Degeneracy Breaking Research Articles

Giant Valley Zeeman Splitting in Vanadium-Doped WSe2 Monolayers.

2D dilute magnetic semiconductors (DMS) based on transition metal dichalcogenides (TMD) offer an innovative pathway for advancing spintronic technologies, including the potential to exploit phenomena such as the valley Zeeman effect. However, the impact of magnetic ordering on the valley degeneracy breaking and on the enhancement of the optical transitions g-factors of these materials remains an open question. Here, a giant effective g-factors ranging between ≈-27 and -69 for the bound exciton at 4K in vanadium-doped WSe2 monolayers, obtained through magneto-photoluminescence (PL) experiments is reported. This giant g-factor disappears at room temperature, suggesting that this response is associated with a magnetic ordering of the vanadium impurity states at low temperatures. Ab initio calculations for the vanadium-doped WSe2 monolayer confirm the existence of magnetic ordering of the vanadium states, which leads to degeneracy breaking of the valence bands at K and K'. A phenomenological analysis is employed to correlate this splitting with the measured enhanced effective g-factor. The findings shed light on the potential of defect engineering of 2D materials for spintronicapplications.

Real-time dynamics of angular momentum transfer from spin to acoustic chiral phonon in oxide heterostructures.

Chiral phonons have recently been explored as a novel degree of freedom in quantum materials. The angular momentum carried by these quasiparticles is generated by the breaking of chiral degeneracy of phonons, owing to the chiral lattice structure or the rotational motion of ions of the material. In ferromagnets, a mechanism for generating non-equilibrium chiral phonons has been suggested, but their temporal evolution, which obeys Bose-Einstein statistics, remains unclear. Here we report the real-time dynamics of thermalized chiral phonons in an artificial superlattice composed of ferromagnetic metallic SrRuO3 and non-magnetic insulating SrTiO3. Following the photo-induced ultrafast demagnetization in the SrRuO3 layer, we observed the appearance of a magneto-optic signal in the superlattice, which is absent in the SrRuO3 single films. This magneto-optic signal exhibits thermally driven dynamic properties and a clear correlation with the thickness of the non-magnetic SrTiO3 layer, implying that it originates from thermalized chiral phonons. We use numerical calculations considering the magneto-elastic coupling in SrRuO3 to validate our experimental observations and the angular momentum transfer mechanism between the lattice and spin systems in ferromagnetic systems and also to the non-magnetic system.

Nuclear magnetism in the deformed halo nucleus 31Ne

Based on the point-coupling density functional, the time-odd deformed relativistic Hartree-Bogoliubov theory in continuum (TODRHBc) is developed. The effects of nuclear magnetism on halo phenomenon are explored by taking the experimentally suggested deformed halo nucleus 31Ne as an example. For 31Ne, nuclear magnetism contributes 0.09 MeV to total binding energy, and the breaking of Kramers degeneracy results in a 0 – 0.2 MeV splitting in the canonical single particle spectra. The blocked neutron level has a dominant component of the p wave and is marginally bound. However, if we ignore nuclear magnetism, the level becomes unbound. This shows a subtle mechanism that nuclear magnetism changes the single particle energies, causing a nucleus to become bound. Based on the TODRHBc results, a prolate one-neutron halo is formed around the near-spherical core in 31Ne. The nucleon current is mostly contributed by the halo rather than the core, except near the center of the nucleus. A layered feature in the neutron current distribution is observed and studied in detail.

Cosmology before noon with multiple galaxy populations

Near-future facilities observing the high-redshift universe (2 < z < 5) will have an opportunity to take advantage of “multi-tracer” cosmology by observing multiple tracers of the matter density field: Lyman alpha emitters (LAE), Lyman break galaxies (LBG), and CMB lensing κ. In this work we use Fisher forecasts to investigate the effect of multi-tracers on next-generation facilities. In agreement with previous work, we show that multiple tracers improve constraints primarily from degeneracy breaking, instead of the traditional intuition of sample variance cancellation. Then, we forecast that for both BBN and CMB primary priors, the addition of lensing and LAEs onto a LBG-only sample will gain 25% or more in many parameters, with the largest gains being factor of ∼ 10 improvement for f EDE. We include a preliminary approach towards modelling the impact of radiative transfer (RT) on forecasts involving LAEs by introducing a simplified model at linear theory level. Our results, albeit preliminary, show that while RT influences LAE-only forecasts strongly, its effect on composite multi-tracer forecasts is limited.

Assessing the dark degeneracy through gas mass fraction data

It is well-known that Einstein’s equations constrain only the total energy–momentum tensor of the cosmic substratum, without specifying the characteristics of its individual constituents. Consequently, cosmological models featuring distinct decompositions within the dark sector, while sharing identical values for the sum of dark components’ energy–momentum tensor, remain indistinguishable when assessed through observables based on distance measurements. Notably, it has been already demonstrated that cosmological models with dynamical descriptions of dark energy, characterized by a time-dependent equation of state (EoS), can always be mapped into a model featuring a decaying vacuum (w=−1) coupled with dark matter. We explore the possibility of breaking this degeneracy by using measurements of the gas mass fraction observed in massive and relaxed galaxy clusters. This data is particularly interesting for this purpose because it isolates the matter contribution, possibly allowing the degeneracy breaking. We study the particular case of the wCDM model with its interactive counterpart. We compare the results obtained from both descriptions with a non-parametric analysis obtained through Gaussian Process. Even though the degeneracy may be broken from the theoretical point of view, we find that current gas mass fraction data seems to be insufficient for a final conclusion about which approach is favored, even when combined with SNIa, BAO and CMB.

Exchange-Driven Chern States in High-Mobility Intrinsic Magnetic Topological Insulators.

The layer-dependent Chern number (C) in MnBi_{2}Te_{4} is characterized by the presence of a Weyl semimetal state in the ferromagnetic coupling. However, the influence of a key factor, namely, the exchange coupling, remains unexplored. This study focuses on characterizing the C=2 state in MnBi_{2}Te_{4}, which is classified as a higher C state resulting from the anomalous n=0 Landau levels (LLs). Our findings demonstrate that the exchange coupling parameter strongly influences the formation of this Chern state, leading to a competition between the C=1 and 2 states. Moreover, the emergence of odd-even LL sequences, resulting from the breaking of LL degeneracy, provides compelling evidence for the strong exchange coupling strength. These findings highlight the significance of the exchange coupling in understanding the behavior of Chern states and LLs in magnetic quantum systems.

Multi-tracer power spectra and bispectra: formalism

The power spectrum and bispectrum of dark matter tracers are key and complementary probes of the Universe. Next-generation surveys will deliver good measurements of the bispectrum, opening the door to improved cosmological constraints and the breaking of parameter degeneracies, from the combination of the power spectrum and bispectrum. Multi-tracer power spectra have been used to suppress cosmic variance and mitigate the effects of nuisance parameters and systematics. We present a bispectrum multi-tracer formalism that can be applied to next-generation survey data. Then we perform a simple Fisher analysis to illustrate qualitatively the improved precision on primordial non-Gaussianity that is expected to come from the bispectrum multi-tracer. In addition, we investigate the parametric dependence of conditional errors from multi-tracer power spectra and multi-tracer bispectra, on the differences between the biases and the number densities of two tracers. Our results suggest that optimal constraints arise from maximising the ratio of number densities, the difference between the linear biases, the difference between the quadratic biases, and the difference between the products b 1 b Φ for each tracer, where b Φ is the bias for the primordial potential.

QSym2: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure.

Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, and they are not able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym2 that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym2 is able to address all of these shortcomings. To illustrate these capabilities of QSym2, four sets of case studies are examined in detail in this article: (i) high-symmetry C84H64, C60, and B9- to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)63- to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H3+ to demonstrate the analysis of density symmetries.

Topological-edge-state spin transport in asymmetric three-terminal silicenelike nanodevice

We theoretically investigate the topological-edge-state spin transport in asymmetric three-terminal silicene-like nanodevice. Since silicene-like materials are honeycomb structures with considerable spin-orbit interaction (SOI), they possess both Dirac electron and topology insulator behaviors. In the three-terminal silicene-like nanodevice, the SOI realizes helical edge state and brings fully spin polarization selectively without external field. Firstly, we find that the spin degeneracy breaking gives rise to spin-polarized transport, i.e., up-spin electron and down-spin electron propagating to different leads from the top lead. The distribution of edge-state spin-dependent current in the real space indicates that an up-/down-spin channel to the left/right lead is opened at the interface of the present nanodevice. Secondly, the spin-polarized transport behavior has a competition with the effect of asymmetric transport, which prefers propagating the up- and down-electrons from top lead to the same (right) lead. Interestingly, as the geometric size variation is considered, the results show that the width increase of the horizontal armchair (top vertical zigzag) lead reinforces the spin-polarized (asymmetric) transport. However, when both the armchair and zigzag leads increase simultaneously, the spin-polarized transport becomes the dominant effect. Therefore, this edge-state spin-polarized transport behavior is topologically protected and very robust as the whole geometric size of the nanodevice increases. These properties of the topological-edge-state spin transport enable the asymmetric three-terminal silicene-like nanodevice a spin filter or a spin valve, and might contribute to the silicene-like nanocircuit engineering and spintronics application.

Higher-order multipoles in metaphotonic structures: reviewing symmetric approaches and constructing a comprehensive theoretical method

This research explores localized electric fields in two-dimensional (2D) photonic crystals, focusing on higher-order multipoles. Novel formulas are developed to accurately describe and analyze these complex electromagnetic modes. By considering various crystal element arrangements, we investigate the formation and interactions of electric, magnetic, and toroidal moments. We examine the effects of symmetry on the localized electromagnetic fields in 2D periodic structures and explain how bound states in the continuum (BICs) arise and behave in different symmetry classes. It is important to point out that every singularity point that occurs in multipolar series expansions depends on a BIC point, and it inspires us to study the characteristics of them. Furthermore, we analyze a variety of BICs and use perturbed and degeneracy breaking to investigate high-Q-factor quasi-BICs. The results provide a thorough understanding of how symmetry and multipolar interactions affect potential applications in cutting-edge metasurfaces and photonic devices (metaphotonic).

Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene.

Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes pronounced due to the significant reduction in kinetic energy. In this study, we employ phonon-polariton-assisted near-field infrared imaging to determine the stacking orders of tetralayer graphene devices. Through quantum transport measurements, we observe a range of spontaneous broken-symmetry states and their transitions, which can be finely tuned by carrier density n and electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n = D = 0 with a gap of approximately 15 meV. Increasing D allows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning n and D, we observe isospin-polarized metals, including spin-valley-polarized and spin-polarized metals. These transitions are associated with changes in the Fermi surface topology and are consistent with the Stoner criteria. Our findings highlight the efficient fabrication of specially stacked multilayer graphene devices and demonstrate that crystalline multilayer graphene is an ideal platform for investigating a wide range of broken symmetries driven by Coulomb interactions.

Topological degeneracy breaking in synthetic frequency lattice by Floquet engineering

AbstractSynthetic frequency dimensions provide important opportunities to investigate novel topological phenomena. Previously, many theoretical proposals have been studied and relevant experiments have been performed very recently. However, all these works consider models in the weak modulation regime, where static lattice models are constructed. Here we explore a Floquet Su–Schrieffer–Heeger (SSH) model with time-dependent hoppings in the frequency dimension by dynamically modulating ring resonators ultrastrongly, and find that the topological states, originally degenerate in conventional SSH lattices, are separated in eigenenergies. There exists a series of edge states from band folding at the 0 andπenergy bandgaps, which exhibit complex multi-frequency oscillations due to the inclusion of counter-rotating terms with higher order oscillation frequencies. Such a system with stronger modulations can widen the bandgap and therefore it provides an effective way to localize pulses in synthetic frequency dimensions. Our work shows a photonic platform with the synthetic dimension in exploring exotic Floquet topological phenomena and shows potential applications in optical storage and communications.

Extensive breaking of genetic code degeneracy with non-canonical amino acids

Genetic code expansion (GCE) offers many exciting opportunities for the creation of synthetic organisms and for drug discovery methods that utilize in vitro translation. One type of GCE, sense codon reassignment (SCR), focuses on breaking the degeneracy of the 61 sense codons which encode for only 20 amino acids. SCR has great potential for genetic code expansion, but extensive SCR is limited by the post-transcriptional modifications on tRNAs and wobble reading of these tRNAs by the ribosome. To better understand codon-tRNA pairing, here we develop an assay to evaluate the ability of aminoacyl-tRNAs to compete with each other for a given codon. We then show that hyperaccurate ribosome mutants demonstrate reduced wobble reading, and when paired with unmodified tRNAs lead to extensive and predictable SCR. Together, we encode seven distinct amino acids across nine codons spanning just two codon boxes, thereby demonstrating that the genetic code hosts far more re-assignable space than previously expected, opening the door to extensive genetic code engineering.

Breaking the τT–f degeneracy of the kinetic Sunyaev–Zel’dovich cosmology in redshift space

ABSTRACT The ‘optical depth–linear growth rate’ (τT − f) degeneracy is a long-standing problem in the kinetic Sunyaev–Zel’dovich (kSZ) cosmology. It can be broken in redshift space, where the velocity field leaves its own distinct imprint on the galaxies’ redshift space positions and provides valuable information of the linear growth rate. We validate this idea with the Fisher matrix and Monte Carlo Markov chain techniques in this work, finding that the level of this degeneracy breaking is further enhanced on non-linear scales due to the non-linear evolution of the density and velocity fields, if we have a good prior knowledge of the non-linear bias of galaxies. This result emphasizes the importance of the redshift space analysis of the kSZ effect and its potential as a powerful cosmological probe, especially on non-linear scales. As a by-product, we develop a non-linear model of the redshift space density-weighted pairwise kSZ power spectrum. The fitted f and τT values from this model are shown to be accurate within 1σ–2σ ranges of the fiducial ones when confronted to the mock galaxies mimicking a DESI + CMB-S4 survey combination, even on small scales of k ∼ 0.5h Mpc−1.

Noise canceled graphene-microcavity fiber laser sensor for ultrasensitive gas detection

Optical microcavities offer a promising platform for highly efficient light–matter interactions. Recently, the combination of microresonators and 2D materials in the nanoscale has further enriched the optoelectronics of microcavity geometries, spurring broad advances including lasers, nonlinear converters, modulators, and sensors. Here, we report the concept of compact dual-laser cogeneration in a graphene-microcavity fiber, which offers a way to cancel the optical common mode noises. Driven by a single 980 nm pump, orthogonally polarized laser lines are generated in a pair of degeneracy breaking modes. The two laser lines produce a heterodyne beat note at 118.96 MHz, with frequency noise down to 200 Hz2/Hz at 1 MHz offset, demonstrating a linewidth of 930 Hz in vacuum. This compact device enables on-line and label-free NH3 gas detection with high resolution, realizing a detection limit on a single pmol/L level, and a capability to quantitatively trace gas–graphene interactions. Such a combination of graphene optoelectronics and microcavity photonics demonstrates a novel physical paradigm for microlaser control and offers a new scheme for in situ chemical sensing.

Spin-orbit interactions in plasmonic crystals probed by site-selective cathodoluminescence spectroscopy.

The study of spin-orbit coupling (SOC) of light is crucial to explore the light-matter interactions in sub-wavelength structures. By designing a plasmonic lattice with chiral configuration that provides parallel angular momentum and spin components, one can trigger the strength of the SOC phenomena in photonic or plasmonic crystals. Herein, we explore the SOC in a plasmonic crystal, both theoretically and experimentally. Cathodoluminescence (CL) spectroscopy combined with the numerically calculated photonic band structure reveals an energy band splitting that is ascribed to the peculiar spin-orbit interaction of light in the proposed plasmonic crystal. Moreover, we exploit angle-resolved CL and dark-field polarimetry to demonstrate circular-polarization-dependent scattering of surface plasmon waves interacting with the plasmonic crystal. This further confirms that the scattering direction of a given polarization is determined by the transverse spin angular momentum inherently carried by the SP wave, which is in turn locked to the direction of SP propagation. We further propose an interaction Hamiltonian based on axion electrodynamics that underpins the degeneracy breaking of the surface plasmons due to the spin-orbit interaction of light. Our study gives insight into the design of novel plasmonic devices with polarization-dependent directionality of the Bloch plasmons. We expect spin-orbit interactions in plasmonics will find much more scientific interests and potential applications with the continuous development of nanofabrication methodologies and uncovering new aspects of spin-orbit interactions.

How cation nature controls the bandgap and bulk Rashba splitting of halide perovskites.

Because of instability issues presented by metal halide perovskites based on methylammonium (MA), its replacement to has emerged as an alternative to improve the materials' durability. However, the impact of this replacement on electronic properties, especially gap energy and bulk Rashba splitting remains unclear since electrostatic interactions from organic cations can play a crucial role. Through first-principles calculations, we investigated how organic/inorganic cations impact the electronic properties of and perovskites. Although at high temperatures the organic cation can assume spherical-like configurations due to its rotation into the cages, our results provide a complete electronic mechanism to show, from a chemical perspective based on ab initio calculations at , how the dipoles suppression can reduce the gap energy by promoting a degeneracy breaking in the electronic states from the framework, while the dipole moment reinforcement is crucial to align theory experiment, increasing the bulk Rashba splitting through higher off-centering motifs. The lack of permanent dipole moment in results in polymorphs with a pronounced on-centering-like feature, which causes suppression in their respective bulk Rashba effect.

Time-reversal symmetry adaptation in relativistic density matrix renormalization group algorithm.

In the nonrelativistic Schrödinger equation, the total spin S and spin projection M are good quantum numbers. In contrast, spin symmetry is lost in the presence of spin-dependent interactions, such as spin-orbit couplings in relativistic Hamiltonians. Therefore, the relativistic density matrix renormalization group algorithm (R-DMRG) only employing particle number symmetry is much more expensive than nonrelativistic DMRG. In addition, artificial breaking of Kramers degeneracy can happen in the treatment of systems with an odd number of electrons. To overcome these issues, we propose time-reversal symmetry adaptation for R-DMRG. Since the time-reversal operator is antiunitary, this cannot be simply achieved in the usual way. We introduce a time-reversal symmetry-adapted renormalized basis and present strategies to maintain the structure of basis functions during the sweep optimization. With time-reversal symmetry adaptation, only half of the renormalized operators are needed, and the computational costs of Hamiltonian-wavefunction multiplication and renormalization are reduced by half. The present construction of the time-reversal symmetry-adapted basis also directly applies to other tensor network states without loops.

Band structure for relativistic charge carriers submitted to a helical electric field

We study the relativistic dynamics of electrons submitted to a uniform harmonic electric fields longitudinally applied to the electron velocity. In order to obtain explicitly the set of time-dependent equations for the bi-spinors components, we write down the corresponding Dirac equation for this system. By performing a suitable transformation to this set of equations, we get a matrix equation whose eigenvalues can be found directly. We found analytically the band structure and show a break of degeneracy and the existence of three bands: two total and one partial. The thicker band preventing from the Schwinger mechanisms can be shortened by proper combination of the frequency and amplitude of the applied electric field.

Align, then memorise: the dynamics of learning with feedback alignment* *This article is an updated version of: Refinetti M, D’Ascoli S, Ohana R and Goldt S 2021 Align, then memorise: the dynamics of learning with feedback alignment Proc. 38th Int. Conf. Machine Learning vol 139 ed M Meila and T Zhang pp 8925–35.

Direct feedback alignment (DFA) is emerging as an efficient and biologically plausible alternative to backpropagation for training deep neural networks. Despite relying on random feedback weights for the backward pass, DFA successfully trains state-of-the-art models such as transformers. On the other hand, it notoriously fails to train convolutional networks. An understanding of the inner workings of DFA to explain these diverging results remains elusive. Here, we propose a theory of feedback alignment algorithms. We first show that learning in shallow networks proceeds in two steps: an alignment phase, where the model adapts its weights to align the approximate gradient with the true gradient of the loss function, is followed by a memorisation phase, where the model focuses on fitting the data. This two-step process has a degeneracy breaking effect: out of all the low-loss solutions in the landscape, a network trained with DFA naturally converges to the solution which maximises gradient alignment. We also identify a key quantity underlying alignment in deep linear networks: the conditioning of the alignment matrices. The latter enables a detailed understanding of the impact of data structure on alignment, and suggests a simple explanation for the well-known failure of DFA to train convolutional neural networks. Numerical experiments on MNIST and CIFAR10 clearly demonstrate degeneracy breaking in deep non-linear networks and show that the align-then-memorize process occurs sequentially from the bottom layers of the network to the top.