Orbital Degeneracy Research Articles

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.

Loss of C4 rotational symmetry in pristine and functionalized FePc on reactive metals: Rh(1 1 1) and Ru(0 0 0 1)

The aim of this work is to use spin polarized density functional theory (DFT) to explore how functionalizing the periphery of FePc with F atoms affects its adsorption properties on reactive metals, specifically Rh and Ru. The results show that the interaction between FePc and the substrates is of chemisorption nature, which leads to a reduction in symmetry of the original four-fold rotational symmetry of FePc to C2 or lower. The symmetry reduction has a mixed electronic and geometric character, caused by the breakup of degenerate dxzanddyz orbitals, as well as the incommensurability between molecule and surface symmetries. Introducing fluorine to FePc weakens the interaction between the Ru (Rh) substrates and the organic part of the molecule, resulting in a C2 rotational symmetry reduction. Furthermore, this functionalization enhances the charge transfer to the molecule, which could be of interest to electronic applications.

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.

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.

Weighing the Darkness. II. Astrometric Measurement of Partial Orbits with Gaia

Over the course of several years, stars trace helical trajectories as they traverse across the sky due to the combined effects of proper motion and parallax. It is well known that the gravitational pull of an unseen companion can cause deviations to these tracks. Several studies have pointed out that the astrometric mission Gaia will be able to identify a slew of new exoplanets, stellar binaries, and compact object companions with orbital periods as short as tens of days to as long as Gaia's lifetime. Here, we use mock astrometric observations to demonstrate that Gaia can identify and characterize black hole companions to luminous stars with orbital periods longer than Gaia's lifetime. Such astrometric binaries have orbital periods too long to exhibit complete orbits, and instead are identified through curvature in their characteristic helical paths. By simultaneously measuring the radius of this curvature and the orbital velocity, constraints can be placed on the underlying orbit. We quantify the precision with which Gaia can measure orbital accelerations and apply that to model predictions for the population of black holes orbiting stars in the stellar neighborhood. Although orbital degeneracies imply that many of the accelerations induced by hidden black holes could also be explained by faint low-mass stars, we discuss how the nature of certain putative black hole companions can be confirmed with high confidence using Gaia data alone.

Possible Violation of the Spin-Hamiltonian Concept in Interpreting the Zero-Field Splitting.

The majority of experimental data in electron spin resonance and molecular magnetism are interpreted in terms of the spin-Hamiltonian (SH) formalism. However, this is an approximate theory that requires a proper testing. In the older variant, the multielectron terms are used as a basis in which the D-tensor components are evaluated by employing the second-order perturbation theory (PT) for nondegenerate states; here, the spin-orbit interaction expressed via the spin-orbit splitting parameter λ serves for the perturbation. The model space is restricted only to the fictitious spin functions |S, M⟩. In the case of the orbital (quasi) degeneracy of the ground term, the PT tends to diverge and the subtracted D, E, and g parameters are false. In the second variant working in the "complete active space" (CAS), the spin-orbit coupling operator is involved by the variation method resulting in the spin-orbit multiplets (energies and eigenvectors) The multiplets can be evaluated either by applying ab initio CASSCF + NEVPT2 + SOC calculations or by using semiempirical generalized crystal-field theory (with the one-electron SOC operator depending upon ξ). The resulting states can be projected onto the subspace of the spin-only kets in the way that the eigenvalues stay invariant. Such an effective Hamiltonian matrix can be reconstructed using six independent components of the symmetric D-tensor from which the D and E values are obtained by solving linear equations. The eigenvectors of the spin-orbit multiplets in the CAS allow determining the dominating composition of the spin projection─cumulative weights of |±M⟩. These are conceptually different from those generated by the SH alone. It is shown that in some cases, the SH theory works satisfactorily for a series of transition-metal complexes; however, sometimes it fails. The ab initio calculations on the SH parameters are compared with the approximate generalized crystal-field theory conducted at the experimental geometry of the chromophore. In total, 12 metal complexes have been analyzed. One of the criteria that assesses the validity of SH is the projection norm N for spin multiplets (this has not to be far from 1). Another criterion is the gap in the spectrum of the spin-orbit multiplets that separates the hypothetical (fictitious) spin-only manifold from the rest of the states.

Robust magnetism of the cluster assembled (Fe@In6)Ba2 crystal

Fe@In6 is the smallest transition metal doped endohedral cage cluster. Its anion, with an octahedral geometry of Oh symmetry, has three singly occupied degenerate orbitals with the ground electronic state 4A1g. Global optimization based on the evolutionary algorithm combined with density functional theories shows that the lowest energy structure of the crystal assembled by Fe@In6 and Ba2 is spin polarized, and the crystal structure is slightly deviated from the fcc (face centered cubic) structure due to the spin-polarization. The magnetic moment is 2.45 μB per Fe@In6Ba2 unit, and the magnetism is very robust. The formation enthalpy of the crystal reaches −1.1 eV per atom, and the spin-polarized state is 2.36 eV lower in energy than the non-polarized state. Calculations also demonstrate that the magnetic moments change linearly with the pressures imposing on the polarization direction. The present study provides a new way for designing cluster assembled magnetic materials by transition metal doped clusters.

Dynamics of photoinduced ferromagnetism in oxides with orbital degeneracy

By using intense coherent electromagnetic radiation, it may be possible to manipulate the properties of quantum materials very quickly, or even induce new and potentially useful phases that are absent in equilibrium. For instance, ultrafast control of magnetic dynamics is crucial for a number of proposed spintronic devices, and it can also shed light on the possible dynamics of correlated phases out of equilibrium. Inspired by recent experiments on spin-orbital ferromagnet ${\mathrm{YTiO}}_{3}$, we consider the nonequilibrium dynamics of a Heisenberg ferromagnetic insulator with low-lying orbital excitations. We model the dynamics of the magnon excitations in this system following an optical pulse that resonantly excites infrared-active phonon modes. As the phonons ring down, they can dynamically couple the orbitals with the low-lying magnons, leading to a dramatically modified effective bath for the magnons. We show that this transient coupling can lead to a dynamical acceleration of the magnetization dynamics, which is otherwise bottlenecked by small anisotropy. Exploring the parameter space more, we find that the magnon dynamics can also even completely reverse, leading to a negative relaxation rate when the pump is blue-detuned with respect to the orbital bath resonance. We therefore show that by using specially targeted optical pulses, one can exert a much greater degree of control over the magnetization dynamics, allowing one to optically steer magnetic order in this system. We conclude by discussing interesting parallels between the magnetization dynamics we find here and recent experiments on photoinduced superconductivity, where it is similarly observed that depending on the initial pump frequency, an apparent metastable superconducting phase emerges.

Mechanism of proton-coupled electron transfer described with QM/MM implementation of coupled-perturbed density-functional tight-binding.

Coupled-perturbed equations for degenerate orbitals were implemented for third order density-functional tight binding, which allowed the use of Mulliken charges as reaction coordinates. The method was applied to proton-coupled electron transfer (PCET) reactions in a model system and thoroughly tested for QM and QM/MM setups (i.e., coupled quantum and molecular mechanics). The performed enhanced sampling simulations were stable, and the obtained potentials of the mean force were able to address the thermodynamic and kinetic features of the reactions by showing the expected topography and energy barriers. Hence, this method has the potential to distinguish between concerted and sequential mechanisms and could next be applied to proton-coupled electron transfer reactions in more complex systems like proteins.

Hund's coupling and spin-orbit interaction in the three-band Hubbard model: Anomalous mass renormalization in Sr2RuO4

We study electronic correlation effects in the three-band Hubbard model in presence of Hund's and spin-orbit couplings using slave-spin mean-field theory. We consider three different regimes of hopping parameter values for the model on a square lattice. For orbital diagonal and isotropic hopping, we show that spin-orbit coupling (SOC), in general, enhances electronic correlations via the reduction of orbital degeneracy. In presence of Hund's coupling $J$, SOC tends to oppose the effect of $J$ on electronic correlations. Considering symmetry allowed anisotropic hopping, we find that the quasiparticle weights become orbital selective in presence of interaction. The effect of $J$ is particularly interesting for the band filling of two particles per site. Here, the Janus-faced effect of $J$ on correlation is obtained only in the narrower band, whereas electronic correlation in the wider band get reduced by $J$ for all values of Hubbard repulsion $U$. For model parameters corresponding to ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, interestingly, we find that the mass renormalizations in the bands become anomalous in presence of strong $U$ and $J$. The effective mass enhancement in the wider band becomes greater compared to that in the narrower band. We show that it originates in the peculiar electronic band structure of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, in which the spinon Fermi surface topology changes in a particular way in the presence of interactions.

Geometric frustration of Jahn-Teller order in the infinite-layer lattice.

The Jahn-Teller effect, in which electronic configurations with energetically degenerate orbitals induce lattice distortions to lift this degeneracy, has a key role in many symmetry-lowering crystal deformations1. Lattices of Jahn-Teller ions can induce a cooperative distortion, as exemplified by LaMnO3 (refs. 2,3). Although many examples occur in octahedrally4 or tetrahedrally5 coordinated transition metal oxides due to their high orbital degeneracy, this effect has yet to be manifested for square-planar anion coordination, as found in infinite-layer copper6,7, nickel8,9, iron10,11 and manganese oxides12. Here we synthesize single-crystal CaCoO2 thin films by topotactic reduction of the brownmillerite CaCoO2.5 phase. We observe a markedly distorted infinite-layer structure, with ångström-scale displacements of the cations from their high-symmetry positions. This can be understood to originate from the Jahn-Teller degeneracy of the dxz and dyz orbitals in the d7 electronic configuration along with substantial ligand-transition metal mixing. A complex pattern of distortions arises in a [Formula: see text] tetragonal supercell, reflecting the competition between an ordered Jahn-Teller effect on the CoO2 sublattice and the geometric frustration of the associated displacements of the Ca sublattice, which are strongly coupled in the absence of apical oxygen. As a result of this competition, the CaCoO2 structure forms an extended two-in-two-out type of Co distortion following 'ice rules'13.

Kondo screening of single magnetic impurity doped type-II Ising superconductors

We theoretically study the Kondo effect in type-II Ising superconductors with a single magnetic impurity. Type-II Ising superconductivity was found in two-dimensional centrosymmetric materials with multiple degenerate orbitals, such as in few-layer stanene [Falson et al., Science 367, 1454 (2020)] and ultrathin ${\mathrm{PdTe}}_{2}$ films [Liu et al., Nano Lett. 20, 5728 (2020)]. The type-II Ising spin-orbit coupling (SOC) in these materials generates out-of-plane effective Zeeman fields orienting opposite directions for opposing orbitals, which strongly protects the interorbital superconducting pairing states against in-plane magnetic fields. We show that the SOC-induced band splitting and the chemical potential significantly influence the formation of a localized magnetic moment, with particle-hole asymmetry in the phase boundary between magnetic and nonmagnetic states. The behaviors of spin-induced Yu-Shiba-Rusinov bound states and low-temperature magnetic susceptibility demonstrate that the SOC suppresses the Kondo screening of the magnetic moment, while the interorbital mixing weakens the SOC at finite momentum, then enhances the Kondo effect. The quantum phase transition between magnetic doublet and Kondo singlet ground states can be tuned through chemical potential in experiments.

Triply-Reduced Hexa-peri-hexabenzocoronenes: Solid-State Structures and Magnetic Properties

Discotic polycyclic aromatics have attracted great interest in both fundamental chemistry and material science due to their degenerate frontier orbitals, high molecular symmetry, unique solid-state packing, and ability to bear a certain number of unpaired electrons that can be applied in molecular spintronics and quantum computing. In this work, chemical reduction of hexa-peri-hexabenzocoronenes, HBC (1) and tBu-HBC (2), as “superbenzenes”, has been investigated with K metal in THF solution. These reactions readily afforded the triply reduced HBC-based products which have been isolated as single-crystalline materials. The X-ray diffraction study confirmed the formation of π-complexes [K+(18-crown-6)(THF)2][{K+(18-crown-6)}2(13–)] (3) and [K+(18-crown-6)(THF)2][{K+(18-crown-6)}2(23–)] (4). In 3 and 4, two potassium ions were found to bind the central six-membered rings of 13– and 23– with one potassium counterion remaining solvent-separated from the complexes. A notable geometry distortion of the HBC core upon three-electron acquisition and metal binding was revealed in both complexes. The presence of bulky substituents in 2 affected the coordination and crystal packing of otherwise similar building units in 4 vs 3. The magnetic properties of 4 supported the existence of a well-isolated S = 3/2 ground state of the 23– triradical in the solid state.

Do quantum interference effects manifest in acyclic aliphatic molecules with anchoring groups?

The ability to control single molecule electronic conductance is imperative for achieving functional molecular electronics applications such as insulation, switching, and energy conversion. Quantum interference (QI) effects are generally used to control electronic transmission through single molecular junctions by tuning the molecular structure or the position of the anchoring group(s) in the molecule. While previous studies focussed on the QI between σ and/or π channels of the molecular backbone, here, we show that single molecule electronic devices can be designed based on QI effects originating from the interactions of anchoring groups. Furthermore, while previous studies have concentrated on the QI mostly in conjugated/cyclic systems, our study showcases that QI effects can be harnessed even in the simplest acyclic aliphatic systems-alkanedithiols, alkanediamines, and alkanediselenols. We identify band gap state resonances in the transmission spectrum of these molecules whose positions and intensities depend on the chain length, and anchoring group sensitive QI between the nearly degenerate molecular orbitals localized on the anchoring groups. We predict that these QI features can be harnessed through an external mechanical stimulus to tune the charge transport properties of single molecules in the break-junction experiments.

Effects of monolayer and bilayer silica films on Fe-Phthalocyanine adsorption properties

We explore the adsorption properties of Fe-Phthalocyanine (FePc) molecule at various configurations of silica films supported by Ru(0001) and report on the geometric, electronic and magnetic features of the energetically preferred structures to fully understand the influence of the silica films on the adsorption properties of the FePc molecule. The investigation is carried out with the use of density of functional theory calculations and the self-consistent inclusion of van der Waals interaction. In addition, Oxygen atoms are added to govern the atomic structure of the silica overlayers on the surface. Our results show that both FePc/silica thin film systems exhibit both physisorption and chemisorption simultaneously. In addition, the FePc molecule on each substrate undergoes a symmetry reduction driven by mismatch with the substrates' symmetry as well as the breakup of the degenerate orbitals of Fe.

Local magnetic moments due to loop currents in metals

We present Hartree-Fock calculations on a simple model to obtain the conditions of formation of local magnetic moments due to loop currents ${L}_{o}$ and spin-loop currents ${L}_{s}$ and compare them to the conditions of formation of local spin moments $M$ which were given long ago in a similar approximation by Anderson. A model with three degenerate orbitals sitting on an equilateral triangle, with on-site and nearest-neighbor repulsions $U$ and $V$, respectively, and intersite kinetic energy, hybridizing with conduction electrons with a parameter $\mathrm{\ensuremath{\Delta}}$ is investigated. ${L}_{o}$ and ${L}_{s}$ are promoted by large $V/\mathrm{\ensuremath{\Delta}}$ and their magnitude is relatively unaffected by $U/\mathrm{\ensuremath{\Delta}}$. Spin-magnetic moments $M$ promoted by large $U/\mathrm{\ensuremath{\Delta}}$ on the other hand are adversely affected by $V/\mathrm{\ensuremath{\Delta}}$. In this model, ${L}_{o}$ for $V$ multiplied by the number of neighbors is approximately the same as the $M$ promoted by $U$ in Anderson's local model for $M$. ${L}_{o}$ and ${L}_{s}$ are degenerate if exchange interactions and Hund's rule are neglected but ${L}_{o}$ is favored when they are included. Many of the qualitative results are visible in an expression for the Hartree-Fock ground state energy derived as a function of small ${L}_{o}, {L}_{s}$, and $M$. Numerical minimization of the Hartree-Fock energy is presented for larger values. We also briefly discuss the connection and differences of the interaction-generated orbital currents and spin currents discussed here and generalized to a lattice with the topological states in metals and semiconductors.

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

Josephson current via spin and orbital states of a tunable double quantum dot

Supercurrent transport is experimentally studied in a Josephson junction hosting a double quantum dot (DQD) with tunable symmetries. The QDs are parallel-coupled to two superconducting contacts and can be tuned between strong inter-dot hybridization and a ring geometry where hybridization is suppressed. In both cases, we observe supercurrents when the two interacting orbitals are either empty or filled with spins, or a combination. However, when each QD hosts an unpaired spin, the supercurrent depends on the spin ground state. It is strongly suppressed for the ring geometry with a spin-triplet ground state at zero external magnetic field. By increasing the QD hybridization, we find that a supercurrent appears when the ground state changes to spin-singlet. In general, supercurrents are suppressed in cases of spin doublet ground state, but an exception occurs at orbital degeneracy when the system hosts one additional spin, as opposed to three, pointing to a broken particle-hole symmetry.

NiMn2O4 revisited: Temperature‐dependent cation distribution from in situ neutron diffraction and thermopower studies

AbstractThe cation distribution of the negative temperature coefficient (NTC) thermistor spinel NiMn2O4 was studied in the temperature range from 55 to 900°C, using a combined in situ neutron diffraction and thermopower study. Rietveld refinements of in situ neutron diffraction data reveal a temperature dependence of the degree of inversion with an inversion parameter of 0.70(1) at 900°C and 0.87(1) at 55°C. Thermopower measurements were evaluated using a modified Heikes formula, and the [Mn4+]/[Mn3+] ratio on octahedral sites of the spinel structure was calculated considering spin and orbital degeneracy. The inversion degree and disproportionation parameter, determined independently as function of temperature, were used to calculate the cation distribution of NiMn2O4 in the whole temperature range. At high temperature, within the stability range of the spinel, the cation distribution is characterized by a moderate degree of inversion with a concentration of = 0.71(2) and small tendency toward disproportionation with a high concentration of = 0.98(2). At 55°C, cation inversion is enhanced as illustrated by a large concentration of = 0.87(2), and a small = 0.24(2) content indicates extensive Mn‐disproportionation. Finally, conclusions regarding possible ageing mechanisms of this important NTC thermistor material are drawn.