Fractional Charge Research Articles

Strongly coupled QFT dynamics via TQFT coupling

We consider a class of quantum field theories and quantum mechanics, which we couple to ℤN topological QFTs, in order to classify non-perturbative effects in the original theory. The ℤN TQFT structure arises naturally from turning on a classical background field for a ℤN 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to ℤN TQFT, the non-perturbative expansion parameter is exp[−SI/N] = exp[−8π2/g2N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T3 × {S}_L^1 can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in mathbbm{CP} 1 model, and mass gap for arbitrary θ in mathbbm{CP} N−1, N ≥ 3 on ℝ2.

Unquantized anomalies in topological semimetals

Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial topology in momentum space and crystal symmetry, wherein topological charges may be assigned to point band-touching nodes, preventing gap opening, unless protecting crystal symmetries are violated. These topological charges, however, are defined from noninteracting band eigenstates, which raises the possibility that the physics of topological semimetals may be modified qualitatively by electron-electron interactions. Here we ask the following question: what makes the topological semimetals nontrivial beyond band theory? Alternatively, can strong electron-electron interactions open a gap in topological semimetals without breaking the protecting symmetries or introducing topological order? We demonstrate that the answer is generally no, and what prevents it is their topological response, or quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses are detectable as fractional symmetry charges induced on certain gauge defects. We discuss the cases of type-I Dirac semimetals and time-reversal invariant Weyl semimetals in detail. For type-I Dirac semimetals, we also show that the anomaly vanishes, in a nontrivial manner, if the momenta of the Dirac nodes satisfy certain exceptional conditions.

Electric polarization in inhomogeneous crystals

We derive the charge density up to second order in spatial gradient in inhomogeneous crystals using the semiclassical coarse graining procedure based on the wave packet method. It can be recast as divergence of polarization, whose first-order contribution consists of three parts, a perturbative correction to the original Berry connection expression, a topological part that can be written as an integral of the Chern-Simons 3-form, and a previously-unknown, quadrupolelike contribution. The topological part can be related to the quantized fractional charge carried by a vortex in two-dimensional systems. We then generalize our results to the multiband case and show that the quadrupolelike contribution plays an important role, as it makes the total polarization gauge-independent. Finally, we verify our theory in several model systems.

Multiorbital model reveals a second-order topological insulator in 1H transition metal dichalcogenides

Recently, a new class of second-order topological insulators (SOTIs) characterized by an electronic dipole has been theoretically introduced and proposed to host topological corner states. As a novel topological state, it has been attracting great interest and experimentally realized in artificial systems of various fields of physics based on multisublattice models, e.g., breathing kagome lattice. In order to realize such kind of SOTI in natural materials, we proposed a symmetry-faithful multiorbital model. Then, we reveal several familiar transition metal dichalcogenide (TMD) monolayers as a material family of two-dimensional SOTI with large bulk gaps. The topologically protected corner state with fractional charge is pinned at Fermi level due to the charge neutrality and filling anomaly. Additionally, we propose that the zero-energy corner state is preserved in the heterostructure composed of a topological nontrivial flake embedded in a trivial material. The novel second-order corner states in familiar TMD materials hold promise for revealing unexpected quantum properties and applications.

Machine learning based accurate recognition of fractional optical vortex modes in atmospheric environment

Optical vortex beam with fractional orbital angular momentum (OAM) has great potential to increase the capacity of optical communication and information processing in classical and quantum regimes. However, atmospheric turbulence (AT) in free space distorts the helical phase-front of vortex beams and causes the mode diffusion, seriously hindering the practical application. Herein, using a convolutional neural network approach with an improved residual neural network architecture, we overcome the hurdle to give the accurate recognition of the fractional OAM in the AT. As demonstrated on the petal interference patterns, a type of hybrid beams carrying double OAM modes is utilized to provide two controllable degrees of freedom for greater recognition of more subtle OAM modes, e.g., the fractional topological charge number l and the angular ratio n. Our studies show that with various l and n, the recognition accuracy of OAM over 20 000 images is as high as 85.30% even under the strong AT parameter (Cn2 = 5 × 10−14 m−2/3) and the long propagation distance (z = 1500 m). Our findings represent a remarkable achievement toward highly accurate recognition of fractional OAM with broad bandwidth in the atmospheric environment, expanding the applications for the general interest of machine learning based OAM optical communication.

Density Functional Calculations Based on the Exponential Ansatz.

This work explores the application of the singles-based exponential ansatz to density functional calculations. In contrast to the standard approach where Kohn-Sham (KS) orbitals are determined prior to computing molecular quantities of interest, we consider the single-reference Hartree-Fock wave function as a starting point. Applying the exponential ansatz to this single reference gives an auxiliary wave function that is employed to calculate the electronic properties of the system. This wave function is determined self-consistently through the standard KS Hamiltonian but evaluated over the Hartree-Fock molecular orbital basis. By using spin-symmetry breaking, we recover size-consistent results free of unphysical fractional charges in the dissociation limit. Our method shows consistency with standard KS density functional calculations when the system geometry is similar to the equilibrium one or in repulsive configurations. For moderately long distances between atoms, not at dissociation, because of self-interaction the exponential ansatz may give instabilities in the form of large cluster amplitudes. To avoid these, this work introduces a relatively simple regularization method that preserves size-consistency and penalizes high amplitudes of the cluster operator, whereas the results remain physically meaningful. We also present the time-dependent extension of our theory and show that it can feature quantum states where multiple electrons are excited.

Evaluation the potential of carboxyl functionalized BC2N nanotubes as a drug delivery vehicle for chlormethine anti-cancer drug

Today, a new biomedical application of various nanomaterials is the utilization of them as drug delivery systems (DDSs) for several anti-cancer medicines to decrease their problems by carrying them to the target tumor cell zone. In the recent project, we have studied the efficiency of the pristine BC2NNTs and functionalized BC2NNTs as a DDS for chlormethine (CM) anti-cancer drug applying the density functional theory B3LYP/6-31G (d, p). It was detected that CM interacted weakly with the pristine BC2N nanotubes (−13.60 kcal mol−1). Therefore, the functionalized BC2NNTs were studied for CM interaction. In comparison to pristine BC2NNTs, in the adsorption and stabilization of the investigated compounds as well as their thermodynamic energy, our computations revealed that H bonds between active positions of carboxyl functionalized BC2NNTs and CM were the key factors. The fractional charge transfer, molecular electrostatic potential, and natural bond orbital analyses showed a considerable charge transfer from CM drug to the functionalized BC2NNTs. In addition, it was discovered to be stable in aqueous environments with amounts for solvent energies, which is appropriate for CM drug delivery uses. This project proposes a novel plan to achieve a high-density CM drug on the BC2NNTs’ surfaces.

The capability of boron carbide nanotube as a nanocarrier for fluorouracil anticancer drug delivery; DFT study

Various nanostructures are investigated mainly to discover their potential applications in drug delivery for cancer treatment. In fact, the delivery of anti-cancer drugs to specific tumour cells leads to the reduction of adverse side effects. In the present study, the capability of the pure NC3 carbon-like nanotube (NC3NT) for the drug delivery of an anti-cancer drug, Fluorouracil (5FU), was evaluated by performing the density functional theory calculations (B3LYP-D3/6-31G (d, p) level of theory). Based on our calculations, the energy of adsorption (Eads) for 5FU@NC3NT structures is approximately −20.88 in the gas phase and −34.91 kcal mol−1 in the aqueous phase. Also, energies of adsorption in the solvent phase, which have negative values, indicated that not only the solubility of the nanotubes enhanced but also the interaction between these nanostructures and the drug was changed in a solvent medium. Furthermore, a considerable transfer of charge was detected from the 5FU molecules to the surface of the NC3NT via natural bond orbital (NBO) and fractional charge transfer studies. Moreover, based on the UV–visible investigations, a shift toward smaller wavelengths (∼23 nm) with a blue color was observed in the electronic spectra of the drug\ anostructure structures. Therefore, according to the calculations performed in this study, the NC3NT could be employed as a suitable carrier for delivering 5FU.

Higher-order topological phases in tunable C3 symmetric photonic crystals

We demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods. By tuning a single geometry parameter, the photonic corner and edge states emerge or disappear with higher-order topological transitions. Two distinct higher-order topological insulator phases and a normal insulator phase are revealed. Their topological indices are obtained from symmetry representations. A photonic analog of the fractional corner charge is introduced to distinguish the two higher-order topological insulator phases. Our predictions can be readily realized and verified in configurable dielectric photonic crystals.

Angular momentum of the vortex ultrashort pulsed beam with a smaller beam waist.

The angular momentum (AM) of light has important implications for many fields of optics research, such as optics communication, quantum information and laser-scan microscopy. Thus, in this paper, we intend to investigate the average AM of the vortex ultrashort pulsed beam (VUPB), which is generated and widely applied in the field of high-intensity and ultrafast regimes. According to the vector potential, we firstly derive the electromagnetic field of the VUPB, then analyze the spatial intensity, the phase profile and the polarization state of the beam. We explore that the total AM per photon of VUPB is not n ℏ value when the beam waist w0 is of wavelength or sub-wavelength order, since the polarization of VUPB is changed from linear to circular polarization with the decrease of beam waist, which introduces the conversion of the orbital AM to the spin AM. Moreover, based on the conservation of the total AM, the minimum waist of VUPB can be obtained, which is dependent on the pulse duration time α and topological charge n. Finally, the average AM of the fractional VUPB expressed by the superposition of the integer VUPB with different weights, is analyzed, which is not equal to the AM of fractional CW beam μ - sin (2μπ)/2π (μ is the fractional topological charge), but is associated with the beam waist w0 and α. Therefore, we think that the AM of VUPB can be controlled by adjusting the α and w0.

NC3 carbon-like nanotube as promising nanocarriers for anticancer drugs delivery; density functional theory studies

One of the widespread applications of nano-materials which is currently investigated is in drug delivery vehicles for various anticancer drugs for reducing their serious side effects which is usually done through their transportation into targeted tumor cells. In this study, the performance of a pristine NC3 carbon-like nanotube (NC3NT) was scrutinized as a vehicle to deliver 5-aminosalicylic acid (5-ASA) through density functional theory (DFT) at B3LYP-D3 theory level with 6-31G (d, p) basis set. The adsorption energies (Eads) for the ASA@NC3NT complexes were approximately −18.62 in the gas phase whereas they were approximately 29.73 kcal mol−1 in the water phase. The more negative Ead values in the solvent phase show that the NC3NT has the ability to enhance the solubility of 5-ASA and change the interaction between them in the aqueous phase. Based on fractional and NBO charge transfer analyses, the charge transport from the 5-ASA molecules to the surface of the NC3NT is significant. Moreover, the electronic spectra related to the ASA/NC3NT complexes have a blue shift towards shorter wavelengths of approximately 19 nm based on the ultraviolet–visible analysis. We can conclude, based on our calculations, that the above-mentioned nanotube could be employed as a vehicle for delivering 5-ASA.

Nonlinear control of photonic higher-order topological bound states in the continuum

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

Anomaly indicators and bulk-boundary correspondences for three-dimensional interacting topological crystalline phases with mirror and continuous symmetries

We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases that are protected by the mirror symmetry and continuous symmetries that form a group of $U(1)$, $SU(2)$ or $SO(3)$. In particular, the fermionic cases correspond to a crystalline version of 3D topological insulators and topological superconductors in the famous ten-fold-way classification, with the time-reversal symmetry replaced by the mirror symmetry and with strong interaction taken into account. For surface SETs, the most general interplay between symmetries and anyon excitations is considered. Based on the previously proposed dimension reduction and folding approaches, we re-derive the classification of bulk SPT phases and define a \emph{complete} set of bulk topological invariants for every symmetry group under consideration, and then derive explicit expressions of the bulk invariants in terms of surface topological properties (such as topological spin, quantum dimension) and symmetry properties (such as mirror fractionalization, fractional charge or spin). These expressions are our quantitative bulk-boundary correspondences. Meanwhile, the bulk topological invariants can be interpreted as \emph{anomaly indicators} for the surface SETs which carry 't Hooft anomalies of the associated symmetries whenever the bulk is topologically non-trivial. Hence, the quantitative bulk-boundary correspondences provide an easy way to compute the 't Hooft anomalies of the surface SETs. Moreover, our anomaly indicators are complete. Our derivations of the bulk-boundary correspondences and anomaly indicators are explicit and physically transparent.

Phase interference for probing topological fractional charge in a BiSbTeSe2-based Josephson junction array

Fractional charges can be induced by magnetic fluxes at the interface between a topological insulator (TI) and a type-II superconductor due to axion electrodynamics. In a Josephson junction array with a hole in the middle, these electronic states can have phase interference in an applied magnetic field with period, in addition to the 2π interference of the Cooper pairs. Here, we test an experimental configuration for probing the fractional charge and report the observation of phase interference effect in superconducting arrays with a hole in the middle in both Au- and TI-based devices. Our numerical simulations based on resistive shunted capacitive junction model are in good agreement with the experimental results. However, no clear sign of an axion charge-related interference effect was observed. We will discuss possible reasons and perspectives for future experiments.

Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors $\nu=1/(2l+1)$, where $l$ is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has $2l+1$ different branches that cannot be connected adiabatically, reflecting the $(2l+1)$-fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.

Exact Second-Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory.

We develop a second-order correction to commonly used density functional approximations (DFAs) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are a highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum, and photoexcitation energies beyond previous approximate second-order approaches, thus showing potential for broad applications in computational spectroscopy.

Quasi-stable fractional vortex solitons in nonlocal nonlinear media

This paper studied the propagations of fractional vortex beams in nonlocal nonlinear media, and found that quasi-stable solitons can form when the nonlocality is strong enough and the initial power is equal to the critical power. The propagation properties, including intensity patterns, phase structures, transverse energy flows, and rotation period, were all investigated. The critical power of solitons with different topological charges is the same, however, the orbital angular momentum (OAM) of that increases with the increase of fractional topological charge. In addition, we revealed that fractional vortex solitons have lateral shifts in the y-direction, and the shift values can be controlled by the fractional topological charge. Obviously, the quasi-stable fractional vortex solitons have important academic value and potential application to optical switches, optical wrenches and optical communications, etc.

Quasiparticle states for integer- and fractional-charged electron wave packets

It is well-known that Lorentzian voltage pulses with integer quantum flux can lead to noiseless current in quantum conductors. The current is carried by charged quasiparticles in the Fermi sea of the conductors, which have well-defined wave functions and have been named as "levitons". However, it is not clear how levitons evolve as the flux of the pulses changes continuously toward a fractional value. To answer this question, we introduce a set of Wannier-like single-body wave functions, which can be used to describe the quantum states of the quasiparticles injected by Lorentzian pulses with arbitrary flux. We show that, by tuning the flux of the pulses, levitons can evolve into quasiparticles carrying fractional charges. In the meantime, additional fractional-charged quasiparticles can also be excited, which can form neutral electron-hole pairs. The information of these quasiparticles can be extracted from the shot noise of the current. These knowledge can be helpful for the time-resolved quantum control of propagating electrons in solid-state circuits.

Charge Oscillations in Quantum Spin Hall Constrictions

Constrictions between 1D helical edge states represent a useful tool for the realization of devices based on topological materials. Indeed, they complement superconductivity and magnetic barriers as gaps allowing to enlarge the functionalities of topological nanostructures. Recent experiments point to the direction that electronic interactions are not negligible in such systems. Herein, the interaction‐induced oscillations of the local electronic density at constrictions between helical edges are theoretically inspected. The system is in the quantum dot configuration thanks to magnetic barriers. By means of bosonization, it is shown that the fractional charge oscillations, predicted for single edges, can persist. On top of that, oscillations involving both edges and with different wave vectors can appear. It is argued that the dominant oscillation can be discriminated by varying the angle of magnetization of the barriers, thus providing information about the dominant interaction mechanisms.

Fractionally charged anyons generated by topological path fusion of propagating electron in magnetic flux lattice

Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.