Quasi-band Structure Research Articles

An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems

In this study, we propose an extended plane wave framework to ensure that the electronic structure calculations of twisted bilayer 2D material systems are practically feasible. Based on the foundations presented in Zhou et al. (2019), we extend the PW framework in the following aspects: (1) a tensor-product basis set, which adopts plane waves (PWs) in the incommensurate dimensions and a localized basis in the interlayer dimension; (2) a practical application of a novel cutoff technique that we recently developed; and (3) a quasi-band structure picture under small twist angles and weak interlayer coupling limits. Based on (1) and (2), the dimensions of the Hamiltonian matrix are reduced by approximately two orders of magnitude compared with the original framework. Moreover, (3) enables us to better organize the calculations and understand the results. As a numerical example, we study the electronic structure of a linear bilayer graphene lattice system with a magic twist angle (∼1.05°). The well-known flat bands are reproduced ensuring that their features quantitatively agreed with those obtained experimentally and via other theoretical calculations. Moreover, the extended framework has a much lower computational cost than the commensurate cell approximations and is more extendable than the traditional model Hamiltonians and tight binding models. Finally, this framework readily accommodates nonlinear models, thereby laying the foundation for more effective and accurate density functional theory (DFT) calculations.

Quasi-band structure of quantum-confined nanocrystals

We discuss the electronic properties of quantum-confined nanocrystals. In particular, we show how, starting from the discrete molecular states of small nanocrystals, an approximate band structure (quasi-band structure) emerges with increasing particle size. Finite temperature is found to broaden the discrete states in energy space forming even for nanocrystals in the quantum-confinement regime quasi-continuous bands in k-space. This bands can be, to a certain extend, interpreted along the lines of standard band structure theory, while taking also finite size and surface effects into account. We discuss this on various prototypical nanocrystal systems.

Compatibility relationships in van der Waals quasicrystals

The incommensurate twist structure and the interlayer coupling induce van der Waals quasicrystals (vdW-QCs). Replacing conventional band theory requiring translational symmetry, the resonant coupling Hamiltonian endowing the quasiband structure in $\mathbit{k}$ space is adopted to describe electronic properties of vdW-QCs [Moon et al., Phys. Rev. B 99, 165430 (2019)]. Here we investigate the symmetries of the resonant coupling Hamiltonians in dodecagonal and octagonal vdW-QCs. Through symmetry analyses we derive compatibility relationships (CRs) between $\mathrm{\ensuremath{\Gamma}}$ point and other irreducible pathways and predict the symmetry changes and band splits. Especially, we find that from $\mathrm{\ensuremath{\Gamma}}$ point to Brillouin zone corner points of monolayers, arbitrary twofold degenerate states are split into one ${A}^{\ensuremath{'}}$ and one ${A}^{\ensuremath{''}}$ state, and from $\mathrm{\ensuremath{\Gamma}}$ point to the intersection points of two Brillouin zones of monolayers, arbitrary twofold degenerate states are split into one $A$ and one $B$ state. Instead of projection operation analyses, we discuss the CRs of different point groups between the coupled bilayers and uncoupled monolayers to construct the interlayer hybridization selection rules (IHSRs) [Yu et al., Phys. Rev. B 105, 125403 (2022)], which govern how the interlayer states interact with each other in the resonant coupling systems of dodecagonal and octagonal vdW-QCs. These derived IHSRs indicate that the first two main resonant couplings allow the nonequivalent hybridizations only between ${B}_{1}$ and ${B}_{2}$ states and the equivalent hybridizations for $A$, ${A}_{i}$, ${A}^{\ensuremath{'}}$, ${A}^{\ensuremath{''}}$, $E$, or ${E}_{i}$ states.

Silicon-Tin Alloyed Nanocrystals by Femtosecond Laser Plasma

Silicon’s (Si) indirect bandgap limits its absorption and possible applications, and therefore remarkable efforts are put into the possibility of fabricating a material compatible with the existing silicon technology that is also a direct bandgap material. Tin (Sn) alloying with silicon represents an exciting possibility to tune Si properties. In addition, at the quantum confinement size (<10 nm) when the material becomes a quantum dot, it becomes possible to control the electronic structure of a material by varying the size. Although the possibility to tailor the bandgap of elemental Si over a wide range has been demonstrated, it is very challenging to obtain stable alloyed SiSn quantum dots. In particular, alfa Sn has a crystal structure similar to Si with zero band gap: a diamond cubic crystal structure, and importantly affected by the crystal configuration and a possible change to a direct energy gap at sufficiently high Sn concentration. This therefore makes Sn a favorable element to create an alloy with a lower bandgap than Si. Exploiting these features would make alloyed SiSn NCs an important candidate for a broad range of applications such as next generation photovoltaic cells based on carrier multiplication, super high efficient photodetectors, fluorescent tags for biomedical applications etc. In this contribution we will discuss the synthesis paths and optoelectrical properties in the context of silicon, tin, and silicon/tin alloyed nanocrystals at high alloying concentrations. Our results show that plasma-based processes allow the synthesis of alfa tin alloyed SiSn QDs with unprecedented dimensions and alloying concentrations. We will present SiSn-QDs as the world’s highest alloys fabricated by confined plasma from femtosecond (fs) laser in liquid media with a high tin concentration of approximately 17% ever reported in literature to our knowledge. We have demonstrated for the first time the experimental and exact theoretical calculation determination of the thermal stability of the SiSn-NCs at those concentrations. We study their electronic properties by means of an approximate band structure suitable for finite-sized systems (quasi-band structure) derived from first-principles calculations. This work therefore advances the current state of the art, provides opportunities to compare and verify theoretical results and offer important directions for applications.

Tuning the Bandgap Character of Quantum‐Confined Si–Sn Alloyed Nanocrystals

AbstractNanocrystals in the regime between molecules and bulk give rise to unique electronic properties. Here, a thorough study focusing on quantum‐confined nanocrystals (NCs) is provided. At the level of density functional theory an approximate (quasi) band structure which addresses both the molecular and bulk aspects of finite‐sized NCs is calculated. In particular, how band‐like features emerge with increasing particle diameter is shown. The quasiband structure is used to discuss technological‐relevant direct bandgap NCs. It is found that ultrasmall Sn NCs have a direct bandgap in their at‐nanoscale‐stable α‐phase and for high enough Sn concentration (≈41%) alloyed Si–Sn NCs transition from indirect to direct bandgap semiconductors. The calculations strongly support recent experiments suggesting a direct bandgap for these systems. For a quantitative comparison many‐body GW + Bethe–Salpeter equation (BSE) calculations are performed. The predicted optical gaps are close to the experimental data and the calculated absorbance spectra compare well with the corresponding measurements.

Quasicrystalline electronic states in 30∘ rotated twisted bilayer graphene

The recently realized bilayer graphene system with a twist angle of $30^\circ$ offers a new type of quasicrystal which unites the dodecagonal quasicrystalline nature and graphene's relativistic properties. Here, we introduce a concise theoretical framework that fully respects both the dodecagonal rotational symmetry and the massless Dirac nature, to describe the electronic states of the system. We find that the electronic spectrum consists of resonant states labeled by 12-fold quantized angular momentum, together with the extended relativistic states. The resulting quasi-band structure is composed of the nearly flat bands with spiky peaks in the density of states, where the wave functions exhibit characteristic patterns which fit to the fractal inflations of the quasicrystal tiling. We also demonstrate that the 12-fold resonant states appear as spatially-localized states in a finite-size geometry, which is another hallmark of quasicrystal. The theoretical method introduced here is applicable to a broad class of "extrinsic quasicrystals" composed of a pair of two-dimensional crystals overlaid on top of the other with incommensurate configurations.

Modeling optical coupling of plasmons and inhomogeneously broadened emitters.

Optically coupling quantum emitters to nanoparticles provides the foundation for many plasmonic applications. Including quantum mechanical effects within the calculations can be crucial for designing new devices, but classical approximations are sometimes sufficient. Comprehending how the classical and quantum mechanical descriptions of quantum emitters alter their calculated optical response will lead to a better understanding of how to design devices. Here, we describe how the semiclassical Maxwell-Liouville method can be used to calculate the optical response from inhomogeneously broadened states. After describing the Maxwell-Liouville algorithm, we use the method to study the photon echoes from quantum dots and compare the results against analytical models. We then modify the quantum dot's state distribution to match a PbS 850 nm quantum dot's absorption spectra to see how the complete quasi-band structure affects their coupling to gold nanoislands. Finally, we compare the results with previously published work to demonstrate where the complete quantum dot description is necessary.

Electronic structure of (ZnO)1−x(InN)x alloys calculated by interacting quasi-band theory

We calculated the electronic structure of (ZnO)1−x(InN)x, (=ZION), which belongs to a novel category of hybrid (II–VI)1−x(III–V)x alloys, by the interacting quasi-band theory aided by the sp3 tight-binding model of the wurzite structure. The tight-binding parameters of the irregular bonds (Zn–N and In–O) were estimated by iterating the relevant normal bonds and the absolute atomic levels were corrected by the electron affinities of ZnO and InN. We thus obtained the quasi-band structure of ZION at various concentrations. Across the entire range of concentrations, ZION exhibited a direct energy gap at Γ, and the band-gap energy continuously changes from 0.7 to 3.3 eV with a large band-gap bowing. A particularly, large shift was observed around x = 0.5. The obtained theoretical results imply that ZION (x = 0.1–0.3) is a suitable material for visible-light devices.

Interlayer interaction in general incommensurate atomic layers

We present a general theoretical formulation to describe the interlayer interaction in incommensurate bilayer systems with arbitrary crystal structures. By using the generic tight-binding description, we show that the interlayer coupling, which is highly complex in the real space, can be simply written in terms of generalized Umklapp process in the reciprocal space. The formulation is useful to describe the interaction in the two-dimensional interface of different materials with arbitrary lattice structures and relative orientations. We apply the method to the incommensurate bilayer graphene with a large rotation angle, which cannot be treated as a long-range moiré superlattice, and obtain the quasi band structure and density of states within the first-order approximation.

Electronic delocalization in discotic liquid crystals: a joint experimental and theoretical study.

Discotic liquid crystals emerge as very attractive materials for organic-based (opto)electronics as they allow efficient charge and energy transport along self-organized molecular columns. Here, angle-resolved photoelectron spectroscopy (ARUPS) is used to investigate the electronic structure and supramolecular organization of the discotic molecule, hexakis(hexylthio)diquinoxalino[2,3-a:2',3'-c]phenazine, deposited on graphite. The ARUPS data reveal significant changes in the electronic properties when going from disordered to columnar phases, the main feature being a decrease in ionization potential by 1.8 eV following the appearance of new electronic states at low binding energy. This evolution is rationalized by quantum-chemical calculations performed on model stacks containing from two to six molecules, which illustrate the formation of a quasi-band structure with Bloch-like orbitals delocalized over several molecules in the column. The ARUPS data also point to an energy dispersion of the upper pi-bands in the columns by some 1.1 eV, therefore highlighting the strongly delocalized nature of the pi-electrons along the discotic stacks.

Study on the coupled multiple nanocrystal quantum-dot system

We have studied excess electron filling rule in the coupled multiple nanocrystal quantum-dot systems, i.e. quantum chain and quantum pattern, by the unrestricted Hartree–Fock–Roothaan method. Assuming each quantum dot of quantum pattern to be confined in a three-dimensional spherical potential well of finite depth, we have studied the intradot and interdot electron Coulomb and exchange interactions. By varying the center distance d between the coupled quantum dots, the transition from the strong- to weak-coupling situation is realized. For the systems in question, our results show that, with the filling of excess electrons into the quantum pattern, the corresponding chemical potentials form quasi-band structure, which is similar to the energy-band structure of crystal material. In each chemical-potential band of quantum pattern, the number of chemical-potential curves is equal to the number of quantum dots, and the distributions of them depend strongly on the quantum-dot arrangement structure of quantum pattern.

LDA+? (?) Method for the Electronic Structure of Strongly Correlated Antiferromagnetic Materials: Application to La2CuO4

In this paper we present a method for obtaining the quasiband structure and the renormalized density of quasistates of strongly correlated systems with antiferromagnetic ordering. We calculate the electronic structure of La2CuO4 in order to test this method. The first step required is to calculate the electronic structure from the local density approximation (LDA) in order to obtain the initial non-interacting ground state. The LDA density of states in strongly correlated systems usually presents serious discrepancies with experimental results. As is well known, these discrepancies, fundamentally concerning photoemission, are due to the fact that the dynamic correlation effects are not taken into account within the LDA. In order to include these effects, we obtain a self-energy potential which allows the initial LDA electronic structure to connect with that of the antiferromagnetic ground state arising from a Bogolyubov-like transformation. Within this new ground state, we determine an antiferromagnetic self-energy by means of a spin density wave procedure, and the interacting Green function yields a density of states which is in reasonable agreement with the experimental photoemission result.

Observation of theνh11/2sequence in the97Monucleus

High-spin states have been studied in the ${}^{97}\mathrm{Mo}$ nucleus with the reaction ${}^{82}\mathrm{Se}{(}^{19}\mathrm{F},p3n\ensuremath{\gamma})$ at 68 MeV. The main experimental result is the observation of the $\ensuremath{\nu}{h}_{11/2}$ quasiband structure up to the ${31/2}^{\ensuremath{-}}$ state at ${E}_{x}=5.5\mathrm{MeV}.$ The systematic behavior of this structure along the isotopic and isotonic sequences is presented. The structure of the ${}^{97}\mathrm{Mo}\mathrm{}$ is discussed in terms of the interacting boson-fermion model 1.

Crystal structure and molecular mechanics, dynamics and quantum-mechanical ab initio studies of 2,2,4,4,6,6-hexakis(p-phenoxyphenoxy)-2λ5,4λ5,6λ5-cyclotriphosphaza-1,3,5-triene

Molecular mechanics modelling and molecular dynamic (MD) simulations have been carried out for [NP(OC6H4OPh-p)2]3. Force-field parameters developed for cyclotriphosphazenes gave calculated bond lengths and angles in agreement with the values determined by X-ray diffraction analysis of the crystal. Calculated and X-ray diffraction data for the torsional angles were in poor agreement due to crystal-packing forces determining the conformation in the solid. The MD simulation gave a nearly symmetric equilibrium conformation and showed that the fluxional mobility of the phenoxy groups increases on going from the P–O bonds of the phosphazene core to the external fragments of the molecule. The crystals were triclinic, space group P, with a= 15.345(2), b= 15.440(3), c= 15.999(3)A, α= 80.43(1), β= 66.67(1), γ= 60.62(1)° and Z= 2, and the structure was refined to R= 0.057 and R′= 0.066. The force-field parameter set for MD well reproduces the energy difference between the solid and gas-phase conformations calculated by the ab-initio(STO-3G*) method. The calculated small energy differences between the molecular orbitals indicate a possible quasi-band structure for the bonding electrons. A perturbation of the electronic system localized on the atoms of the external phenyl groups can therefore propagate towards the P and N atoms of the cyclophosphazene ring.

Momentum-dependent excitations in beta -carotene, a finite-size system between molecules and polymers.

Electron-energy-loss spectroscopy has been used to study momentum-dependent excitations of \ensuremath{\pi} electrons in \ensuremath{\beta}-carotene. These investigations illustrate that the orbital levels of \ensuremath{\pi} electrons in finite polyenes and other conjugated oligomers can be mapped out. It turns out that the electronic structure of the \ensuremath{\pi} electrons can be described in terms of a quasi band structure with a finite number of momentum values. The results are compared with theoretical calculations based on an effective Su-Schrieffer-Heeger Hamiltonian.

Even-odd Xe and Ba isotopes in the interacting boson-fermion model.

The even-odd Xe and Ba isotopes were studied in the averaged multi-j fermion orbit interacting boson-fermion model I. The agreements of the experimental and calculated energy spectra are quite good. The analyses on wave functions indicate that the mixture of fermion orbits increases and the quasiband structure becomes less prominent for the heavier even-odd Xe and Ba isotopes. The B(E2) values for $^{131}$,133Xe were calculated and compared with the experimental data.

Boson pair-breaking states in nuclei

The exact dispersion equations for the eigenstates of a system of bosons in a spherical or deformed potential well and interacting through a pairing interaction are used to reproduce the physics of the interacting boson model in three dynamical symmetry limits. These equations are generalised to treat the seniority-zero and -two states by switching on a surface-delta interaction between bosons. The model reproduces the quasiband structure in transition nuclei.

Levels in 74Se, 78, 80Kr and 84Sr and systematics of quasi-γ bands

Quasi-band structures in 74Se, 78, 80Kr and 84Sr have been investigated using (p, 2nγ) reactions. The members of the quasi-γ band have been observed up to 5 + in 74Se, 78, 80Kr and up to 3 + in 84Sr. The analyses of the energy systematics of the quasi-γ bands studied in this mass region as well as in other regions make clear the evolution of the quasi-γ band to the γ-band in well-deformed nuclei. In addition to these positive-parity bands, negative-parity levels were observed in 74Se, 80Kr and 84Sr.

Quasiparticle-Shell-Model Calculations of So-Called Two-Phonon States in Cd and Sn Isotopes

The anharmonicity effect due to the couplings between pamng vibrational modes and quadrupole correlation modes is investigated in the cases of Cd and Sn isotopes by carrying out the quasiparticle-shell-model calculations. It is clarified that the effect is so large in the first excited o+ state in Sn isotopes that its energy drops down dramatically in 114• 116• 11 '• 120Sn. In Cd isotopes, the coupling effect is indispensable for formation of roughly degenerate two­ phonon triplet. The static quadrupole moments and B(E2) values in Cd isotopes are also calculated and the results do not contradict with experiment. §I. Introduction The mechanism of the spherical-cleformecl transition in medium and heavy nuclei 1s considered to be governed by mutual interweaving of two different types of cor­ relation, i.e., the pairing correlation and the quadrupole correlation. Therefore, it is natural to consider that the elementary modes of excitation in these nuclei are pairing vibrational mode and quadrupole phonon mode under the random-phase ap­ proximation (RPA) and that the anharmonicity effects which manifest themselves as couplings between these elementary modes of excitation play an essential role in structure of low-lying states of transitional nuclei. The existence of hidden regu­ larities in the anharmonicity effects has been suggested by the quasi-band structure 1) and there have been a number of theoretical attempts to elucidate the microscopic structure of the anharmonicity effects in transitional nuclei. It has been pointed out in our previous papers 2>.a> that the anharmonicity effects clue to the couplings between pairing vibrational mode and quadrupole phonon mode play so important a role that the so-called two-phonon o+ state and the pairing vibra­ tional state couple with each other and the energy of the first excited o+ state drops do·wn in the transitional nuclei, for example, in Se and Mo isotopes. A similar situation may be expected in Cd and Te isotopes, because the neutron-single­ particle-level structure fairly resembles that in Se region. On the other hand, Cd isotopes have so far been referred to as typical examples of appearance of two­ phonon-triplet states. Standing on the viewpoint of usual phonon (boson) picture, we find no structural difference between the members of the two-phonon triplet. However, if the excited o+ state is strongly affected by the pairing vibrational mode,

Transition rates of high-spin states inCo56andFe56: Possible coexistence of prolate- and oblate-like configurations inFe56

The decay properties of the high-spin states in $^{56}\mathrm{Co}$ and $^{56}\mathrm{Fe}$ have been investigated via the $^{54}\mathrm{Fe}(\ensuremath{\alpha},pn)^{56}\mathrm{Co}^{*}(\ensuremath{\gamma})$ and $^{54}\mathrm{Fe}(\ensuremath{\alpha},2p)^{56}\mathrm{Fe}^{*}(\ensuremath{\gamma})$ reactions in the energy range 20.4-29.5 MeV. From measurements of excitation functions and angular distributions of individual $\ensuremath{\gamma}$ rays with a Ge(Li)-NaI(T1) anti-Compton spectrometer, and from $\ensuremath{\gamma}\ensuremath{\gamma}$-coincidence experiments new levels in $^{56}\mathrm{Co}$ have been identified at 2282.6 (${7}_{1}^{+}$), 2371.9 (${6}_{1}^{+}$), 3638.0 (${8}_{1}^{+}$), 4180.2 (${9}_{1}^{+}$), and 5274.6 (${10}_{1}^{+}$) keV with the deduced ${J}^{\ensuremath{\pi}}$ values in parentheses. Similarly levels in $^{56}\mathrm{Fe}$ have been confirmed at 3388.4 (${6}_{1}^{+}$), 3755.8 (${6}_{2}^{+}$), 4700.6 (${7}_{1}^{+}$), 5255.3 (${8}_{1}^{+}$), and 5626.8 (${8}_{2}^{+}$) keV and the ${J}^{\ensuremath{\pi}}$ values in parentheses have been deduced. The angular distributions in conjunction with the associated attenuation factors were analyzed to yield multipole mixing ratios $\ensuremath{\delta}(\frac{E2}{M1})$.The mean lifetimes $\ensuremath{\tau}$ of these states were also carefully measured by extrapolation to the detection threshold of the effective mean lifetimes extracted from Doppler-broadened line shapes obtained at four bombardment energies between 20.4 and 29.5 MeV. The values obtained in $^{56}\mathrm{Co}$ are 2282.6 KeV (&gt;2000 fs), 2371.9 keV (60 \ifmmode\pm\else\textpm\fi{} 30 fs), 3638.0 keV (${80}_{\ensuremath{-}30}^{+40}$ fs), 4180.2 keV (590 \ifmmode\pm\else\textpm\fi{} 60 fs), and 5274.6 keV (${60}_{\ensuremath{-}20}^{+40}$ fs); and those in $^{56}\mathrm{Fe}$ are 3388.4 keV (&gt;2000 fs), 3755.8 keV (${180}_{\ensuremath{-}30}^{+40}$ fs), 4700.6 keV (120 \ifmmode\pm\else\textpm\fi{} 40 fs), 5255.3 keV (500 \ifmmode\pm\else\textpm\fi{} 50 fs), and 5626.8 keV (${100}_{\ensuremath{-}20}^{+40}$ fs). For most of the transitions from the high-spin states in $^{56}\mathrm{Co}$ and $^{56}\mathrm{Fe}B(\ensuremath{\Lambda})$ values were obtained. The results for $^{56}\mathrm{Fe}$ are compared with recent calculations based on the aligned coupling scheme indicating possible coexistence of quasiband structures with prolate- and oblate-like configurations. The results for $^{56}\mathrm{Co}$ are compared with other recent shell-model calculations and good agreement is observed.NUCLEAR REACTIONS $^{54}\mathrm{Fe}(\ensuremath{\alpha},pn)^{56}\mathrm{Co}^{*}(\ensuremath{\gamma})$ and $^{54}\mathrm{Fe}(\ensuremath{\alpha},2p)^{56}\mathrm{Fe}^{*}(\ensuremath{\gamma})$, $E=21\ensuremath{-}30$ MeV, enriched targets. Measured, ${E}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}(\ensuremath{\theta})$, $\ensuremath{\sigma}(E)$, ${\ensuremath{\Delta}\overline{E}}_{\ensuremath{\gamma}}(E,\ensuremath{\tau})$, $\ensuremath{\gamma}\ensuremath{\gamma}$ coin., deduced levels in $^{56}\mathrm{Co}$ and $^{56}\mathrm{Fe}$, $J$, $\ensuremath{\pi}$, branching ratios, ${\ensuremath{\tau}}_{\mathrm{level}}$, $\ensuremath{\delta}(\frac{E2}{M1})$, $B(E2)$ and $B(M1)$ values; Ge(Li) detectors, Ge(Li)-NaI(T1) anti-Compton spectrometer, 2.2. keV at 1332.5 keV.