Degenerate Levels Research Articles

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. I. Wavefunction-based methods.

In this paper, we investigate the role of electron correlation in predicting the S1-S0 and T1-S0 excitation energies and, hence, the singlet-triplet gap (ΔEST) in a set of cyclazines, which act as templates for potential candidates for fifth generation organic light emitting diode materials. This issue has recently garnered much interest with the focus being on the inversion of the ΔEST, although experiments have indicated near degenerate levels with both positive and negative being within the experimental error bar [J. Am. Chem. Soc. 102, 6068 (1980), J. Am. Chem. Soc. 108, 17(1986)]. We have carried out a systematic and exhaustive study of various excited state electronic structure methodologies and identified the strengths and shortcomings of the various approaches and approximations in view of this challenging case. We have found that near degeneracy can be achieved either with a proper balance of static and dynamic correlation in multireference theories or with state-specific orbital corrections, including its coupling with correlation. The role of spin contamination is also discussed. Eventually, this paper seeks to produce benchmark numbers for establishing cost-effective theories, which can then be used for screening derivatives of these templates with desirable optical and structural properties. Additionally, we would like to point out that the use of domain-based local pair natural orbital-similarity transformed EOM-coupled cluster singles and doubles as the benchmark for ΔEST [as used in J. Phys. Chem. A 126(8), 1378 (2022), Chem. Phys. Lett. 779, 138827 (2021)] is not a suitable benchmark for these classes of molecules.

Impact of valley degeneracy on the thermoelectric properties of zig-zag graphene nanoribbons with staggered sublattice potentials and transverse electric fields.

This study investigates the band inversion of flat bands in zig-zag graphene nanoribbons (ZGNRs) using a tight-binding model. The band inversion results from symmetry breaking in the transverse direction, achievable through deposition on specific substrates such as separated silicon carbide or hexagonal boron nitride sheets. Upon band inversion, ZGNRs exhibit electronic structures characterized by valley degeneracy and band gap properties, which can be modulated by transverse electric fields. To explore the impact of this level degeneracy on thermoelectric properties, we employ Green's function techniques to calculate thermoelectric quantities in ZGNR segments with staggered sublattice potentials and transverse electric fields. Two carrier transport scenarios are considered: the chemical potential is positioned above and below the highest occupied molecular orbital. We analyze thermionic-assisted transport (TAT) and direct ballistic transport (DBT). Level degeneracy enhances the electric power factors of ZGNRs by increasing electrical conductance, while the Seebeck coefficient remains robust in the TAT scenario. Conversely, in DBT, the enhancement of the power factor primarily stems from improvements in the Seebeck coefficient at elevated temperatures.

Slowing down the hot electron cooling to activate near-infrared photocatalytic activity in potassium/carbon co-doped polymeric carbon nitride

The research on hot electron cooling in photocatalysis has been neglected. Here, taking polymeric carbon nitride as an example, a potassium/carbon (K/C) co-doping strategy is proposed to slow down hot electron cooling. The K/C co-doping reduces the specific arrangement and overlap of electronic band structures, and decreases the degeneracy of conduction band energy levels, thus exciting phonon bottleneck effect to effectively suppress the relaxation of hot electrons by reducing the interaction between hot electrons and phonons. Our work benefits to improve the efficiency of photocatalytic energy conversion.

Infrared optical spectra of a silicene quantum dot modulated by spin-orbit coupling and uniaxial strain

Abstract We theoretically study the electronic structure and light absorption spectra of a triangular silicene quantum dot (TZSQD) modulated by spin-orbit coupling (SOC) and the uniaxial strain from a symmetry point of view. After considering the SOC, the symmetry of the system decreases and the degenerate energy level split, creating the absorption peaks in the far infrared region and some multimodal structures in the near-infrared region and visible region. In addition, the intensity of the SOC also affects the degree of splitting of the energy levels, which makes the absorption peaks in the far infrared region are blueshifted to the mid-infrared region, and absorption edge in the near infrared region is redshifted to the mid-infrared region. We also find that when a uniaxial strain and SOC coexist at the same time, the symmetry of the system is further reduced, and the number of absorption peaks is increased. Moreover, the uniaxial strain intensity can efficiently regulate the frequency position of the absorption edge in the near-infrared region, and make its spectral range greatly expanded.

Observation of Pairwise Level Degeneracies and the Quantum Regime of the Arrhenius Law in a Double-Well Parametric Oscillator

By applying a microwave drive to a specially designed Josephson circuit, we have realized a double-well model system: a Kerr oscillator submitted to a squeezing force. We have observed, for the first time, the spectroscopic fingerprint of a quantum double-well Hamiltonian when its barrier height is increased: a pairwise level kissing (coalescence) corresponding to the exponential reduction of tunnel splitting in the excited states as they sink under the barrier. The discrete levels in the wells also manifest themselves in the activation time across the barrier which, instead of increasing smoothly as a function of the barrier height, presents steps each time a pair of excited states is captured by the wells. This experiment illustrates the quantum regime of Arrhenius’s law, whose observation is made possible here by the unprecedented combination of low dissipation, time-resolved state control, 98.5% quantum nondemolition single shot measurement fidelity, and complete microwave control over all Hamiltonian parameters in the quantum regime. Direct applications to quantum computation and simulation are discussed. Published by the American Physical Society 2024

Local aromatic ring cleaves the global aromatic ring in hexaphyrin(2.1.2.1.2.1)

Novel benzo-bridged hexaphyrin(2.1.2.1.2.1) and its copper complex were synthesized. Single-crystal structures showed typical figure-of-eight Hückel topologies. NMR, NICS, HOMA, ACID, and EDDB analysis supported their non-aromatic properties owning to the strong local aromatic benzo rings cutting the global aromatic ring of the benzo-bridged figure-of-eight hexaphyrin(2.1.2.1.2.1). The redox properties and degenerate HOMOs and LUMOs levels indicate multielectron donating and accepting abilities.

Two atoms in a harmonic trap with spin-orbital-angular-momentum coupling

We study the problem of two harmonically trapped atoms in the presence of spin-orbital-angular-momentum (SOAM) coupling. The two-body energy spectrum is numerically calculated by utilizing the exact diagonalization method. We analyze how the degeneracy of energy levels is lifted under the interplay between the interatomic interaction and SOAM coupling. The exact numerical results show excellent agreement with that of perturbation theory in the weak-interaction limit as well as that in the absence of SOAM coupling. The properties of correlations between the two atoms are also discussed with respect to the interaction strength. The findings in this paper may provide valuable insights into few-body physics subjected to SOAM coupling and the possible experimental detection of spectrum functions in many-body systems, such as radiofrequency spectroscopy. Published by the American Physical Society 2024

Valley landau level crossings in weakly coupled bilayer WSe2

Abstract WSe2 is a p-type 2D-semiconductor that can be mechanically exfoliated down to atomic layers. Unlike the Bernal stacked bilayer graphene, the two layers in a bilayer WSe2 flake are weakly coupled. The electric displacement field can easily break the layer degeneracy of the bilayer WSe2. Together with the strong spin–orbit coupling, it exhibits many novel quantum physical properties. In this work, we fabricate high quality dual-gated bilayer WSe2 devices and observe twofold degenerate Landau levels(LLs) and density-dependent quantum Hall states which show transitions between even and odd filling. When introducing carriers into the system from the valence band edge by gating, two WSe2 layers are filled independently and the bottom layer WSe2 shows negative compressibility at the crossover point. Above 9 T, we observe the degeneracy of LLs is completely broken and there are two sets of LL crossings in the top WSe2 layer at Zeeman-to-cyclotron energy ratio E Z / E N ≈ 4 and E Z / E N ≈ 5. The interplay between two LLs from the two WSe2 layers confirms the weak coupling between them. Our results show that the bilayer WSe2 behave like two closely packed independent electronic systems under electric displacement fields.

Dirac fermions in a spinning conical Gödel-type spacetime

Abstract In this paper, we determine the relativistic and nonrelativistic energy levels for Dirac fermions in a spinning conical Gödel-type spacetime in (2+1)-dimensions, where we work with the Dirac equation in polar coordinates and we use the tetrads formalism. Solving a second-order differential equation for the two components of the Dirac spinor, we obtain a generalized Laguerre equation, and the relativistic energy levels, where such levels are quantized in terms of the quantum numbers n and m j, and explicitly depends on the spin parameter s, spinorial parameter u, curvature and rotation parameters α and β, and on the vorticity parameter Ω. In particular, the quantization is a direct result of the existence of Ω (i.e., Ω acts as a kind of ``external field or potential''). We see that for m j>0, the energy levels do not depend on s and u; however, depend on n, m j, α, and β. In this case, α breaks the degeneracy of the energy levels and such levels can increase infinitely in the limit 4Ωβ/α→1. Already for m j<0, we see that the energy levels depend on s, u and n; however, it no longer depends on m j, α and β. In this case, it is as if the fermion ``lives only in a flat Gödel-type spacetime''. Besides, we also study the low-energy or nonrelativistic limit of the system. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of energy levels as a function of Ω, α, and β for three different values of n.

Non-Abelian Holonomy in Degenerate Non-Hermitian Systems.

Non-Abelian holonomy, a noncommutative process that measures the parallel transport of non-Abelian gauge fields, has so far been realized in degenerate Hermitian systems with degenerate eigenstates or nondegenerate non-Hermitian systems with exceptional points. Here, we introduce non-Abelian holonomy into degenerate non-Hermitian systems possessing degenerate exceptional points and degenerate energy topologies. The interplay between energy degeneracy and energy topology around exceptional points leads to a non-Abelian holonomy with multiple energy levels and multiple degenerate levels simultaneously, going beyond that in degenerate Hermitian systems with a single energy level, or in nondegenerate non-Hermitian systems with a single degenerate level. We exploit an on-chip photonic platform to experimentally demonstrate the holonomy induced non-Abelian phenomenon, including the switching of eigenstates associated with different degenerate exceptional points and sequence-dependent holonomic outcomes. Our work shifts the paradigm of non-Abelian holonomy and adds new degrees of freedom for non-Abelian applications.

Understanding multiple timescales in quantum dissipative dynamics: Insights from quantum trajectories

Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of dramatic separation of timescales due to differences between Liouvillian eigenvalues. These metastable states often have nonzero coherences that die off only in the long-time limit once the system reaches thermal equilibrium. We examine two distinct situations that give rise to this effect: one in which dissipative dynamics couple together states only within a nearly degenerate subspace, and one in which they give rise to jumps over finite-energy splittings, between nearly degenerate subspaces. We find, in each case, that a change of basis can often lead to a representation that more naturally captures the impact of the system-bath interaction than does the energy eigenbasis, revealing that separate timescales are associated with separate processes (e.g., decoherence into a nonenergy eigenbasis, decay of population correlations to the initial state). This approach is paired with the inspection of quantum trajectories, which further provide intuition as to how open system evolution is characterized when coherent oscillations, thermal relaxation, and decoherence all occur simultaneously. Published by the American Physical Society 2024

Majorana-Free Bound State in the Continuum in the Double-Channel Fano–Anderson Structure

Abstract We investigate the electron transport through a double-channel Fano–Anderson structure, by considering the side-coupling of Majorana bound states (MBSs). It is found that the bound state in the continuum (BIC) phenomenon can be induced when interchannel dot–lead couplings are identical to the intrachannel dot–lead couplings, whose signature is manifested as a halved quantum transmission ability. If the balance between the dot–lead couplings is broken, the BIC phenomenon will also be destroyed, leading to further suppression of the transmission ability. Next, when MBSs are introduced to this system, the BIC phenomenon can be modified efficiently. For the case of two MBSs side-coupled to the quantum dots in a symmetric way, level degeneracy causes a new BIC phenomenon. As only one MBS is incorporated, it suppresses the electron transmission by inducing new transmission dips. When the interdot Coulomb interaction is considered, the BIC phenomena are still robust despite the complicated changes of the transmission ability spectra. One can then understand the realization of BICs in coupled quantum dots and their variation due to the presence of side-coupled MBSs.

Crystalline electric field and large anomalous Hall effect in NdGaGe single crystals

We grew NdGaGe single crystals and investigated their magnetic and electrical transport properties. The magnetic susceptibility data revealed that NdGaGe orders magnetically at Tm≈ 8.8 K; also confirmed by heat capacity and electrical resistivity data. In ordered state, the heat capacity and electrical resistivity data exhibit a gapped-magnon behavior with an energy gap of ∼ 4.7 K. Our detailed crystalline electric field analysis of magnetic susceptibility, magnetization, and heat capacity data indicates that the (2J+1) degenerate energy levels of Nd3+ ion split into five doublets with an overall splitting of ∼ 123 K. We observe a large anomalous Hall conductivity (AHC) ∼ 530 Ω−1 cm−1 at 2 K, which is close to the theoretical expected value due to intrinsic Berry-curvature. Moreover, the scaling parameter between anomalous Hall resistivity and magnetoresistivity together with the linear relationship between AHC and saturation magnetization suggests that the origin of large AHC in NdGaGe is due to the intrinsic Berry curvature.

The effects of common reservoirs on the performance of a quantum refrigerator

In this work, we study and find that the performance of an autonomous refrigerator can be improved by means of collective dissipations of common reservoirs. The refrigerator is based on a four-level system with two degenerate levels, coupled to three thermal reservoirs with different temperatures. Our study reveals that utilizing only one common reservoir can not significantly enhance the refrigerator’s performance. However, when two reservoirs are shared simultaneously, the performance improvement becomes more evident. Furthermore, we find that the refrigerator’s performance can be further enhanced by operating in a regime where the decoherence-free subspace is present. Our results indicate that careful engineering is essential to maximize the benefits of common reservoirs in enhancing the performance of quantum thermal machines.

A note on degeneracy of excited energy levels in massless Dirac fermions

We propose a mechanism to construct the eigenvalues and eigenfunctions of the massless Dirac-Weyl equation in the presences of magnetic flux Φ localized in a restricted region of the plane. Using this mechanism we analyze the degeneracy of the existed energy levels. We find that the zero and first energy level has the same N+1 degeneracy, where N is the integer part of Φ2π. In addition, and contrary to what is described in the literature regarding graphene, we show that higher energy levels are N+m degenerate, being m the level of energy. In other words, this implies an indefinite growth of degenerate states as the energy level grows.

Fermion self-energy and damping rate in a hot magnetized plasma

We derive a general expression for the fermion self-energy in a hot magnetized plasma by using the Landau-level representation. In the one-loop approximation, the Dirac structure of the self-energy is characterized by five different functions that depend on the Landau-level index n and the longitudinal momentum pz. We derive general expressions for all five functions and obtain closed-form expressions for their imaginary parts. The latter receive contributions from three types of on shell processes, which are interpreted in terms of Landau-level transitions, accompanied by a single photon (gluon) emission or absorption. By making use of the imaginary parts of the self-energy functions, we also derive the Landau-level dependent fermion damping rates Γn(pz) and study them numerically in a wide range of model parameters. We also demonstrate that the two-spin degeneracy of the Landau levels is lifted by the one-loop self-energy corrections. While the spin splitting of the damping rates is small, it may be important for some spin and chiral effects. We argue that the general method and the numerical results for the rates can have interesting applications in heavy-ion physics, astrophysics, and cosmology, where strongly magnetized QED or QCD plasmas are ubiquitous. Published by the American Physical Society 2024

Electron transport through degenerate electron level in single-molecular junction in the presence of electron-vibrational coupling and attractive electron-electron correlations

Electron transport through a molecular junction consisted of a single molecule coupled to macroscopic leads is studied in the nonequilibrium regime. The molecule is modeled as a degenerate energy level with an electron-vibrational interaction and attractive electron-electron correlation which lifts the degeneracy. The level occupancy and differential conductance are calculated in the antiadiabatic regime with an account of molecule-lead coupling at low temperature and finite voltage. The method of transport spectroscopy made it possible to determine through which of the split levels tunneling takes place depending on the applied voltages and to estimate the current through these levels. The cases of a negative differential conductance are discussed. The influence of the electron-vibrational coupling of different strength on electron tunneling through 2- and 4-fold degenerate level on the molecule in the presence of the attractive electron-electron interaction is analyzed.

Red Shift in the Absorption Spectrum of Phototropin LOV1 upon the Formation of a Semiquinone Radical: Reconstructing the Orbital Architecture.

Flavin mononucleotide (FMN) is a ubiquitous blue-light pigment due to its ability to drive one- and two-electron transfer reactions. In both light-oxygen-voltage (LOV) domains of phototropin from the green algae Chlamydomonas reinhardtii, FMN is noncovalently bound. In the LOV1 cysteine-to-serine mutant (C57S), light-induced electron transfer from a nearby tryptophan occurs, and a transient spin-correlated radical pair (SCRP) is formed. Within this photocycle, nuclear hyperpolarization is created by the solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) effect. In a side reaction, a stable protonated semiquinone radical (FMNH·) forms undergoing a significant bathochromic shift of the first electronic transition from 445 to 591 nm. The incorporation of phototropin LOV1-C57S into an amorphous trehalose matrix, stabilizing the radical, allows for application of various magnetic resonance experiments at ambient temperatures, which are combined with quantum-chemical calculations. As a result, the bathochromic shift of the first absorption band is explained by lifting the degeneracy of the molecular orbital energy levels for electrons with alpha and beta spins in FMNH· due to the additional electron.

Theoretical investigation on the optical absorption spectra in cyclo[[formula omitted]]carbons ([formula omitted] 10, 14, 18)

The optical absorption spectra of cyclo[n]carbons (n= 10, 14, 18) are investigated in the framework of time-dependent density functional theory. The collective plasmon excitations well develop as the increases of the ring size and the symmetry group of cyclo[n]carbons. An increase in intensity for the main peaks with the growing number of atoms in cyclo[n]carbons is observed. With the increase of the radius of the monocyclic ring, as more electrons participate in the dipole oscillation the main excitation peaks are red-shifted to the lower energy. The highly symmetrical structures of cyclo[n]carbons (Dnh) possess degenerate levels, leading to simpler spectra with fewer peaks. The Fourier transform of the induced electron density of the cyclo[n]carbons (n= 10, 14, 18) is investigated at the excitation frequencies.

Achieving High Thermoelectric Performance in ZnSe-Doped CuGaTe2 by Optimizing the Carrier Concentration and Reducing Thermal Conductivity.

The CuGaTe2 thermoelectric material has garnered widespread attention as an inexpensive and nontoxic material for mid-temperature thermoelectric applications. However, its development has been hindered by its low intrinsic carrier concentration and high thermal conductivity. This study investigates the band structure and thermoelectric properties of (CuGaTe2)1-x (ZnSe)x (x = 0, 0.25%, 0.5%, 1%, 1.5%, and 2%). The research revealed that the incorporation of Zn and Se atoms enhanced the level of band degeneracy and electron density of states near Fermi level, significantly raising carrier concentration through the formation of point defects. Simultaneously, when the doping content reached 1.5%, the ZnTe second phase emerged, collaborating with point defects and high-density dislocations, effectively scattering phonons and substantially reducing lattice thermal conductivity. Therefore, introducing ZnSe can simultaneously optimize the material's electrical and thermal transport properties. The (CuGaTe2)0.985(ZnSe)0.015 sample reaches peak ZT of 1.32 at 823 K, representing a 159% increase compared to pure CuGaTe2.