Spin Character Research Articles

(Invited) Interfacial Coupling between Nanostructures and Molecular Chromophores

The combination of nanostructures with molecular chromophores offers new opportunities to control excited-state photophysics and photochemistry for several potential applications and has fundamental interest for tuning the exciton states that lie at the interface. Semiconductor quantum dots (QDs) are naturally decorated with molecular ligands that can be exchanged for those with tailored properties. We have chosen polyacene ligands with the potential to create and shuttle triplet photoexcited states across the surface of the PbS QDs with tunable rates and efficiencies. Changing the tetracene orientation and packing density with respect to the surface alters the states involved and the rate of energy/charge transfer. The mechanism of this process is unclear, and we present a systematic control of key variables to elucidate the important features of the hybrid system. We find transfer times varying from femtoseconds to nanoseconds, depending on the extent of coupling at the interfaces.Similarly, two-dimensional materials such as transition metal dichalcogenides (TMDCs) can be combined with molecules to provide intimate contact between the two species. The molecular layer can influence the properties of the TMDC, including altering the exciton population and spin-valley relaxation time. Through control of a molecular layer thickness (i.e., vanadyl phthalocyanine) deposited onto monolayer tungsten diselenide (WSe2), we discover that hybrid exciton states undergo ultrafast decoherence if molecular layers are less than 10 nm thick. Thicker layers produce slower spin-valley relaxation, presumably through exciton dissociation that reduces exchange coupling but without hybridization that destroys the initial spin character in the WSe2. We further characterize this effect through temperature dependence and a suite of spectroscopic and structural experiments.

Chiral edge transport along domain walls in magnetic topological insulator nanoribbons

Quantum anomalous Hall insulators are topologically characterized by non-zero integer Chern numbers, the sign of which depends on the direction of the exchange field that breaks time-reversal symmetry. This feature allows the manipulation of the conducting chiral edge states present at the interface of two magnetic domains with opposite magnetization and opposite Chern numbers. Motivated by this broad understanding, the present study investigates the quantum transport properties of a magnetized Bi2Se3 topological insulator nanoribbon with a domain wall (DW) oriented either parallel or perpendicular to the transport direction. Employing an atomistic tight-binding model and a non-equilibrium Green’s function formalism, we calculate the quantum conductance and explore the nature of the edge states. We elucidate the conditions leading to exact conductance quantization and identify the origin of deviations from this behavior. Our analysis shows that although the conductance is quantized in the presence of the horizontal DW, the quantization is absent in the perpendicular DW case. Furthermore, the investigation of the spin character of the edge modes confirms that the conductance in the horizontal DW configuration is spin polarized. This finding underscores the potential of our system as a simple three dimensional spin-filter device.

L -gap surface resonance at Pt(111): Influence of atomic structure, d bands, and spin-orbit interaction

Pt(111) hosts a surface resonance with peculiar properties concerning energy vs momentum dispersion and spin texture. At variance with the free-electron-like behavior of the L-gap Shockley-type surface states on the fcc(111) surfaces of Au, Ag, and Cu, it splits into several branches with distinct spin polarization around the center of the surface Brillouin zone Γ¯. Theoretical predictions based on density-functional theory vary depending on the particular functionals used. To clarify this issue, we investigate the atomic structure of Pt(111) by low-energy electron diffraction and the unoccupied electronic structure by spin- and angle-resolved inverse photoemission. The experimental results are backed by theoretical studies using different functionals, which show that the characteristics of the surface band depend critically on the lattice constant. From the analysis of the energy-dependent low-energy electron diffraction intensities, we derive structural parameters of the Pt(111) surface relaxation with high accuracy. In addition, we give an unambiguous definition of the nonequivalent mirror-plane directions Γ¯M¯ and Γ¯M¯′ at fcc(111) surfaces, which is consistent with band-structure calculations and inverse-photoemission data. Concerning the surface resonance at the bottom of the L gap, we identified a delicate interplay of several contributions. Lattice constant, hybridization with d bands, and the influence of spin-orbit interaction are critical ingredients for understanding the peculiar energy dispersion and spin character of the unoccupied surface resonance. Published by the American Physical Society 2024

Infinite Families of Congruences Modulo 5 for the Number of Irreducible Characters of the Alternating Groups

In 1919, Ramanujan proved red three congruences for the partition function p(n) which denotes the number of partitions of n. The partition function p(n) can be understood as the number of irreducible characters of the symmetric group Sn . Recently, Nath and Sellers, and Xia established a number of congruences modulo 2, 3, and 5 for the numbers of spin characters of S ̂ n and A ̂ n , where S ̂ n and A ̂ n are the double covering group of Sn and the double covering group of the alternating group An , respectively. Motivated by their work, we establish infinite families of congruences modulo 5 for a(n), which denotes the number of irreducible characters of the alternating group An . In particular, we prove some strange congruences modulo 5 for a(n). For example, we prove that for k ≥ 0 , a ( 95 × 73 2 k + 1 24 ) ≡ − 3 k ( mod 5 ) .

Decomposition Matrix for the projective Characters S_28, p=11

In this work, we compute the decomposition matrix to the spin characteristics of S_28 for a given field of characteristic p=11, the connections between the irreducible modular spin characters and the irreducible spin characters of S_28. The technique employed in this study is (r,r ̅ )-inducing, which creates projective characters for S_28 by using the projective characters of S_27. Maple was used to seeing all available columns and then choosing the potentially appropriate columns of them. In order to explore irreducible modular spin characteristics, general correlations and theorems will be discovered as a result of this research.

Characters and spin characters of alternating and symmetric groups determined by values on $l^\prime$-classes

Characters and spin characters of alternating and symmetric groups determined by values on $l^\prime$-classes

Intra-Zero-Energy Landau Level Crossings in Bilayer Graphene at High Electric Fields.

The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.

Decomposition Matrix for the spin Characters,S_25 if the field characteristic is p=7

In this work, we compute decomposition matrix for the spin characters , connected between irreducible spin characters and irreducible modular spin characters, if the field characteristic is 7. The method used in this work is -inducing in a way to generate projective character for by projective character of and used maple program to see all the possible of columns and then choose the possible the right columns of them. The aim of this research is to pave the way for finding general relationships and theorems to study irreducible modular spin characters.

Amyloid Fibers Increase Free Radicals of Synthetic Melanin.

Functional amyloid fibers are crucial in melanogenesis, but their roles are incompletely understood. In particular, their relationship with intrinsic spin characters of melanin remains unexplored. Here, we show that adding an amyloid scaffold greatly augments the spin density in synthetic melanin. It also brings about concurrent alterations in water dispersibility, bandgaps, and radical scavenging properties of the synthetic melanin, which facilitates its applications in solar water remediation and protection of human keratinocytes from UV irradiation. This work provides implications in the unrevealed role of functional amyloid in melanogenesis and in the origin of the superiority of natural melanin toward its synthetic variants in terms of the spin-related properties.

Inducing Single Spin-Polarized Flat Bands in Monolayer Graphene.

Due to the fundamental and technological implications in driving the appearance of non-trivial, exotic topological spin textures and emerging symmetry-broken phases, flat electronic bands in 2D materials, including graphene, are nowadays a relevant topic in the field of spintronics. Here, via europium doping, single spin-polarized bands are generated in monolayer graphene supported by the Co(0001) surface. The doping is controlled by Eu positioning, allowing for the formation of a -valley localized single spin-polarized low-dispersive parabolic band close to the Fermi energy when Eu is on top, and of a π* flat band with single spincharacter when Eu is intercalated underneath graphene. In the latter case, Eu also induces a bandgap opening at the Dirac point while the Eu 4f states act as a spin filter, splitting the π band into two spin-polarized branches. The generation of flat bands with single spin character, as revealed by the spin- and angle-resolved photoemission spectroscopy (ARPES) experiments, complemented by density functional theory (DFT) calculations, opens up new pathways toward the realization of spintronic devices exploiting such novel exotic electronic and magnetic states.

Spin Characters' Decomposition Matrix, S24 modulo, p=7

In this work, we compute decomposition matrix for the spin characters , connected between irreducible spin characters and irreducible modular spin characters, when the field characteristic equal to 7. The method used in this work is -inducing in a way to generate projective character for by projective character of and used maple program to see all the possible of columns and then choose the possible the right columns of them. The aim of this research is to pave the way for finding general relationships and theorems to study irreducible modular spin characters.

Decomposition matrices and Brauer trees of spin characters for S_25 , p=17

In this paper, we will find the Brauer trees and the decomposition matrices of the symmetric groups , when n=25 for p=17 by using -inducing for calculates modular characters from the ordinary characters of the symmetric group. Also, we find all the blocks of defect 0 and 1 and we will depend on the results of the decomposition matrices of the symmetric groups when n=24 for p=17

On the Decomposition Matrix for the Spin Characters S_29 Modulo p=11

Background:
 In this work, we compute the decomposition matrix to the spin (projective) characters of , which is the correlations between the irreducible spin characters and the irreducible modular spin characters of , for a given field characteristic of . We may obtain it by figuring out all irreducible spin characters for , by fixing all bar partitions, as well as all irreducible modular spin characters for , , where we generate projective character for by projective character of and used Maple program to see all the possible of columns to choose the possible the right columns of them. The aim of this study is to pave the way for finding general relationships and theorems to study irreducible modular spin characters.
 Materials and Methods:
 We have used the -inducing to generate projective character by projective character of and Maple program to choose the possible the right columns
 Results:
 We find decomposition matrix to the spin (projective) characteristics of for a given field characteristic of which equals … 
 Conclusions:
 We have conducted multiple studies to get sufficient data to identify new characteristics and theorems if the field characteristic is prime because there is no standard approach for researching the issue, especially when we prove the field and the change of groups. Prior scholars achieved this when they looked at the division matrix in the field where the characteristic is 0, We used the -inducing also, we used Maple programming to view every possible columns.

Spin-dependent polarization and quantum Hall conductivity in decorated graphene: influence of locally induced spin–orbit-couplings and impurities

We study spin transport through graphene-like substrates in the presence of one or several, locally induced spin–orbit coupling (SOC) terms resulting from periodically placed strips, on their top and decorated with a random distribution of impurities. Intrinsic SOC, Rashba SOC and/or pseudo-spin-inversion-asymmetry coupling are considered. A systematic investigation of the spin conductance identifies the main SOC terms which lead to its energy dependence as well as the extent to which the impurity concentration and each SOC term can affect or tune it, In addition, the spin current flow is considered in the presence of different SOC impurities and their related group symmetry such C 6v , C 3v , D 6h and D 3h . Further, we show that the quantum spin-Hall effect (QSHE) related to the spin edge states depends only on the spin character when the PIA and ISO terms are not sublattice resolved, and on both the spin and sublattice character when they are. In addition, we show that the RSO term plays a major role in obtaining edge states that are either protected on both edges or only on one edge against backscattering. This Rashba term creates an anticrosing gap that affects the symmetry in the edge localizations and leads to half-topological states. The results can facilitate the experimental choice of appropriately decorated strips to (i) develop spin-transistor devices by tuning the Fermi energy, (ii) control the robustness of the QSHE against backscattering even in the presence of on-site sublattice asymmetry induced by a transverse electric field or functionalizations, and (iii) provide a strong theoretical support for spintronic quantum devices.

VTaNbAl: A class of spin gapless semiconductors with topological nontrivial features

We report a class of spin gapless semiconductors (SGSs) hosting topological nontrivial features along with a fully compensated ferrimagnetic behavior in VTaNbAl, a quaternary Heusler alloy. Unlike conventional SGSs, this class of compounds acquires a unique band structure with opposite spin characters in the valence and conduction band edges, making them potential candidates for spin valves and a large anomalous Nernst effect. Interestingly, despite compensated ferrimagnetic (CF) behavior, VTaNbAl shows a reasonably large anomalous Hall effect possibly arising from the intrinsic nonvanishing Berry curvature. The CF state breaks the time-reversal symmetry and hence opens the possibility of Weyl nodes. We found four pairs of Weyl nodes located near the Fermi level leading to the nonvanishing Berry curvature, and hence a large anomalous Hall conductivity ($\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$). Our experimental synthesis confirms VTaNbAl to crystallize in a cubic Heusler structure with $A2$-type disorder. A magnetization measurement shows a very small saturation moment ($\ensuremath{\sim}{10}^{\ensuremath{-}3}{\textmu{}}_{B}/\text{f.u.}$), which agrees fairly well with our theoretical findings of fully compensated ferrimagnetism in the alloy. Resistivity shows a metalliclike nature, with the signature of disorder-induced weak localization in the low-temperature limit. The overall variation with varying temperature, however, is extremely weak.

Tunable spin and valley excitations of correlated insulators in Γ-valley moiré bands.

Moiré superlattices formed from transition metal dichalcogenides support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley degree of freedom affects optoelectronic properties in the constituent transition metal dichalcogenides, it has yet to be fully explored in moiré systems. Here we establish twisted double-bilayer WSe2 as an experimental platform to study electronic correlations within Γ-valley moiré bands. Through local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré fillings. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with spin-polaron quasiparticle excitations. In addition, an applied displacement field induces a metal-insulator transition driven by tuning between Γ- and K-valley moiré bands. Our results demonstrate control over the spin and valley character of the correlated ground and excited states in this system.

SL2 quantum trace in quantum Teichmüller theory via writhe

Quantization of the Teichm\"uller space of a punctured Riemann surface $S$ is an approach to $3$-dimensional quantum gravity, and is a prototypical example of quantization of cluster varieties. Any simple loop $\gamma$ in $S$ gives rise to a natural trace-of-monodromy function $\mathbb{I}(\gamma)$ on the Teichm\"uller space. For any ideal triangulation $\Delta$ of $S$, this function $\mathbb{I}(\gamma)$ is a Laurent polynomial in the square-roots of the exponentiated shear coordinates for the arcs of $\Delta$. An important problem was to construct a quantization of this function $\mathbb{I}(\gamma)$, namely to replace it by a noncommutative Laurent polynomial in the quantum variables. This problem, which is closely related to the framed protected spin characters in physics, has been solved by Allegretti and Kim using Bonahon and Wong's ${\rm SL}_2$ quantum trace for skein algebras, and by Gabella using Gaiotto, Moore and Neitzke's Seiberg-Witten curves, spectral networks, and writhe of links. We show that these two solutions to the quantization problem coincide. We enhance Gabella's solution and show that it is a twist of the Bonahon-Wong quantum trace.

Photochemical Upconversion.

Photochemical upconversion is a process whereby two lower-energy photons are converted into a higher-energy photon by sensitized triplet-triplet annihilation. While recent interest in this process has been motivated by improving the efficiencies of solar cells, many applications are being explored. In this review, we address the underlying physicochemical phenomena that are responsible for photochemical upconversion. We review their kinetics, and the requirements for annihilators and sensitizers to design efficient upconversion systems. We discuss the spin physics of the bi-excitonic interactions and how the spin character of the triplet pairs can fundamentally limit the upconversion efficiency and give rise to the magnetic field effect on delayed photoluminescence. Finally, we address light-matter coupling phenomena that could be employed to enhance photochemical upconversion.

The structural, magnetic, and pressure-induced elastic predictions of ZrPd2O4 oxide spinel via GGA, GGA+mBJ, and GGA+U approximations

According to the electronic, structural and magnetic results, ZrPd2O4 oxide spinel was obtained as a magnetic semiconductor material with both up and down spin characters. The different calculation approximations applied have affected the semiconductor band gaps. The largest difference in band gaps was obtained when using the GGA + mBJ approach. The U values applied according to the Coulomb interaction parameters increased the band gaps and equilibrium lattice parameters. While the equilibrium lattice parameter was obtained as 9.16 Å in the GGA approach, the lattice parameter values for U = 1, 2, 3, and 4 eV values were obtained as 9.17 Å, 9.18 Å, 9.19 Å and 9.20 Å, respectively. The energetically most stable state was obtained in the GGA approach. The magnetic moment value of the ZrPd2O4 spinel was calculated as 8.00 µB/cell. The magnetic moment values at the equilibrium lattice point of the Pd, Zr, and O atoms were obtained as 1.301 µB/f.u, 0.0754 µB/f.u. and 0.273 µB/f.u, respectively. ZrPd2O4 oxide spinel is resistant to mechanical deformations according to its elastic properties. The Debye temperature was obtained as 417 K at 0 GPa.

The quantum UV-IR map for line defects in mathfrak{gl} (3)-type class S theories

We consider the quantum UV-IR map for line defects in class S theories of mathfrak{gl} (3)-type. This map computes the protected spin character which counts framed BPS states with spin for the bulk-defect system. We give a geometric method of computing this map motivated by the physics of five-dimensional mathcal{N} = 2 supersymmetric Yang-Mills theory, and compute it explicitly in various examples. As a spin-off we propose a new way of computing a certain specialization of the HOMFLY polynomial for links in ℝ3, as a sum over BPS webs attached to the link.