal Electrodes

We develop a novel mean-field theoretical approach for the outer-sphere heterogeneous electron transfer (OS-HET) rate constant at an atomically stepped nanocorrugated metal surface. Theory accounts for the contributions from the nature of the metal, local curvature of the nanocorrugated atomic step, the density of atomic steps and kinks, dipolar solvents, and the frontier molecular orbital of electroactive molecules. Our theoretical approach develops a novel model for the free energy of activation obtained using the alignment of the Fermi energy level in the metal with one of the frontier molecular orbitals of the electroactive species. The activation free energy is obtained as a product of a modified work function (WF) and the fractional electronic charge of activation for the alignment of levels. Metal surface local curvatures at atomic steps are modeled as a hyperbolic tangent functional with a random nanocorrugated step edge. The influence of step density and edge fluctuations (or kinks) on the activation free energy is included through the surface average mean curvature and the mean-square gradient dependent modified WF. The theoretical results highlight the step density-dependent nonmonotonic variation in WF, fractional electronic charge, and activation free energy. The increase in step density shifts the Fermi energy level toward LUMO and away from HOMO energy levels. This causes the reduced (for the LUMO) and enhanced (for the HOMO) activation free energy for ET kinetics compared to the basal plane. The dichotomy in the OS-HET kinetics at the atomically stepped metal results in anomalous enhancement and suppression for the LUMO and HOMO, respectively. The strong influence of kinks along the step edge on the HET rate constant is predicted up to 6 decades (compared to the basal surface of Pt metal). Finally, theory shows agreement with the reported experimental data of WF and exchange current density for single crystal Pt electrodes.

Revisiting the Low-Index Surfaces of LaCoO3 with a Passivation Strategy

A proper modeling is essential for calculating the surface properties of complex oxides, for example, perovskite oxides. Many studies have shown that traditional selections of slab models, either symmetric or asymmetric ones, may vary the calculated results of the polar surfaces, which will finally affect the perception of surface properties. To solve this issue, we proposed a passivation method to handle the complex polar surfaces, where the pseudo-atoms with fractional charges were used to balance non-zero net charges on one side of the surfaces. Based on this method, we revisited the low-index surfaces of LaCoO3, including (11̅02), (1̅104), and (0001) surfaces, with different terminations. The results suggested that the (11̅02)-LaO, (11̅02)-CoO2, and (0001)-LaO3 terminations were stable surfaces in different O and Co chemical environments. The oxygen vacancy formation energies (EOv) of the (11̅02)-LaO and (11̅02)-CoO2 terminations were also evaluated. Different from the unpassivated cases, the EOv of the passivated LaO and CoO2 terminations converged rapidly when slab thickness increased. The upward shift trend of the EOv after passivation was more consistent with the experimental results. The electronic structure analysis indicated that the oxygen vacancy mainly changed the valence state of the surrounding Co atoms. This work provides a more accurate calculation method, which may benefit the study on catalytic properties of complex oxides.

Fractional Charge Density Functional Theory and Its Application to the Electro-inductive Effect

We employed the chemical potential equalization principle to demonstrate that fractional electrons are involved in the electro-inductive effect as well as the vibrational Stark effect. By the chemical potential model, we were able to deduce that the frontier molecular orbitals of immobilized molecules can provide valuable insight into these effects. To further understand and quantify these findings, we introduced fractional charge density functional theory (FC-DFT), a canonical ensemble approach for open systems. This method allows for the calculation of electronic energies, nuclear gradients, and the Hessian matrix of fractional electronic systems. To correct the spurious delocalization error commonly found in approximate density functionals for small systems, we imposed the Perdew-Parr-Levy-Balduz (PPLB) condition through linear interpolation of two adjacent integer points (LI-FC-DFT). Although this approach is relatively simple in terms of molecular modeling, the results obtained through LI-FC-DFT calculations predict the same trend seen in experimental reactivity and the frequency change of immobilized molecules.

Semi-microscopic Theory for the Current Rectification Phenomenon in Nanogap Molecular Devices.

A semi-microscopic theory is developed for heterogeneous electron transfer (HET) kinetics based on the energy level alignment approach at self-assembled monolayer (SAM) covered metal electrodes. Theory provides the electronic and molecular property-dependent equations for the HET rate constant (k0) and the transfer coefficient (α) for potential. k0 is formulated using the activation free energy as a product of the SAM covered metal work function (WF) and fractional electronic charge exchanged at the transition state (attained through the alignment of the frontier molecular orbital (FMO) energy level of the electroactive group with the WF of metal). k0 is a function of the metal jellium electronic screening length and dielectric and of the molecular self-assembly (through its dipole moment, size, and packing density) and the FMO energies of electroactive groups. The operative potential at the transition state is governed by α, which is a function of molecular spacer length and characteristic electronic-dipolar coupling length. The current rectification phenomenon in nanogap molecular devices is theoretically analyzed using equations for k0 and α for SAM covered source and drain electrodes. Theory unravels the LUMO or HOMO dichotomy for a given metal: (i) for the HOMO assisted ET, the metal with a high WF has a high current rectification ratio (RR), while (ii) for the LUMO assisted ET, the metal with a low WF has a high current RR in asymmetrical devices. Theory predicts the reversal in current rectification by altering the dipole moment of the anchoring molecule, the HOMO/LUMO energy of the electroactive groups, and the nature of the metal. Finally, theory shows qualitative and quantitative coherence with the reported experimental current-potential response of molecular device.

Lattice Mismatch Guided Nickel‐Indium Heterogeneous Alloy Electrocatalysts for Promoting the Alkaline Hydrogen Evolution

AbstractThe immiscibility of crystallographic facets in multi‐metallic catalysts plays a key role in driving the green H2 production by water electrolysis. The lattice mismatch between tetragonal In and face‐centered cubic (fcc) Ni is 14.9 % but the mismatch with hexagonal close‐packed (hcp) Ni is 49.8 %. Hence, in a series of Ni−In heterogeneous alloys, In is selectively incorporated in the fcc Ni. The 18–20 nm Ni particles have 36 wt % fcc phase, which increases to 86 % after In incorporation. The charge transfer from In to Ni, stabilizes the Ni0 state and In develops a fractional positive charge that favors *OH adsorption. With only 5 at% In, 153 mL h−1 H2 is evolved at −385 mV with mass activity of 57.5 A g−1 at—400 mV, 200 h stability at −0.18 V versus reversible hydrogen electrode (RHE), and Pt‐like activity at high current densities, due to the spontaneous water dissociation, lower activation energy barrier, optimal adsorption energy of OH− ions and the prevention of catalyst poisoning.

Lattice Mismatch Guided Nickel-Indium Heterogeneous Alloy Electrocatalysts for Promoting the Alkaline Hydrogen Evolution.

The immiscibility of crystallographic facets in multi-metallic catalysts plays a key role in driving the green H2 production by water electrolysis. The lattice mismatch between tetragonal In and face-centered cubic (fcc) Ni is 14.9 % but the mismatch with hexagonal close-packed (hcp) Ni is 49.8 %. Hence, in a series of Ni-In heterogeneous alloys, In is selectively incorporated in the fcc Ni. The 18-20 nm Ni particles have 36 wt % fcc phase, which increases to 86 % after In incorporation. The charge transfer from In to Ni, stabilizes the Ni0 state and In develops a fractional positive charge that favors *OH adsorption. With only 5 at% In, 153 mL h-1 H2 is evolved at -385 mV with mass activity of 57.5 A g-1 at-400 mV, 200 h stability at -0.18 V versus reversible hydrogen electrode (RHE), and Pt-like activity at high current densities, due to the spontaneous water dissociation, lower activation energy barrier, optimal adsorption energy of OH- ions and the prevention of catalyst poisoning.

Direct Measurement of Acoustic Spectral Density and Fractional Topological Charge

LDOS is a fundamental spectral property that plays a central role in various physical phenomena, such as wave-matter interactions and spontaneous emissions. The role of LDOS in acoustics was uncovered only in recent years and the measurement of acoustic LDOS has not yet been achieved. Here, we report on the direct measurement of the LDOS in acoustic systems. The acoustic LDOS is quantified here through the measurement of the volume flow rate and the acoustic pressure with a local excitation-probe configuration. Based on this method, we detect the LDOS in the one-dimensional acoustic Su-Schrieffer-Heeger model and observe the fractional topological charge of the system. Our work unveils the role of the LDOS in acoustic phenomena and paves the way toward characterizing and tailoring the LDOS in acoustic systems, which holds promise for applications in acoustic emission control, energy localization, and wave-matter interaction.