Collective Band Structures Research Articles

Recent progress of transport theory in Dirac quantum materials

Dirac quantum materials comprise a broad category of condensed matter systems characterized by low-energy excitations described by the Dirac equation. These excitations, which can manifest as either collective states or band structure effects, have been identified in a wide range of systems, from exotic quantum fluids to crystalline materials. Over the past several decades, they have sparked extensive experimental and theoretical investigations in various materials, such as topological insulators and topological semimetals. The study of Dirac quantum materials has also opened up new possibilities for topological quantum computing, giving rise to a burgeoning field of physics and offering a novel platform for realizing rich topological phases, including various quantum Hall effects and topological superconducting phases. Furthermore, the topologically non-trivial band structures of Dirac quantum materials give rise to plentiful intriguing transport phenomena, including longitudinal negative magnetoresistance, quantum interference effects, helical magnetic effects, and others. Currently, numerous transport phenomena in Dirac quantum materials remain poorly understood from a theoretical standpoint, such as linear magnetoresistance in weak fields, anomalous Hall effects in nonmagnetic materials, and three-dimensional quantum Hall effects. Studying these transport properties will not only deepen our understanding of Dirac quantum materials, but also provide important insights for their potential applications in spintronics and quantum computing. In this paper, quantum transport theory and quantum anomaly effects related to the Dirac equation are summarized, with emphasis on massive Dirac fermions and quantum anomalous semimetals. Additionally, the realization of parity anomaly and half-quantized quantum Hall effects in semi-magnetic topological insulators are also put forward. Finally, the key scientific issues of interest in the field of quantum transport theory are reviewed and discussed.

Conflicting Coupling of Unpaired Nucleons and the Structure of Collective Bands in Odd-Odd Nuclei

The conflicting coupling of unpaired nucleons in odd-odd nuclei is discussed. A very simple explanation is suggested for the damping of the energy spacing of the lowest levels in the rotational bands in odd-odd nuclei with the ``conflicting'' coupling of an odd proton and an odd neutron comparative to those of the bands based on the state of a strongly coupled particle in the neighboring odd nucleusentering the "conflicting" configuration.

Low-Energy Nuclear Excitations along the α-Decay Chains of Superheavy ^{292}Lv and ^{294}Og.

We present the first triaxial beyond-mean-field study of the excitation spectra of even-even superheavy nuclei. As representative examples, we have chosen the members of the α-decay chains of ^{292}Lv and ^{294}Og, the heaviest even-even nuclei which have been synthesized so far using ^{48}Ca-induced fusion-evaporation reactions. In our calculations, the effective finite-range density-dependent Gogny force is used and the angular-momentum and particle-number symmetries are restored. Configuration-mixing calculations are performed to determine ground- and excited-state deformations and to establish the collective band structures of these nuclei. Rapidly varying characteristics are predicted for the members of both decay chains, which are further accentuated when compared to the predictions of simple collective models. Based on the present calculations, the prospect of observing α-decay fine structures in future experiments is discussed.

Underlying Structure of Collective Bands and Self-Organization in Quantum Systems.

The underlying structure of low-lying collective bands of atomic nuclei is discussed from a novel perspective on the interplay between single-particle and collective degrees of freedom, by utilizing state-of-the-art configuration interaction calculations on heavy nuclei. Besides the multipole components of the nucleon-nucleon interaction that drive collective modes forming those bands, the monopole component is shown to control the resistance against such modes. The calculated structure of ^{154}Sm corresponds to the coexistence between prolate and triaxial shapes, while that of ^{166}Er exhibits a deformed shape with a strong triaxial instability. Both findings differ from traditional views based on β/γ vibrations. The formation of collective bands is shown to be facilitated from a self-organization mechanism.

Excited states and reduced transition probabilities in Os168

The level scheme of the neutron-deficient nuclide 168Os has been extended and mean lifetimes of excited states have been measured by the recoil distance Doppler-shift method using the JUROGAM \gamma-ray spectrometer in conjunction with the IKP K\oln plunger device. The 168Os \gamma rays were measured in delayed coincidence with recoiling fusion-evaporation residues detected at the focal plane of the RITU gas-filled separator. The ratio of reduced transition probabilities B(E2;4_1^+ \rightarrow 2_1^+)/B(E2;2_1^+ \rightarrow 0_1^+) is measured to be 0.34(18), which is very unusual for collective band structures and cannot be reproduced by IBM-2 model calculations based on the SkM* energy-density functional.

Population and decay of aKπ=8−two-quasineutron isomer inPu244

Here, the decay of a Kπ = 8– isomer in 244Pu and the collective band structures populating the isomer were studied using deep inelastic excitations with 47Ti and 208Pb beams, respectively. Precise measurements of M1/E2 branching ratios in the band confirm a 9/2–[734]νⓍ7/2+[624]ν configuration assignment for the isomer, validating the systematics of Kπ = 8–, two-quasineutron isomers observed in even-Z, N = 150 isotones. These isomers around the deformed shell gap at N = 152 provide critical benchmarks for theoretical predictions of single-particle energies in this gateway region to superheavy nuclei.

Band structure inSn113

The structure of collective bands in $^{113}\mathrm{Sn}$, populated in the reaction $^{100}\mathrm{Mo}(^{19}\mathrm{F},\phantom{\rule{0.16em}{0ex}}p5n)$ at a beam energy of 105 MeV, has been studied. A new positive-parity sequence of eight states extending up to 7764.9 keV and spin $(39/{2}^{+})$ has been observed. The band is explained as arising from the coupling of the odd valence neutron in the ${g}_{7/2}$ or the ${d}_{5/2}$ orbital to the deformed 2p-2h proton configuration of the neighboring even-$A$ Sn isotope. Lifetimes of six states up to an excitation energy of 9934.9 keV and spin $47/{2}^{\ensuremath{-}}\mathrm{belonging}$ to a $\mathrm{\ensuremath{\Delta}}I=2$ intruder band have been measured for the first time, including an upper limit for the last state, from Doppler-shift-attenuation data. A moderate average quadrupole deformation ${\ensuremath{\beta}}_{2}=0.22\ifmmode\pm\else\textpm\fi{}0.02$ is deduced from these results for the five states up to spin $43/{2}^{\ensuremath{-}}$. The transition quadrupole moments decrease with increase in rotational frequency, indicating a reduction of collectivity with spin, a feature common for terminating bands. The behavior of the kinematic and dynamic moments of inertia as a function of rotational frequency has been studied and total Routhian surface calculations have been performed in an attempt to obtain an insight into the nature of the states near termination.

Shape phase transition atN=88–90inBa144,146

Background: The neutron-rich Ba isotopes with only six valence protons represent the beginning of the collective rotation-vibration band structure. The sharp shape phase transition at $N=88\text{--}90$ observed in Ce-Gd isotones is not exhibited in $^{144\text{--}146}\mathrm{Ba}$, which renders their analysis interesting. Also there are ambiguities in the spin and band assignments.Purpose: To study their spectra empirically and to compare with predictions from an interacting boson model and microscopic dynamic pairing plus quadrupole model to explain the smooth shape transition at $N=88\text{--}90$.Method: We compare the results of the calculation in the interacting boson models (IBM-1) and IBM-2 and the dynamic pairing plus quadrupole model with experiment and illustrate the variation in level structure of the Ba isotopes with N. The absence of sharp phase transition at $N=88\text{--}90$ is examined.Results: The ambiguous spin and parity of levels of the vibrational bands are assigned on the basis of calculated K components and the decay characteristics.Conclusion: The second ${I}^{\ensuremath{\pi}}={2}^{+}$ states in $^{144,146}\mathrm{Ba}$ have $K=0$ predominance, and ${I}^{\ensuremath{\pi}}={2}_{3}^{+}$ states are $K=2$. The smooth transition at $N=88\text{--}90$ is explained.

Reinvestigation of the collective band structures in odd-odd 138Pm nucleus

The high-spin states in the odd-odd 138Pm nucleus have been reinvestigated via the 124Te(19F, 5n) reaction at the beam energy of 103 MeV. Most of the known transitions and levels are confirmed. A number of bands are revised and one new band has been established. For the yrast πh 11/2⊗νh 11/2 band based on 8+ state, no evidence supporting the occurence of signature inversion is found. The experimental and theoretical B(M1)/B(E2) ratios have been calculated for band (2), which support the πg 7/2[413]5/2+ ⊗ νh 11/2[514]9/2− Nilsson configuration assignment. Four bands with ΔI = 2 transitions are tentatively assigned as doubly decoupled bands. The other three bands are proposed as oblate-triaxial bands. The possible configuration assignments for these bands are also discussed under the calculations of total Routhian surface and particle-rotor model.

Collective band structure of 166,168Hf in IBM and DPPQ models

166,168Hf are the lightest isotopes of Hf, for which the spectral information for non-yrast levels is now available from recent experiments. The algebraic Interacting Boson Model IBM-1 is employed to reproduce their level structures and to predict the E2 transition probabilities. The pairing plus quadrupole model is used to predict their spectra and E2 transition rates and the static moments in a microscopic approach. The spin assignments I π of new levels and their K-band structures are studied. The validity of the inclusion of 166,168Hf as members of a U(12) super group is studied using various empirical observables. The potential energy surfaces for the two isotopes are compared and the filling of the nucleons in Nilsson orbits is analyzed, to yield a consistent comprehensive view of the spectra of the two Z = 72 isotopes.

Contrasting vortex-gyration dispersions for different lattice bases in one-dimensional magnetic vortex arrays

We performed micromagnetic numerical and analytical calculations in studying the effects of change in the primitive unit cells of one-dimensional (1D) vortex arrays on collective vortex-gyration dispersion. As the primitive basis, we consider alternating constituent materials (NiMnSb vs. Permalloy) and alternating dimensions including constituent disk diameter and thickness. In the simplest case, that of one vortex-state disk of given dimensions and single material in the primitive cell, only a single branch of collective vortex-gyration dispersion appears. By contrast, two constituent disks' different alternating materials, thicknesses, and diameters yield characteristic two-branch dispersions, the band widths and gaps of which differ in each case. This work offers not only an efficient means of manipulating collective vortex-gyration band structures but also a foundation for the development of a rich variety of 1D or 2D magnonic crystals and their band structures based on dipolar-coupled-vortex arrays.

High-spin structures in the139Pr nucleus

Background: ${}^{139}$Pr is located in a transitional region of neutron number close to the $N=82$ shell. The study of its high-spin states and collective bands is important for systematically understanding the nuclear structural characteristics in this region.Purpose: To investigate the high-spin levels and to search for oblate bands in ${}^{139}$Pr.Methods: The high-spin states of ${}^{139}$Pr have been studied via the reaction ${}^{124}$Sn(${}^{19}$F,4$n$) at a beam energy of 80 MeV. The experiment was carried out at the HI-13 Tandem Accelerator at the China Institute of Atomic Energy (CIAE). The data analysis was done by using the $\ensuremath{\gamma}$-$\ensuremath{\gamma}$ coincidence method.Results: The level scheme of ${}^{139}$Pr has been expanded with spin up to 45/2$\ensuremath{\hbar}$. A total of 39 new levels and 45 new transitions are identified. Four collective band structures at high-spin states have been newly established. From systematic analysis, one of the bands is proposed as a double decoupled band; two bands are proposed as oblate bands with $\ensuremath{\gamma}\ensuremath{\sim}\ensuremath{-}{60}^{\ensuremath{\circ}}$; another band is suggested as an oblate-triaxial band with $\ensuremath{\gamma}\ensuremath{\sim}\ensuremath{-}{90}^{\ensuremath{\circ}}$. The other characteristics for these bands are discussed.Conclusions: A new level scheme in ${}^{139}$Pr has been established and the collective bands at high spin have been identified. The result shows that the strong oblate shape-driving effect is caused by neutrons at the high-spin states in ${}^{139}$Pr.

High-Spin States in 141Pm

The high-spin states of 141Pm nucleus have been studied by using in-beam γ-ray spectroscopy technology through the126Te(19F, 4n) reaction at a beam energy of 90 MeV. The previous level scheme has been extended with spin up to 49/2 ℏ. Many new levels and transitions are identified. Five collective band structures are observed. Based on systematic comparison with the neighboring nuclei, two bands with strong ΔI = 1 M1 transitions inside the bands are proposed as the oblate bands with γ∼−60°, and three bands with large signature splitting have been suggested as the oblate-triaxial deformation with γ∼−90°. The characteristics for these bands have been discussed.

High-spin states and collective band structures in the odd–odd 140Pm nucleus

The high-spin states of 140Pm have been investigated through the reaction 126Te(19F, 5n) at a beam energy of 90 MeV. A previous level scheme based on the 8− isomer has been updated with spin up to 23 ℏ. A total of 22 new levels and 41 new transitions were identified. Six collective bands were observed. Five of them were expanded or re-constructed, and one of them was newly identified. The systematic signature splitting and inversion of the yrast πh11/2⊗νh11/2 band in Pr and Pm odd–odd isotopes has been discussed. Based on the systematic comparison, two ΔI = 2 bands were proposed as double-decoupled bands; other two bands with strong ΔI = 1 M1 transitions inside the bands were suggested as oblate bands with γ ∼ −60°; another band with large signature splitting has been proposed with oblate-triaxial deformation with γ ∼ −90°. The characteristics for these bands have been discussed.

Collective Band Structures and Identification of One-Phonon and Two-Phonon γ-Vibrational Bands in 109Tc

The high spin states of the neutron-rich 109Tc nucleus are reinvestigated by observing prompt γ-rays from the spontaneous fission of 252Cf. The previously known yrast band based on the 7/2+ state is updated. A side band built on the 11/2+ state is expanded and a new band based on the 15/2+ state is identified. Band crossing in the yrast band occurs around ħω ≈ 0.36MeV. This band crossing is associated with the alignment of two h11/2 neutrons according to the cranked shell model calculations. The band based on the 11/2+ state is proposed as a candidate for the one-phonon γ-vibrational band, and the band built on the 15/2+ state is proposed as a candidate for the two-phonon γ-vibrational band. Other characteristics for the observed bands are discussed.

Collective band structures in neutron-richTc106,107

The high spin states of neutron-rich $^{106,107}\mathrm{Tc}$ nuclei have been reinvestigated by observing prompt $\ensuremath{\gamma}$ rays from the spontaneous fission of $^{252}\mathrm{Cf}$. In $^{106}\mathrm{Tc}$, a previously known collective band is expanded, and a new collective band is identified. In $^{107}\mathrm{Tc}$, a collective band based on the $\ensuremath{\pi}5/{2}^{\ensuremath{-}}[303]$ orbital is confirmed and extended. Inconsistencies in the configuration assignments for positive parity bands in $^{105,107}\mathrm{Tc}$ in the previous reports are clarified. The spins and parities as well as the configurations for the two bands in $^{106}\mathrm{Tc}$ are assigned according to the angular momentum alignments and $g$-factor calculations. Other characteristics for the observed bands are discussed.

Collective rotation and vibration in neutron-richHf180,182nuclei

High-spin states in neutron-rich Hf-180 and Hf-182 nuclei were populated through inelastic and transfer reactions with a Xe-136 beam incident on a thin Hf-180 target, and investigated using particle-gamma coincidence techniques. New collective band structures were observed, and previously known rotational and vibrational bands in these nuclei were extended to higher angular momenta. No obvious nucleon alignment was observed in the ground state band of either nucleus up to h omega=0.43 MeV, a significant delay compared to lighter even-even Hf isotopes. Woods-Saxon cranking calculations were performed to predict the nature of the first band crossings and shape evolution in Hf-180,Hf-182.

High-Kisomers and rotational structures inW174

High-spin states in $^{174}\mathrm{W}$ (Z = 74) have been populated using the reaction $^{128}\mathrm{Te}$($^{50}\mathrm{Ti}$, 4n)$^{174}\mathrm{W}$ at beam energies of 215 and 225 MeV. The Gammasphere array was used to detect the \ensuremath{\gamma} rays emitted by the evaporation residues. Four previously known collective band structures have been extended, and 16 new rotational sequences observed. Two are built upon isomeric states, one corresponding to a two-quasiparticle K = 8 isomer, the other to a four-quasiparticle K = 12 isomer, with the latter exhibiting strong K-violating $\ensuremath{\Delta}K=12$ decays to the ground state band. Nucleonic configurations for the two- and four-quasiparticle excitations are proposed, and Woods-Saxon cranking calculations are presented to understand the rotational structures. Decay mechanisms of multi-quasiparticle K isomers are discussed in terms of the prevalent phenomenological models, with special emphasis on \ensuremath{\gamma}-tunneling calculations. Surprisingly, the latter underpredict the decay hindrance for the K = 12 isomer by three orders of magnitude, unlike all other isomer decays in this mass region.

Rotational structures in the 125Cs nucleus

The collective band structures of the 125Cs nucleus have been investigated by in-beam γ-ray spectroscopic techniques following the 110Pd ( 19F, 4n) reaction at 75MeV. The previously known level scheme, with rotational bands built on πg7/2, πg9/2 and πh11/2 orbitals, has been extended and evolves into bands involving rotationally aligned ν(h11/2)2 and π(h11/2)2 quasiparticles. A strongly coupled band has been reassigned a high-K πh11/2 ⊗ νg7/2 ⊗ νh11/2 three-quasiparticle configuration and a new side band likely to be its chiral partner has been identified. Configurations assigned to various bands are discussed in the framework of Principal/Tilted Axis Cranking (PAC/TAC) model calculations.

New insights into neutron rich nuclei from fission

Neutron-rich nuclei populated in spontaneous fission are providing new tests for microscopic models. The neutron-rich 104–108Mo, 108–114Ru and 112–116Pd exibit a variety of rapidly changing collective band structures to high spins. The first evidence for chiral band doublets in any even-even nucleus are reported.