One-dimensional Band Research Articles

Synthesis, structure and characterizations of the first alkali-metal/alkaline-earth-metal oxalatophosphate Na4Mg3(HPO4)4(C2O4)·2H2O

The first alkali-metal/alkaline-earth-metal oxalatophosphate Na4Mg3(HPO4)4(C2O4)·2H2O with monoclinic P21/n space group was successfully synthesized by a conventional solvothermal method. Na4Mg3(HPO4)4(C2O4)·2H2O crystal exhibits a typical three-dimensional structure built by isolated [C2O4] and [HPO4] anionic groups connected by Na and Mg atoms. The HPO42− groups are linked by hydrogen bonds to form an unique one-dimensional zigzag band ∞[HPO4]2-, which exhibits a stable “Mortise-Tenon” structure configuration within the bc plane. Fourier transform infrared (FTIR) spectrum and Raman spectrum confirm the crystal structure of Na4Mg3(HPO4)4(C2O4)·2H2O. UV–visible near infrared (UV–Vis–NIR) diffuse reflectance and band structure calculation indicate that Na4Mg3(HPO4)4(C2O4)·2H2O is an indirect bandgap semiconductor with a bandgap of 4.42 eV. In addition, Na4Mg3(HPO4)4(C2O4)·2H2O shows a moderate birefringence of 0.046 at 550 nm.

Design of photonic crystals for nanokelvin-resolution thermometry

High-resolution thermometry is key for the development of calorimeters, bolometers, and high-stability light sources, as well as for probing dissipation and transport in microelectronics and quantum devices. Achieving nanokelvin-level temperature resolution at room temperature requires using large optical cavities, which are unsuitable for microscale integration. Here we computationally design a one-dimensional photonic crystal Band Edge Thermometer that achieves significant temperature sensitivity by combining: (i) the abrupt variation in optical properties of a direct bandgap semiconductor at the band edge, and (ii) a large quality factor in a resonant photonic structure. Two devices are designed which are constructed from GaAs/AlAs and GaN/AlN multilayer structures. The optimal sensor design features an extremely large thermoreflectance coefficient of 60.6 K−1 and a thermal time constant of 1.1 µs, with a sensor thickness of only 6.7 µm. The projected thermometry noise floor is 84 nK.Hz-½ for the GaAs/AlAs sensor and 35 nK.Hz-½ for the GaN/AlN sensor. The designed sensor architecture is expected to enable a broad range of applications in microcalorimetry and bolometry where a high temperature resolution combined with microscale sensor footprint is required.

Critical regions in a one-dimensional flat band lattice with a quasi-periodic potential

In our previous work, the concept of critical region in a generalized Aubry–André model (Ganeshan–Pixley–Das Sarma’s model) has been established. In this work, we find that the critical region can be realized in a one-dimensional flat band lattice with a quasi-periodic potential. It is found that the above flat band lattice model can be reduced to an effective Ganeshan–Pixley–Das Sarma’s model. Depending on various parameter ranges, the effective quasi-periodic potential may be bounded or unbounded. In these two cases, the Lyapunov exponent, mobility edge, and critical indices of localized length are obtained exactly. In this flat band model, the localized-extended, localized-critical and critical-extended transitions can coexist. Furthermore, we find that near the transitions between the bound and unbounded cases, the derivative of Lyapunov exponent of localized states with respect to energy is discontinuous. At the end, the localized states in bounded and unbounded cases can be distinguished from each other by Avila’s acceleration.

One-dimensional non-Hermitian band structures as Riemann surfaces

One-dimensional non-Hermitian band structures as Riemann surfaces

Surface band structure of the reconstructed Ir(001)-[formula omitted] surface

It is well known that the atomic structure of the Ir(001)-(5 × 1) surface consists of a quasi-hexagonal topmost layer on top of quadratic substrate layers. In the present work, we investigate how the electronic structure of Ir(001)-(1 × 1) is modified by the (5 × 1) reconstruction. For this purpose, we perform a first-principles density functional theory (DFT) calculation for semi-infinite Ir(001)-(1 × 1) and -(5 × 1) surfaces by employing the surface embedded Green’s function technique. It will be shown that surface bands on the (1 × 1) surface are strongly modified upon reconstruction. At the same time, we will demonstrate that one-dimensional (1D) surface bands localized in atomic rows in the [110] direction characterizing the buckled hexagonal layer emerge on the reconstructed surface.

Emergent Dirac Fermions in Epitaxial Planar Silicene Heterostructure.

Silicene, a single layer of Si atoms, shares many remarkable electronic properties with graphene. So far, silicene has been synthesized in its epitaxial form on a few surfaces of solids. Thus, the problem of silicene-substrate interaction appears, which usually depresses the original electronic behavior but may trigger properties superior to those of bare components. We report the direct observation of robust Dirac-dispersed bands in epitaxial silicene grown on Au(111) films deposited on Si(111). By performing in-depth angle-resolved photoemission spectroscopy measurements, we reveal three pairs of one-dimensional bands with linear dispersion running in three different directions of an otherwise two-dimensional system. By combining these results with first-principles calculations, we explore the nature of these bands and point to strong interaction between subsystems forming a complex Si-Au heterostructure. These findings emphasize the essential role of interfacial coupling and open a unique materials platform for exploring exotic quantum phenomena and applications in future-generation nanoelectronics.

Giant Rashba-splitting of one-dimensional metallic states in Bi dimer lines on InAs(100).

Bismuth produces different types of ordered superstructures on the InAs(100) surface, depending on the growth procedure and coverage. The (2 × 1) phase forms at completion of one Bi monolayer and consists of a uniformly oriented array of parallel lines of Bi dimers. Scanning tunneling and core level spectroscopies demonstrate its metallic character, in contrast with the semiconducting properties expected on the basis of the electron counting principle. The weak electronic coupling among neighboring lines gives rise to quasi one-dimensional Bi-derived bands with open contours at the Fermi level. Spin- and angle-resolved photoelectron spectroscopy reveals a giant Rashba splitting of these bands, in good agreement with ab initio electronic structure calculations. The very high density of the dimer lines, the metallic and quasi one-dimensional band dispersion and the Rashba-like spin texture make the Bi/InAs(100)-(2 × 1) phase an intriguing system, where novel transport regimes can be studied.

Variational Quantum Simulators Based on Waveguide QED.

Waveguide QED simulators are analog quantum simulators made by quantum emitters interacting with one-dimensional photonic band gap materials. One of their remarkable features is that they can be used to engineer tunable-range emitter interactions. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms for certain problems. In particular, we illustrate their power in creating wave function Ansätze that capture accurately the ground state of quantum critical spin models (XXZ and Ising) with fewer gates and optimization parameters than other variational Ansätze based on nearest-neighbor or infinite-range entangling gates. Finally, we study the potential advantages of these waveguide Ansätze in the presence of noise. Overall, these results evidence the potential of using the interaction range as a variational parameter and place waveguide QED simulators as a promising platform for variational quantum algorithms.

Hyperspectral inversion of soil water and salt information based on fractional order derivative technology.

Accurate and efficient acquisition of soil water and salt information is a prerequisite for the improvement and sustainable utilization of saline lands. With the ground field hyperspectral reflectance and the measured soil water-salt content as data sources, we used the fractional order differentiation (FOD) technique to process hyperspectral data (with a step length of 0.25). The optimal FOD order was explored at the correlation level of spectral data and soil water-salt information. We constructed two-dimensional spectral index, support vector machine regression (SVR) and geographically weighted regression (GWR). The inverse model of soil water-salt content was finally evaluated. The results showed that FOD technique could reduce the hyperspectral noise and explore the potential spectral information to a certain extent, improve the correlation between spectrum and characteristics, with the highest correlation coefficients of 0.98, 1.35 and 0.33. The combination of characteristic bands screened by FOD and two-dimensional spectral index were more sensitive to characteristics than one-dimensional bands, with the optimal responses of order 1.5, 1.0 and 0.75. The optimal combinations of bands for maximum absolute correction coefficient of SMC were 570, 1000, 1010, 1020, 1330 and 2140 nm, pH were 550, 1000, 1380 and 2180 nm, and salt content were 600, 990, 1600 and 1710 nm, respectively. Compared with the original spectral reflectance, the validation coefficients of determination (Rp2) of the optimal order estimation models for SMC, pH, and salinity were improved by 1.87, 0.94 and 0.56, respectively. The overall GWR accuracy in the proposed model was better than SVR, where the GWR optimal order estimation models Rp2 were 0.866, 0.904 and 0.647, and the relative per-centage difference were 3.54, 4.25 and 1.86, respectively. The overall spatial distribution of soil water and salt content in the study area was characterized by low in the west and high in the east, with more serious soil alkalinization problems in the northwest and less severe in the northeast. The results would provide scientific basis for the hyperspectral inversion of soil water and salt in the Yellow River Irrigation Area and a new strategy for the implementation and management of precision agriculture in saline soil areas.

One-dimensional flat bands and Dirac cones in narrow zigzag dice lattice ribbons

We show that four narrow zigzag dice lattice ribbons, which have the minimal widths among their separate categories, constitute a unique collection of systems to study physics related to one-dimensional Dirac cones and flat bands. In zero magnetic field, all three combinations, including only Dirac cones, only flat bands, coexisting Dirac cones and flat bands, are realized in the low-energy band structures of one or two of the four ribbons. In particular, we identify flat bands and Dirac cones corresponding to the edge states of wide ribbons. In a perpendicular magnetic field that gives half a flux quantum per elementary rhombus, two of the four minimal ribbons have fully pinched spectrum, and dynamical evolutions from initially localized wave packets always lead to compact Aharonov-Bohm (AB) cages. The experimental realizations of these narrow zigzag dice lattice ribbons, and the opportunities of exploring novel single-body and many-body physics therein are discussed.

Dislocations as natural quantum wires in diamond

We study the electronic properties of the glide set of dislocations in diamond from first principles using hybrid exchange correlation functionals and find that the atomic-scale dislocation core states give rise to a prototypical one-dimensional (1D) band structure, i.e., natural quantum wires. The position and character of the core states varies strongly with local structure, where mixed dislocations with dangling bonds exhibit a 1D metallic band with a characteristic 1D density of states ($1/\sqrt{E}$). This 1D Fermi gas is spatially localized to a single atomic diameter orbital chain along the dislocation core. When the dangling bonds within the core are reconstructed, the 1D metallic band disappears. In contrast, pure edge dislocations in diamond reveal a 1D semiconductor with a direct band gap of 3.21 eV. These calculations provide a possible explanation to the long-standing observation of a blue luminescence band correlated with dislocations in diamond. This opens the door to using dislocations as 1D quantum phases with functional (electronic and optical) properties arising from the atomic-scale core states.

Multiple-symmetry-protected lantern-like nodal walls in lithium-rich compound LiRuO2

Topological semimetals have attracted wide attention due to their potential applications, such as electronic devices and electrocatalysis. Herein, based on the first-principles calculations and symmetry analysis, we first report that ternary compound pnnm-type LiRuO2 is a typical lantern-like nodal wall semimetal. Specifically, without considering spin-orbit coupling (SOC), one-dimensional (1D) two-fold degenerate bands on the ki = ±π (i = x, y) planes form the two-dimensional (2D) topological state (namely, nodal surface) under the constraint of multiple symmetry operations. In addition, the symmetry-enforced nodal network is formed on the kz = ±π planes. Finally, these nodal networks and nodal surfaces are coupled together to form lantern-like nodal walls. Remarkably, these topological states are protected by multiple symmetries, namely, nonsymmorphic two-fold screw-rotational symmetry [S2i (i = x, y)], time-reversal symmetry (T), inversion symmetry (I), glide plane symmetry (σz), and two-fold rotational symmetry (C2x/y). In addition, we further discuss the effect of spin-orbit coupling on the lantern-like nodal walls. We find that even if LiRuO2 contains S2z and T symmetries, these nodal surfaces and nodal networks are still broken. Then, due to the existence of I and T symmetries, Dirac nodal lines and Dirac points are formed in the low-energy region. Therefore, our work indicates that LiRuO2 is an excellent material platform for researching multiple topological states.

Multidimensional soil salinity data mining and evaluation from different satellites

Soil salinization, a common land degradation mode, restricts the ecological environment and is a global issue due to climate change. Accurately, quickly and effectively monitoring soil salinity is critical for governmental institutions that develop hazard prevention and mitigation strategies. Remote sensing (RS) technology provides a viable alternative to traditional field work due to its large area coverage, abundant spectral information and nearly constant observations. Key issues in RS-based soil salinity monitoring include the lack of both data-mining techniques for obtaining spectral band information and comprehensive considerations of synergies among different spectra. The main objective of this study was to provide in-depth explorations of data mining and integration algorithms from different satellites to multidimensionally evaluate soil salinity models. The Ebinur Lake Wetland Reserve (Xinjiang Province, China) was selected as a case study. First, ground-measured visible and near infrared (VIS-NIR) spectral data were combined with the RS band to simulate Landsat 8 (L8) and Sentinel 2 (S2) and 3 (S3) data. Second, one-dimensional RS bands and 15 soil salinity and vegetation indices were selected, and 15 spectral data transformations (reciprocal, differential, absorbance, etc.) were obtained. Two- and three-dimensional spectral indices were constructed, and the response relationships between different spectral indices and soil electrical conductivity (EC) were comprehensively explored. Finally, an integrated multidimensional algorithm was used to estimate soil salinity in high-performance models for the three satellites. The results showed that all data-mining-based model combinations performed well for all satellites (R2 > 0.80). However, with multidimensional model combinations, S3 presented the highest predictive capability (R2 = 0.89, RMSE = 2.57 mS·cm−1, RPD = 2.05), followed by S2 (R2 = 0.86, RMSE = 2.71 mS·cm−1, RPD = 1.90) and L8 (R2 = 0.85, RMSE = 2.84 mS·cm−1, RPD = 1.87). Therefore, data mining with integration algorithms in model combinations performs significantly better than previous models and could be considered a promising method for obtaining improved results from soil salinity susceptibility models in similar cases.

Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system

In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system. It is found that, when the potential is sufficiently strong, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Consequently, there exist some BIC in the effective potential well. These bound states are protected by the infinitely high potential barriers, which could not decay into the continuum. Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strengths, near which the bound state energy can go to infinity. For a sufficiently strong exponential potential, there exist two different bound states with a same number of wave function nodes. The existence of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for the existence of BIC is that the maximum of potential is larger than two times band gap.

A time-fractional dual-phase-lag framework to investigate transistors with TMTC channels (TiS3, In4Se3) and size-dependent properties

In this study, a time fractional dual-phase-lag model with temperature jump boundary condition as a choice for the Fourier's law replacement in thermal modeling of transistors, is utilized. In more details, the numerical simulation of heat transfer in newly proposed TMTC field effect transistors using fractional DPL equation has been investigated. Moreover, the Caputo fractional derivative is employed to formulate the finite difference scheme for discretization of the fractional DPL model. In order to obtain more precise results for the peak temperature rise, the temperature and heat flux profiles, the size-dependent thermal properties are taken into account. Also, the temperature jump boundary condition has been also applied by means of a mixed-type boundary condition. It is obtained that considering size-dependent thermal characteristics for transistors under study, results in an increase of the peak temperature rise. As an instance, considering the film dependent thermal properties for a 1-D silicone MOSFET with uniform heat generation at the upper part, makes the maximum temperature increase up to 250%. Furthermore, considering constant bulk thermal properties for the silicon MOSFET, certain oscillations are observed in the time-variation of the peak temperature rise for α = 0.7, 0.9 and 1. This presents the so-called negative bias temperature instability appearing in electronic nano-semiconductor devices. Finally, the hotspot temperature has been researched in transistors containing two-dimensional materials with quasi one-dimensional band structure channels. It is obtained that among the studied FETs, titanium trisulfide with maximum temperature increase of 19.63 K exhibits the least peak temperature rise. This presents that TiS3 may be an acceptable silicon channel replacement as far as the thermal issues are concerned.

Experimental Observation of Non-Abelian Earring Nodal Links in Phononic Crystals.

Nodal lines are symmetry-protected one-dimensional band degeneracies in momentum space, which can appear in numerous topological configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian topological physics have been proposed in space-time inversion (PT) symmetric systems. One of the most special configurations in such systems is the earring nodal link, composing of a nodal chain linking with an isolated nodal line. Such earring nodal links have not been observed in real systems. We designed phononic crystals with earring nodal links, and experimentally observed two different kinds of earring nodal links by measuring the band structures. We found that the order of the nodal chain and line can be switched after band inversion but their link cannot be severed. Our Letter provides experimental evidence for phenomena unique to non-Abelian band topology and our acoustic system provides a convenient platform for studying the new materials carrying non-Abelian charges.

A Generalization of Quaternions and Their Applications

There are a total of 64 possible multiplication rules that can be defined starting with the generalized imaginary units first introduced by Hamilton. Of these sixty-four choices, only eight lead to non-commutative division algebras: two are associated to the left- and right-chirality quaternions, and the other six are generalizations of the split-quaternion concept first introduced by Cockle. We show that the 4×4 matrix representations of both the left- and right-chirality versions of the generalized split-quaternions are algebraically isomorphic and can be related to each other by 4×4 permutation matrices of the C2×C2 group. As examples of applications of the generalized quaternion concept, we first show that the left- and right-chirality quaternions can be used to describe Lorentz transformations with a constant velocity in an arbitrary spatial direction. Then, it is shown how each of the generalized split-quaternion algebras can be used to solve the problem of quantum-mechanical tunneling through an arbitrary one-dimensional (1D) conduction band energy profile. This demonstrates that six different spinors (4×4 matrices) can be used to represent the amplitudes of the left and right propagating waves in a 1D device.

Two-dimensional weak topological insulators in inversion-symmetric crystals

The Su-Schrieffer-Heeger (SSH) chain is an one-dimensional lattice that comprises two dimerized sublattices. Recently, Zhu, Prodan, and Ahn (ZPA) proposed in [L. Zhu, E. Prodan, and K. H. Ahn, Phys. Rev. B \textbf{99}, 041117 (2019)] that one-dimensional flat bands can occur at topological domain walls of a two-dimensional array of the SSH chains. Here, we newly suggest a two-dimensional topological insulator that is protected by inversion and time-reversal symmetries without spin-orbit coupling. It is shown that the two-dimensional SSH chains realize the proposed topological insulator. Utilizing the first Stiefel-Whitney numbers, a weak type of $\mathbb{Z}_2$ topological indices are developed, which identify the proposed topological insulator, dubbed a two-dimensional Stiefel-Whitney insulator (2DSWI). The ZPA model is employed to study the topological phase diagrams and topological phase transitions. It is found that the phase transition occurs via the formation of the massless Dirac points that wind the entire Brillouin zone. We argue that this unconventional topological phase transition is a characteristic feature of the 2DSWI, manifested as the one-dimensional domain wall states. The new insight from our work could help efforts to realize topological flat bands in solid-state systems.

Infinite bound states and 1/n energy spectrum induced by a Coulomb-like potential of type III in a flat band system

In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis ∣1〉. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength α. When the bound state energies are very near the flat band, they are inversely proportional to the natural number n (e.g., E n ∝ 1/n, n = 1, 2, 3, …). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength α c at which the bound state energy reaches the threshold of continuous spectrum. After crossing the threshold, the bound states in the continuum (BIC) would exist in such a flat band system.

CSiT: A Multiscale Vision Transformer for Hyperspectral Image Classification

The hyperspectral image (HSI) has nearly continuous spectral information, thus, the target of interest can be accurately identified by the subtle details of spectral properties. Spectral resolution at different scales can capture different levels of spectral features: small-scale spectral bands are beneficial for extracting global details in vision transformers, while large-scale spectral bands are more effective for local features. Transformer shows advantages in global information extraction with self-attention module and even surpasses CNNs in various tasks. Some works based on the vision transformer have performed surprisingly in HSI classification. However, single-scale vision transformers are insufficient to balance the extraction of local details and redundancy on different scales. The recent work, a multi-scale vision transformer, has provided a solution with spatial patch-wise features in image classification. Inspired by this, we propose the Cross-spectral vision transformer (CSiT) with two branches to extract pixel-wise multi-scale features and further design a multi-scale spectral embedding module to enhance local details between neighboring spectral bands. Moreover, based on the cross-attention operation, a single token for each branch is recognized as a query and used to exchange information with other branches. We evaluate the classification performance of the proposed CSiT in three classic HSI datasets with extensive experiments, showing the multi-scale vision transformer architecture has a promising result for HSI classification with one-dimensional spectral bands.