Symmetry Of Wave Function Research Articles

Wave Function Engineering on Superconducting Substrates: Chiral Yu-Shiba-Rusinov Molecules.

Magnetic adatoms on superconductors give rise to Yu-Shiba-Rusinov (YSR) states that hold considerable interest for the design of topological superconductivity. Here, we show that YSR states are also an ideal platform to engineer structures with intricate wave function symmetries. We assemble structures of iron atoms on the quasi-two-dimensional superconductor 2H-NbSe2. The Yu-Shiba-Rusinov wave functions of individual atoms extend over several nanometers enabling hybridization even at large adatom spacing. We show that the substrate can be exploited to deliberately break symmetries of the adatom structure leading to hybridized YSR states exhibiting symmetries that cannot be found in orbitals of iso-structural planar molecules in the gas phase. We exploit this potential by designing chiral YSR wave functions of triangular adatom structures. Our results significantly expand the range of interesting quantum states that can be engineered using arrays of magnetic adatoms on superconductors.

Comparative analysis of absorption resonances between carbynes and cyclo [n] carbons

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo [n] carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and the ab initio time-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following the Nring=2Nchain+2 rule, which states that the number of atoms in an atomic ring Nring is twice the number of atoms on a finite chain Nchain with two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes with N=7and8 carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo[18]carbon. Despite the mismatch in resonance peaks, molecular orbital transitions of both carbynes N = 7 and 8 and cyclo[18]carbon reveal a wave function symmetry change from inversion to reflection and vice versa for allowed molecular orbital transitions, which results in electron density redistribution along the polyynic carbyne axis or the cyclo[18]carbon circumference. Our investigation of the correlation of optical absorption peaks between carbynes and cyclo [n] carbons is a step towards enhancing the reliability of allotrope identification in advanced molecular device spectroscopy. Moreover, this work could facilitate the non-invasive, rapid and crucial assessment of these sensitive 1D allotropes by providing accurate descriptions of their electronic and optical properties, particularly in controlled synthesis environments.

Gap engineering and wave function symmetry in C and BN armchair nanoribbons

Gap engineering and wave function symmetry in C and BN armchair nanoribbons

Magneto-optical and high-frequency electron paramagnetic resonance spectroscopy of Er3+ ions in CaMoO4 single crystal

We present the optical and magneto-optical spectroscopy and electron paramagnetic resonance (EPR) investigations of CaMoO4 single crystals doped with the erbium ions. Telecom-wavelength resonance transition inhomogeneous line width of Er3+ is relatively narrow for oxide crystals which makes this material promising for quantum technologies applications. The hyperfine structure in optical spectra of 167Er3+ isotope is well resolved. Energies and symmetries of wavefunctions of 39 energy levels of Er3+ ions in the crystal-field (CF) of S4 symmetry and g-factors of some CF Kramers doublets were measured and successfully simulated on the basis of CF calculations. The obtained set of CF parameters was used for modeling the hyperfine structure profiles observed in the optical absorption spectra.

Modular symmetry in magnetized T2g torus and orbifold models

We study the modular symmetry in magnetized T2g torus and orbifold models. The T2g torus has the modular symmetry Γg=Sp(2g,Z). The magnetic flux background breaks the modular symmetry to a certain normalizer Ng(H). We classify remaining modular symmetries by magnetic flux matrix types. Furthermore, we study the modular symmetry for wave functions on the magnetized T2g and certain orbifolds. It is found that wave functions on magnetized T2g as well as its orbifolds behave as the Siegel modular forms of weight 1/2 and N˜g(H,h), which is the metaplectic congruence subgroup of the double covering group of Ng(H), N˜g(H). Then, wave functions transform nontrivially under the quotient group, N˜g,h=N˜g(H)/N˜g(H,h), where the level h is related to the determinant of the magnetic flux matrix. Accordingly, the corresponding four-dimensional chiral fields also transform nontrivially under N˜g,h modular flavor transformation with modular weight −1/2. We also study concrete modular flavor symmetries of wave functions on magnetized T2g orbifolds. Published by the American Physical Society 2024

Visualizing localized nematic states in twisted double bilayer graphene.

Direct visualization of the states originating from electron-electron interactions is of great importance for engineering the surface and interfacial properties of graphene-based quantum materials. For instance, the rotational symmetry breaking or nematic phase inferred from spectroscopic imaging has confirmed the existence of correlated states in a wide range of moiré materials. Here, we study the atomic-scale spatial distributions and symmetry of wave functions in gate-tunable twisted double bilayer graphene by employing scanning tunneling microscopy/spectroscopy and continuum model calculations. A series of spectroscopic imaging analyses are used to identify dominant symmetry breaking of the emergent states. Interestingly, in non-integer hole fillings, a completely new localized electronic state with rotational symmetry breaking is observed on the left side of the valence flat band. The degree of anisotropy is found to increase from the conduction flat band through the valence flat band to the new state. Our results provide an essential microscopic insight into the flat band and its adjacent state for a full understanding of their electric field response in twisted graphene systems.

Electronic Structure and Optical Property of 2D MgPX3 (X = S and Se) Monolayer by Density Functional Theory

2D metal phosphorus trichalcogenides (MgPX3) have attracted tremendous research interests in spintronic, electrocatalytic, and photoelectronic applications due to their unique magnetic and optical properties. Herein, a systematical investigation on the electronic structures and optical properties of 2D MgPX3 (X = S and Se) monolayers is performed by density functional theory. Owing to small cleavage energy, 2D MgPX3 monolayers can be obtained by mechanical exfoliation with an excellent structure stability of 2D MgPX3 monolayers demonstrated by elastic tensor, phonon dispersion, and molecular dynamics, respectively. 2D MgPX3 behaves as a direct bandgap semiconductor with a strong optical absorption in UV range whereas a weak adsorption near the band edge, demonstrated by both single‐ and quasiparticle approximations. Upon analyses on transition dipole moment along with the wave function symmetry, the weak optical absorption is attributed to the parity‐forbidden effect where the wave functions almost show the same parity between top valence band and bottom conduction band. The findings indicate that 2D MgPX3 monolayers hold promise as candidate materials for flexible UV photoelectronics devices and provide a theoretical insight into the optical properties of 2D semiconductors.

Static field ionization of the spherically confined hydrogen atom

AbstractThe ionization of the hydrogen atom confined in a spherical potential well and subjected to a static electric field is studied, using the diffusion Monte Carlo (DMC) method. Atomic ionization within a potential well is found to be a stationary, gradual, and reversible process. The value of the electric field at the onset of ionization is of the order of 0.1 atomic units, and depends on the symmetry of the atomic wave function and on the confinement dimension. By decreasing the confinement sphere, the difference between the bound and ionized states disappears, showing that strict confinement leads to pressure ionization of the atom. The off‐center case is studied characterizing the potential energy surface (PES), and the transition between field‐induced and pressure‐induced ionization is confirmed. Except for very weak fields, the minimum of the PES is reached when the proton is in contact with the boundary of the well.

Rydberg State Single-Mode Polariton Lasing with Ultralow Threshold via Symmetry Engineering.

Symmetry plays an essential role in the fundamental properties of a physical system. In this work, we report on the realization of tunable single-mode polariton lasing from highly excited Rydberg states via symmetry engineering. By breaking the symmetry of the polaritonic wave function through potential wells and controlling the spatial overlap between the gain region and the eigen mode, we are able to generate single-mode polariton lasing, reversibly and dynamically, from quantized polariton states. Increasing the asymmetry of the potential well, single-mode lasing can be achieved even for the highly excited Rydberg state with a principle quantum number of N = 14. Moreover, as a result of the excellent reservoir-eigen mode overlap and efficient spatial confinement, the threshold of lasing can be reduced up to 6 orders of magnitude, compared with those conventional pumping schemes. Our results present a new strategy toward the realization of thresholdless polariton lasing with dynamical tunability.

Calculations of Excited Electronic States by Converging on Saddle Points Using Generalized Mode Following.

Calculations of excited electronic states are carried out by finding saddle points on the surface describing the variation of the energy of the system as a function of the electronic degrees of freedom. This approach has several advantages over commonly used methods especially in the context of density functional calculations, as collapse to the ground state is avoided, and yet, the orbitals are variationally optimized for the excited state. Such a state-specific optimization makes it possible to describe excitations with large charge transfer, where calculations based on ground state orbitals, such as linear response time-dependent density functional theory, can be problematic. A generalized mode following method is presented where an nth-order saddle point is found by inverting the components of the gradient in the direction of the eigenvectors of the n lowest eigenvalues of the electronic Hessian matrix. This approach has the distinct advantage of following a chosen excited state by its saddle point order through molecular configurations where the symmetry of the single determinant wave function is broken, thereby making it possible to calculate potential energy curves even at avoided crossings, as demonstrated here in calculations of the ethylene and dihydrogen molecules. Results of calculations are, furthermore, presented for charge transfer excitations in nitrobenzene and N-phenylpyrrole, corresponding to fourth- and sixth-order saddle points, respectively, where an approximate initial estimate of the saddle point order could be found by energy minimization with excited electron and hole orbitals frozen. Finally, calculations of a diplatinum-silver complex are presented, illustrating the applicability of the method to larger molecules.

Understanding remarkably high triplet quantum yield in thione analogs of perylenediimide: A detailed theoretical study.

The diverse and tunable electronic structures of perylenediimide (PDI), together with its high thermal and chemical stability, make the compound suitable for applications in bioimaging, electrical, and optical devices. However, a large singlet-triplet gap (ΔES-T) and almost zero spin-orbit coupling (SOC) between the lowest excited singlet (S1) and triplet (T1) restrict intersystem crossing (ISC) in highly fluorescent pristine PDI, yielding a near zero triplet quantum yield (ΦT). Interestingly, a thione analogs of PDI with varied S content (mS-PDIs, m = 1-4) was experimentally shown to yield ΦT ∼ 1.0 through efficient ISC. Time-dependent optimally-tuned range-separated hybrid calculations are performed to rationalize the experimentally observed red-shifted optical absorption and also the remarkably high ISC with almost zero radiative fluorescence reported for these mS-PDIs. To this end, the relative energies of low-lying excited singlets Sn (n = 1, 2) and a few triplets Tn(n = 1-3), along with their nature (nπ* or ππ*), are assessed for each of the mS-PDIs studied in chloroform. To our surprise and contrary to the earlier reports, both S1 and T1 are found to be of the same ππ* character, originating from the highest occupied to lowest unoccupied orbital transition, which, therefore, leads to a still large ΔES-T and vanishingly small SOC, as expected from the identical wavefunction symmetry. Increasing S content lowers S1(ππ*) due to a greater extent of π-delocalization, which well complements and supports the observed red-shift. More importantly, the T2 (or T3) closely lying to the S1 is of nπ* and, therefore, produces a relatively smaller ΔES-T and larger SOC. Detailed kinetics analysis suggests S1(ππ*) → T2(nπ*) is the primary ISC channel for all mS-PDIs, which is responsible for the remarkably high ΦT observed. In addition, comparable SOC and ΔES-T produce similar ISC rates for all mS-PDIs.

Incorporation sodium ions into monodisperse lead-free double perovskite Cs2AgBiCl6 nanocrystals to improve optical properties

Lead-free double perovskite nanocrystals (NCs) have emerged as a promising candidate in the optical field, owing to their non-toxic, good moist heat and chemical stability. However, their poor optical properties limited their application. To improve the optical properties of lead-free double perovskite NCs, metal ion doping or alloying had been suggested as a promising strategy. Here, we prepared monodisperse, uniformly sized, cubic morphology of Cs2AgBiCl6 NCs with different Na+ incorporation amounts via a simple hot-injection method. The Na+ incorporation broke the parity-forbidden transition by reducing the inversion symmetry of the electron wave function at the Ag site, which changed the parity of the self-trapped exciton wave function and thus allowed radiative recombination. As a result, the photoluminescence quantum yield (PLQY) of Na+-alloyed Cs2AgBiCl6 NCs (12.1%) was higher than that of Cs2AgBiCl6 NCs (2.4%), and the exciton lifetime of Na+-alloyed Cs2AgBiCl6 NCs increased to 36.98 ns from 17.58 ns for Cs2AgBiCl6 NCs. By adjusting the amount of Na+ incorporation, the band gap of Cs2AgBiCl6 NCs can be significantly tuned from ∼2.90 eV to ∼3.50 eV. Furthermore, the temperature-dependent photoluminescence spectra indicated that the Na+-alloyed Cs2AgBiCl6 NCs possessed higher longitudinal optical phonon energy and exciton binding energy compared to Cs2AgBiCl6 NCs. This suggested that there were strong exciton-phonon interactions during exciton recombination, a reduced probability of non-radiative processes, and excellent thermal stability. It offers a promising strategy for improving the optical properties of lead-free double perovskite NCs, and have the potential to replace traditional lead halide perovskite NCs in future optoelectronic applications.

Magnetic-translational sum rule and approximate models of the molecular Berry curvature.

The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct center-of-mass motion during molecular dynamics in these environments. In this work, we demonstrate how these properties of the Berry connection and curvature arise from the translational symmetry of the electronic wave function and how they are fully captured by a finite basis set of London orbitals but not by standard Gaussian basis sets. This is illustrated by a series of Hartree-Fock calculations on small molecules in different basis sets. Based on the resulting physical interpretation of the Berry curvature as the shielding of the nuclei by the electrons, we introduce and test a series of approximations using the Mulliken fragmentation scheme of the electron density. These approximations will be particularly useful in ab initio molecular dynamics calculations in a magnetic field since they reduce the computational cost, while recovering the correct physics and up to 95% of the exact Berry curvature.

Enhanced tunneling magnetoresistance and spin filtering in perovskite magnetic tunnel junctions via oxygen octahedral tilting

Oxygen octahedral tilting significantly reduces the symmetry of perovskites and changes the transport properties of perovskite magnetic tunnel junctions (MTJs). We investigated ${\mathrm{SrRuO}}_{3}/{\mathrm{CaTiO}}_{3}/{\mathrm{SrRuO}}_{3}$ MTJs by first-principles simulation and predicted an intriguing coupling between oxygen octahedral tilting and tunneling magnetoresistance. We obtained higher spin polarization at the Fermi level for the ${\mathrm{SrRuO}}_{3}$ electrodes with tilted octahedra, which increases the tunneling magnetoresistance value. Transmission and complex band structure analysis shows that the majority spin tunneling current in the ${\mathrm{CaTiO}}_{3}$ barrier with tilted octahedra is suppressed by wave function symmetry filtering, thus producing a negative spin filtering with an efficiency close to \ensuremath{-}100% and further enhancing the TMR effect. Both phenomena disappear in the junction without oxygen octahedral tilting, hence they have resulted from lattice distortions. The effective control of the tunneling magnetoresistance via oxygen octahedral tilting could act as a way to improve the performances of perovskite spintronic devices.

Interferometric signature of different spectral symmetries of biphoton states

In this paper, we investigate the influence of the symmetry of the biphoton wave function on the coincidence measurement of the generalized Mach-Zehnder (MZ) interferometer, where there are a temporal and frequency shift operations between the two beam splitters. We show that the generalized MZ interferometer allows the measurement of the short-time Fourier transform of the function modeling the energy conservation of a spontaneous parametric down-conversion process if the full biphoton state is symmetric, and of the symmetric characteristic distribution of the phase-matching function if the state is antisymmetric. Thus, this technique is phase sensitive to the spectral distribution of the photon pairs. Finally, we investigate in detail the signature of a pair of anyons whose peculiar statistics can be simulated by engineering the spectrum of photon pairs.

Observer dependence of photon bunching: The influence of the relativistic redshift on Hong-Ou-Mandel interference

We study the influence of the relativistic redshift on Hong-Ou-Mandel (HOM) interference, and present a genuine quantum test of general relativity. We use Glauber's theory of quantum coherence to predict the coincidence probability of realistic broadband photons in HOM-experiments in a non-relativistic setting. We extend the quantum field theoretical framework previously developed to describe the deformation of the spectral profile of single photons in curved spacetimes to a multi-photon framework, which is exact for inertial observers in a flat spacetime and an approximation when observers are located in a curved spacetime. We find that, in case of frequency entangled photons, a mutual redshift between the sender and the receiver can change the coincidence statistics from photon bunching to photon anti-bunching, and vice versa. This implies that the (anti-) symmetry of the photonic spectral wave function is an observer dependent notion, and that this can be probed via HOM-experiments in a relativistic setting.

Symmetry of Wavefunction at the Interface of Fe/MgO Magnetic Tunneling Junction

We measured the anisotropy of Magnetic Compton profiles (MCP) in the Fe/MgO multilayers and compared it with band structure calculations. At the Fe/MgO interface, the |m| = 1 state in the minority band is suppressed, which in turn promotes the spin-polarized occupation of the |m| = 1 state. At the Fe/FeO interface of intentionally oxidized Fe/MgO multilayers, the occupations of the magnetic quantum number are almost equal (spherical) in the majority band and minority band, and therefore, the spin-polarization occupancy is also almost equal (spherical). These results contribute to the material design for MTJs as high-performance spintronic devices.

Choice of functional for iron porphyrin density functional theory studies: Geometry, spin-state, and binding energy analysis

Simultaneously predicting the geometries, spin states and binding energies of iron porphyrins using DFT methods is challenging, as one method and basis set could lead to the accurate prediction of one aspect but imprecisions on the others. In this work, six functionals and three basis sets were tested based on their description of the geometries, spin states and binding energies of an heme model. An iron porphyrin ring with an axial imidazole (FePIm) was used as the model molecule. Optimized geometries of FePIm and dioxygen-coordinated FePIm-O2 were obtained in their singlet, triplet, and quintet spin states. Energy calculations with zero-point vibrational energy (ZPVE) corrections were performed on the optimized geometries, at the same level of theory used on the geometry optimization. For the oxygen-bonded FePIm-O2, the singlet spin states were calculated to be closed-shell for all the methods, even if an unrestricted wavefunction and broken spin symmetry were imposed on the system. Consequently, the open-shell singlets were obtained using the wavefunction of their corresponding triplet states as the initial guess for the geometry optimizations and energy calculations. The functional B97D with the basis sets A (def2-TZVP on Fe, def2-SVP on other atoms) and C (6–311+G(2df) on Fe atom; 6–311+G(d) on N and O atoms; 6–31G on C and H atoms) was able to produce an accurate geometry, the correct spin states for FePIm (Quintet) and FePIm-O2 (open-shell singlet), and a binding energies of 13.51–13.07 kcal·mol−1, in good agreement to the experimental values. The basis set B resulted in good FePIm geometrical parameters with all the studied functionals, but led to significant errors in the FePIm-O2 geometries and binding energies. For the study of FePIm and similar molecules were the change of spin play a key role, the selection of constraints and initial guess are very important, as the methods could yield multiplicites which do not agree with experimental observations. This study provides valuable information for the selection of a suitable method for DFT studies on small iron porphyrins and their interaction with oxygen, based on the required accuracy for geometry, spin, or binding energies.

Exact and many-body perturbation solutions of the Hubbard model applied to linear chains

This study reports on the accuracy of the GW approximation for the treatment of the Hubbard model compared to exact diagonalization (ED) results. We consider not only global quantities, such as the total energy and the density of states, but also the spatial and spin symmetry of wavefunctions via the analysis of the local density of states. GW is part of the more general Green’s function approach used to develop many-body approximations. We show that, for small linear chains, the GW approximation corrects the mean-field (MF) approach by reducing the total energy and the magnetization obtained from the MF approximation. The GW energy gap is in better agreement with ED, especially in systems of an even number of atoms where, in contrast to the MF approximation, no plateau is observed below the artificial predicted phase transition. In terms of density of states, the GW approximation induces quasi-particles and side satellite peaks via a splitting process of MF peaks. At the same time, GW slightly modifies the localization (e.g., edges or center) of states. We also use the GW approximation results in the context of Löwdin’s symmetry dilemma and show that GW predicts an artificial paramagnetic–antiferromagnetic phase transition at a higher Hubbard parameter than MF does.

Orbital design of flat bands in non-line-graph lattices via line-graph wave functions

Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive interference of Bloch wavefunctions encoded in pure lattice symmetry. Here, we develop a generic atomic/molecular orbital design principle for FBs in non-LG lattices. Based on linear-combination-of-atomic-orbital (LCAO) theory, we demonstrate that the underlying wavefunction symmetry of FBs in a LG lattice can be transformed into the atomic/molecular orbital symmetry in a non-LG lattice. We illustrate such orbital-designed topological FBs in three 2D non-LG, square, trigonal, and hexagonal lattices, where the designed orbitals faithfully reproduce the corresponding lattice symmetries of checkerboard, Kagome, and diatomic-Kagome lattices, respectively. Interestingly, systematic design of FBs with a high Chern number is also achieved based on the same principle. Fundamentally our theory enriches the FB physics; practically it significantly expands the scope of FB materials, since most materials have multiple atomic/molecular orbitals at each lattice site, rather than a single s orbital mandated in graph theory and generic lattice models.