Degenerate Levels Research Articles

Gauge Field Induced Chiral Zero Mode in Five-Dimensional Yang Monopole Metamaterials.

Owing to the chirality of Weyl nodes characterized by the first Chern number, a Weyl system supports one-way chiral zero modes under a magnetic field, which underlies the celebrated chiral anomaly. As a generalization of Weyl nodes from three-dimensional to five-dimensional physical systems, Yang monopoles are topological singularities carrying nonzero second-order Chern numbers c_{2}=±1. Here, we couple a Yang monopole with an external gauge field using an inhomogeneous Yang monopole metamaterial and experimentally demonstrate the existence of a gapless chiral zero mode, where the judiciously designed metallic helical structures and the corresponding effective antisymmetric bianisotropic terms provide the means for controlling gauge fields in a synthetic five-dimensional space. This zeroth mode is found to originate from the coupling between the second Chern singularity and a generalized 4-form gauge field-the wedge product of the magnetic field with itself. This generalization reveals intrinsic connections between physical systems of different dimensions, while a higher-dimensional system exhibits much richer supersymmetric structures in Landau level degeneracy due to the internal degrees of freedom. Our study offers the possibility of controlling electromagnetic waves by leveraging the concept of higher-order and higher-dimensional topological phenomena.

Full counting statistics and coherences: Fluctuation symmetry in heat transport with the unified quantum master equation.

Recently, a "unified" quantum master equationwas derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan form. This equationdescribes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the unified quantum master equationto investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equationgives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the unified equation is simultaneously thermodynamically consistent and more accurate than the fully secular master equation. We exemplify our results for a "V" system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the unified equationto those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential to properly capture the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.

Ideal unconventional charge-2 Dirac fermions in an ultralightweight chiral crystal

When topology meets chirality, it is of great interest to search for possible topological properties in chiral crystals, thereby achieving the effect of making $1+1$ greater than 2. Here, we accomplish a complete list of topological charge-2 (C-2) Dirac fermions based on 65 S\"ohncke space groups. Such emergent fermions occurring in chiral crystals enjoy a higher topological charge number and exhibit more unique characteristics compared to C-0 cases, including multiple Fermi arcs extending to most of the Brillouin zone. For material realization, we propose that an ultralightweight chiral crystal ${\mathrm{N}}_{4}\mathrm{Cl}$ is a high-quality C-2 Dirac semimetal, where the seductive nodal points reside at the Fermi level and exhibit a large linear energy range to overcome the interruption of irrelevant bands. More interestingly, the doubly degenerate Landau levels are described by a Kramers-like degeneracy in such a C-2 Dirac fermion, featuring a doubly degenerate zero mode. Furthermore, the topological phase transitions from Dirac to Weyl states of ${\mathrm{N}}_{4}\mathrm{Cl}$ can be manipulated by applying shear strains. These fascinating findings will certainly evoke continued exploration of unconventional Dirac semimetals, in turn leading to extensive application prospects and uncommon insights.

Degenerate p-Type and n-Type Doping of Diamane by Molecular Adsorption

Motivated by the successful synthesis of two-dimensional diamane [Nat. Nanotechnol. 2020, 15, 59-66], in this work, the electronic and optical properties of diamane with molecular adsorption are investigated by first-principles calculation. Based on the surface transfer doping mechanism, we report the degenerate p-type and n-type doping for hydrogenated diamane (H-diamane) and fluorinated diamane (F-diamane), respectively. Hole accumulation on H-diamane and degenerate levels in the density of states (DOS) are found when organic molecules (tetracyanoethylene, tetracyanoquinodimethane, and tetrafluorotetracyanoquinodimethane) and transition-metal oxides (MoO3, CrO3, WO3, V2O5, and ReO3) are chosen as acceptors on H-diamane. Conversely, F-diamane shows electron accumulation and degenerate levels in DOS when organic molecules (decamethylcobaltocene and cobaltocene2) are adsorbed. The carrier concentration values of H-diamane and F-diamane are 1.91 × 1013 to 3.96 × 1013 cm–2 and 1.96 × 1013 to 3.38 × 1013 cm–2, respectively. After adsorption, the optical absorption increases significantly in the visible-light region. Our findings would provide a feasible route to modulate the electronic and optical properties of diamane.

Impurity effects on the zeroth pseudo-Landau level in twisted bilayer graphene

We theoretically study the impurity effects on the zeroth pseudo-Landau level (PLL) representation of the flat band in a twisted bilayer graphene (TBG) system. Our research investigates the impact of both short-range and long-range charged impurities on the PLL using the self-consistent Born approximation and random phase approximation. Our findings indicate that short-range impurities have a significant effect on the broadening of the flat band due to impurity scattering. In contrast, the impact of long-range charged impurities on the broadening of the flat band is relatively weak, and the primary impact of the Coulomb interaction is the splitting of the PLL degeneracy when a certain purity condition is satisfied. As a result, spontaneous ferromagnetic flat bands with nonzero Chern numbers emerge. Our work sheds light on the effect of impurities on the quantum Hall plateau transition in TBG systems.

Spectral properties of size-invariant shape transformation.

Size-invariant shape transformation is a technique of changing the shape of a domain while preserving its sizes under the Lebesgue measure. In quantum-confined systems, this transformation leads to so-called quantum shape effects in the physical properties of confined particles associated with the Dirichlet spectrum of the confining medium. Here we show that the geometric couplings between levels generated by the size-invariant shape transformations cause nonuniform scaling in the eigenspectra. In particular, the nonuniform level scaling, in the direction of increasing quantum shape effect, is characterized by two distinct spectral features: lowering of the first eigenvalue (ground-state reduction) and changing of the spectral gaps (energy level splitting or degeneracy formation depending on the symmetries). We explain the ground-state reduction by the increase in local breadth (i.e., parts of the domain becoming less confined) that is associated with the sphericity of these local portions of the domain. We accurately quantify the sphericity using two different measures: the radius of the inscribed n-sphere and the Hausdorff distance. Due to Rayleigh-Faber-Krahn inequality, the greater the sphericity, the lower the first eigenvalue. Then level splitting or degeneracy, depending on the symmetries of the initial configuration, becomes a direct consequence of size invariance dictating the eigenvalues to have the same asymptotic behavior due to Weyl law. Such level splittings may be interpreted as geometric analogs of Stark and Zeeman effects. Furthermore, we find that the ground-state reduction causes a quantum thermal avalanche which is the underlying reason for the peculiar effect of spontaneous transitions to lower entropy states in systems exhibiting the quantum shape effect. Unusual spectral characteristics of size-preserving transformations can assist in designing confinement geometries that could lead to classically inconceivable quantum thermal machines.

Persistent currents, revival time and effects of rotation on an attractive inverse-square-type potential in a magnetic quadrupole moment system

We study the appearance of an Aharonov–Bohm-type effect around a cylindrical cavity in a magnetic quadrupole moment system in a rotating reference frame. The analogue of the Aharonov–Bohm-type effect of bound states arises from the interaction of the magnetic quadrupole moment of a neutral particle with an induced electric field when the neutral particle is subject to an attractive inverse-square-type potential, which in turn stems from the interaction of the magnetic quadrupole moment of a neutral particle with a magnetic field. We also discuss how the effects of rotation modify the degeneracy of the energy levels in contrast to the case of absence of rotation. Besides this, we calculate the revival time and the persistent currents.

The effect of energy level degeneracy on symmetry-breaking charge transfer: Excited octupolar dyes.

A three-level model of symmetry-breaking charge transfer (SBCT) in excited octupolar molecules is developed. The model describes the joint dynamics of the solvent and the dye in the excited state. For this, a distribution function in the space of two reaction coordinates is introduced. An evolution equation of this function is derived. A strict definition of the reaction coordinates is given, and its dynamic characteristics are determined. The free energy surface in the space of these coordinates is calculated. To quantify the symmetry-breaking degree, a two-dimensional dissymmetry vector is introduced. The model predicts the absence of SBCT in apolar solvents and an abrupt increase in its degree to half the maximum value in weakly polar solvents. The dye dipole moment is revealed to be directed along a molecular arm independently of the direction and the strength of the electric field of the solvent created by its orientational polarization. The conditions for the occurrence and nature of this effect are discussed. The effect of the degeneracy of excited states, which is inherent in octupolar dyes in the excited state, on SBCT is revealed. Degeneracy of energy levels is shown to lead to a significant increase in the symmetry-breaking degree. The effect of SBCT on the dependence of the Stokes on the solvent polarity is calculated and compared with the available experimental data.

Quantum heat engine with identical particles and level degeneracy

In this paper, the effects of identical particles and energy-level degeneracy on the work output of the quantum Otto and Stirling heat engines are studied. For quantum Otto heat engine, we find the effects of degeneracy in the ground state and in the excited state are same in the high-temperature limitation while the work done by a system with n-fold degeneracy in the excited state (ground state) is n ([Formula: see text]) times the one without degeneracy in the single-particle case. Moreover, the effects of the identical two-level systems with degeneracy in the ground state or excited state as working substances are discussed. The results of such problem for the Stirling and Carnot heat engines are similar. By analytical derivations in two limit conditions, we conclude that for the cycles which are composed of the quantum adiabatic process, isochoric process and isothermal process have similar results.

Modification of Landau Levels in a 2D Ring Due to Rotation Effects and Edge States

AbstractThe properties of a 2D quantum ring under rotating and external magnetic field effects are investigated. The Landau levels and their inertial effects on them are initially analyzed. Among the results obtained, it is emphasized that the rotation lifted the degeneracy of Landau levels. The second part deals with the electronic confinement in a 2D ring modeled by a hard wall potential. The eigenstates are described by Landau states as long as they are not too close to the ring edges. On the other hand, near the ring edges, the energies increase monotonically. These states are known as edge states. Edge states have a significant role in the physical properties of the ring. Thus, the Fermi energy and magnetization are analyzed. In the specific case of magnetization, two approaches are considered. In the first approach, an analytical result for magnetization is obtained but without considering rotation. Numerical results show the de Haas‐Van Alphen (dHvA) oscillations. In the second approach, rotating effects are considered. In addition to the dHvA oscillations, the Aharonov–Bohm‐type (AB) oscillations are verified, which are associated with the presence of edge states. The effects of rotation on the results are discussed and it is found that rotation is responsible for inducing AB oscillations.

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

In this work, we obtain solutions of the deformed Schrödinger equation (DSE) with improved internal energy potential at a finite temperature model in a 3-dimensional nonrelativistic noncommutative phase-space (3D-NRNCPS) symmetries framework, using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). The modified bound state energy spectra are obtained for the heavy quarkonium system such as charmonium cc- and bottomonium bb- at finite temperature. It is found that the perturbative solutions of the discrete spectrum are sensible to the discreet atomic quantum numbers (j,l,s,m) of the ( QQ- (Q=c,b)) state, the parameters of internal energy potential (T,αs(T), mD (T),β,c), which are the Debye screening mass mD (T), the running coupling constant αs(T) the critical temperature β, the free parameter c in addition to noncommutativity parameters (Θ,θ-). The new Hamiltonian operator in 3D-NRNCPS symmetries is composed of the corresponding operator in commutative phase-space and three additive parts for spin-orbit interaction, the new magnetic interaction, and the rotational Fermi-term. The obtained energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium systems (cc- and bb-). The total complete degeneracy of the new energy levels of the improved internal energy potential changed to become equal to the new value 3n2 in 3D-NRNCPS symmetries instead of the value n2 in the symmetries of 3D-NRQM. Our non-relativistic results obtained from DSE will possibly be compared with the Dirac equation in high-energy physics.

Enhancement of Valley Polarization in Monolayer WSe2 Coupled with Microsphere‐Cavity‐Array

AbstractMonolayer transition metal dichalcogenides (ML‐TMDCs) possess degenerate levels with antiparallel spins in K and K′ valleys, providing the intrinsic valley polarization, which attracts great interest for potential applications on quantum information technology and on‐chip nanophotonics. Unfortunately, it is difficult to distinguish the degree of valley polarization (DoP) near room temperature due to the intensive phonon‐assisted intervalley scattering and the long‐range electron‐hole exchange interaction in ML‐TMDCs, limiting their practical applications. In this study, a novel design is proposed for great promotion of DoP in ML‐WSe2 with a microsphere cavity array, introducing Purcell effect and nanofocusing effect into the system. The radiative decay rate is dramatically enhanced owing to Purcell effect in microcavity in weak coupling regime, thus locking more polarized excitons in the corresponding valley under certain circularly‐polarized pumping. In addition, the nanofocusing effect contributes to increasing the number of charged excitons by suppressing the bright to dark exciton conversion. The present work achieves a great DoP of ML‐WSe2 with a simple configuration and promises broad applications from valleytronic devices to chiral optics in the future.

Density Functional Theory Search of 3d Transition Metal Complexes in Diamond for Quantum Sensing Applications

Optically addressable defects in wide‐bandgap semiconductors are of considerable interest as materials platforms for quantum sensing and information systems. Density functional theory is used to identify novel defects in diamond consisting of transition metal + nitrogen complexes with potential for quantum sensing. Defects are characterized with respect to formation energy, ordering and degeneracy of the defect energy levels, optical and charge transition energies, zero‐field‐splitting energies, and thermodynamic stability. Novel defect sites with optically addressable spin states and viable spin sublevel configurations are identified, and analysis of activation energies for atomic migration indicates stability in the lattice.

A New Model to Describe Quarkonium Systems under Modified Cornell Potential at Finite Temperature in pNRQCD

In the present work, the three-dimensional modified radial Schrödinger equation is analytically solved. The nonrelativistic interactions under new modified Cornell potential (NMCP, in short) at finite temperature, are extended to the symmetries of nonrelativistic noncommutative space phase (NRNSP, in short), using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). W generalize this process by adding multi-variable coupling potentials , and together with the modified Cornell potential model in three-dimensional nonrelativistic quantum mechanics noncommutative phase space (3D-NCSP, in short). The new energy eigenvalues and the corresponding Hamiltonian operator are calculated in 3D-NCSP symmetries instead of solving the modified Schrödinger equation with the Weyl Moyal star product. The present results, in (3D-NCSP), are applied to the charmonium and bottomonium masses at finite temperature. The present approach successfully generalizes the energy eigenvalues at finite temperature in 3D-NCSP symmetries. It is found that the perturbative solutions of the discrete spectrum and quarkonium mass can be expressed by the Gamma function, the discreet atomic quantum numbers of the state and the potential parameters ( ), in addition to noncommutativity parameters ( and ). The total complete degeneracy of new energy levels of NMCP changed to become equals to the value instead the values in ordinary quantum mechanics. Our obtained results are in good agreement with the already existing literature in NCSP. Keywords: Schrödinger Equation, Heavy Quarkonium System, Cornell Potential, Noncommutative Space Phase, Bopp’s Shift Method. Subject Classification Numbers: 03.65.-w; 03.65.Ge; 03.65. Fd; 03.65.Ca

Hydrogen states described by solutions of the Dirac equation: Role of spinor invariants

The solution of the Dirac equation with the Coulomb potential is used to analyze bound electron states in a hydrogen atom. The analysis is based on the fact that such states are characterized by a set of quantum numbers which describe definite values of the complete set of physical quantities that can be determined simultaneously. This set includes the energy, square of the total angular momentum, one of its component and a spinor invariant. The latter, spinor invariant gives two-valued quantum number which determines the sign of its eigenvalue. In addition to the known Dirac and Johnson–Lippman invariant, there exists a new one. Operators of these three spinor invariants do not commute between themselves which results in the degeneracy of the energy levels with respect to the two-valued quantum number. Three different systems of the eigenbispinor corresponding to the three spinor invariants are obtained and the generalized solution with free parameters is calculated. Variation of the free parameters transforms one particular solution into any other. It is shown that the electron probability densities and spin polarizations in an electron cloud depend essentially on the invariant set, demonstrating physical difference of the states corresponding to different spinor invariants.

Summary of the Basic Free Electron Transport Characteristics in Donor Doped Silicon

A present summary is assigned to present the transport characteristics of the free randomly moving (RM) electrons in silicon at any doping level by phosphorous donors. The application of the Fermi-Dirac statistics and stochastic description of the free RM electrons lead to obtaining the general expressions of conductivity, the effective density of the free RM electrons, their diffusion coefficient and the drift mobility, which are valid for silicon with any doping level. It is shown that drift mobility of the free RM electrons considerably exceeds the Hall mobility at heavy doping, and that the Einstein relation is fundamental and is conserved at any level of degeneracy. It is estimated what part of electrons in the conduction band of heavily doped silicon is not free and is coupled with phosphorous ions. The main conclusions and formulations can be applicable for holes in acceptor-doped silicon, and other homogeneous materials with one type of the free RM charge carriers as well.

Frustrated mixed-spin ladders: Evidence for a bond-order wave phase between rung-singlet and Haldane phases

In frustrated spin ladders the interplay of frustration and correlations leads to the familiar Haldane (H) and rung-singlet (RS) phases. The nature of the transition between these two phases is still under debate. In this paper we tackle this issue using tools of quantum information theory. We consider frustrated mixed-spin-(1, 1/2) ladders with antiferromagnetic leg, rung and diagonal couplings, and calculate various quantities, such as the entanglement entropy (EE), the Schmidt gap, and the level degeneracy of the entanglement spectrum (ES). We use two numerical techniques, the infinite time-evolving block decimation (iTEBD) and the density matrix renormalization group (DMRG). We demonstrate that there exists an intermediate phase in which the ES levels do not exhibit the characteristic degeneracies of the H and RS phases. To understand the underlying physics in this phase, we investigate short-range spin correlations along legs, rungs and diagonals and show that in this intermediate phase long-wavelength modulations occur, akin to bond order waves.

Double-Λ electromagnetically induced transparency with degenerate atomic levels

The general expression for the transformation matrix of the two input weak arbitrarily polarized probe fields passing through the medium under the conditions of double-Λ electromagnetically induced transparency is obtained for arbitrary values of the amplitudes, phases and polarizations of the control fields and arbitrary values of the angular momenta of resonant levels. The conditions are found for the two input weak probe fields linearly polarized in perpendicular planes to exchange their polarizations after the passage through the medium without absorption. The polarization rotation of the probe fields is studied for the atoms being initially in the equilibrium state.

Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, g mu _B B, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in nu for the R_{xx} minimum, e.g., from nu = 11/7 to nu = 8/5, and a corresponding change in the R_{xy}, e.g., from R_{xy}/R_{K} = (11/7)^{-1} to R_{xy}/R_{K} = (8/5)^{-1}, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the nu = 4/3 and nu = 7/5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of R_{xy} at the R_{xx} minima- the latter occurring for nu = 4/3, 7/5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same nu and R_{xy}, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

Formation of a supergiant quantum vortex in a relativistic Bose-Einstein condensate driven by rotation and a parallel magnetic field

Analysis based on the energy spectrum of noninteracting bosons shows that, under the circumstance of parallel rotation and magnetic field, charged bosons form a Bose-Einstein condensate because of the lift of the Landau level degeneracy by rotation [\textcolor{blue}{Y. Liu and I. Zahed, Phys. Rev. Lett. {\bf120}, 032001 (2018)}]. In this work, we study the interaction effect on the ground state of this Bose-Einstein condensate of charged bosons from the viewpoint of spontaneous symmetry breaking. We employ a minimal model for charged bosons with repulsive self-interaction. We find that the ground state of such a Bose-Einstein condensate is a supergiant quantum vortex, i.e., a quantized vortex with a large circulation. The size of the vortex is as large as the system size. The low-energy dispersion of the excitation spectra exhibits quadratic behavior, which is an anisotropic realization of the type-II Goldstone boson. Our study may give some implications to off-central relativistic heavy ion collisions, where large vorticity and magnetic fields can be generated.