One-dimensional Band Research Articles

Rapid-cycle Thouless pumping in a one-dimensional optical lattice

An adiabatic cycle around a degeneracy point in the parameter space of a one-dimensional band insulator is known to result in an integer valued noiseless particle transport in the thermodynamic limit. Recently, it was shown that in the case of an infinite bipartite lattice the adiabatic Thouless protocol can be continuously deformed into a fine tuned finite-frequency cycle preserving the properties of noiseless quantized transport. In this paper, we numerically investigate the implementation of such an ideal rapid-cycle Thouless pumping protocol in a one-dimensional optical lattice. It is shown that the rapidity will cause first order corrections due to next-to-nearest-neighbour hopping and second order corrections due to the addition of a harmonic potential. Lastly, the quantization of the change in center of mass of the particle distribution is investigated, and shown to have corrections in the first order of the potential curvature.

Graphene with Rashba spin-orbit interaction and coupling to a magnetic layer: Electron states localized at the domain wall

Electron states localized at a magnetic domain wall in a graphene with Rashba spin-orbit interaction and coupled to a magnetic layer are studied theoretically. It is shown that two one-dimensional bands of edge modes propagating along the domain wall emerge in the energy gap for each Dirac point, and the modes associated with different Dirac points $K$ and ${K}^{\ensuremath{'}}$ are the same. The coefficients describing decay of the corresponding wave functions with distance from the domain wall contain generally real and imaginary terms. Numerical results on the local spin density and on the total spin expected in the edge states characterized by the wave number ${k}_{y}$ are presented and discussed. The Chern number for a single magnetic domain on graphene indicates that the system is in the quantum anomalous Hall phase, with two chiral modes at the edges. In turn, the number of modes localized at the domain wall is determined by the difference in Chern numbers on both sides of the wall. These numbers are equal to 2 and $\ensuremath{-}2$, respectively, so there are four modes localized at the domain wall.

Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential. It is found that, in the presence of a Coulomb potential of type I (with three equal diagonal elements), similarly to that in the two-dimensional case, the flat band could not survive. At the same time, the flat band states are transformed into localized states with a logarithmic singularity near the center position. In addition, the wave function near the origin would collapse for an arbitrarily weak Coulomb potential. Due to the wave function collapses, the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter. For a Coulomb potential of type II, there exist infinite bound states that are generated from the flat band. Furthermore, when the bound state energy is very near the flat band, the energy is inversely proportional to the natural number, e.g., En ∝ 1/n, n = 1,2,3,… It is expected that the 1/n energy spectrum could be observed experimentally in the near future.

Negative Photoconductive Effects in Uncooled InAs Nanowire Photodetectors

One-dimensional, direct, and narrow band gap indium arsenide (InAs) nanowires (NWs) have been emerging with great potentials for the next-generation wide-spectrum photodetectors. In this study, metal–semiconductor–metal (MSM) structure InAs NW-based photodetectors were fabricated by transferring MBE-grown NWs onto a sapphire substrate via a mechanical stamping method. These NW detectors exhibit strong negative photoconductive (NPC) effects, which are likely caused by the carrier dynamics in the “core-shell” structure of the NWs. Specifically, under the irradiation of a 405 nm violet laser, the maximum Idark/Ilight ratio reaches ∼102 and the NPC gain reaches 105 at a low bias voltage of 0.2 V. At room temperature, the rise and decay times of InAs NW devices are 0.005 and 2.645 s, respectively. These InAs NW devices with a high Idark/Ilight ratio and NPC gain can be potentially used in the field of vis/near-IR light communication in the future.

Topology of critical chiral phases: Multiband insulators and superconductors

Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically nontrivial phases. We show how this picture generalizes to multiband critical models belonging to any of the chiral symmetry classes AIII, BDI, or CII of noninteracting fermions in one dimension.

Transverse Rashba effect and unconventional magnetocrystalline anisotropy in graphene-nanoribbon-based centrosymmetric antiferromagnet

The transverse Rashba effect in a centrosymmetric antiferromagnet materialized by double-Gd-adsorbed graphene nanoribbon is investigated via the first-principle calculations. The Rashba effect is associated with not only the local transverse dipole fields induced by the off-center adsorption of the Gd adatoms but also the local magnetic moments. It is perfectly realized that the transverse Rashba effect (Rashba parameter αx reaches to 2.205 eV Å) and strong perpendicular magnetocrystalline anisotropy energy (MAE) coexist in antiferromagnetic (AFM) ground-state structure. However, the global Rashba effect disappears in ferromagnetic structure. The origin of the strong MAE is elaborated in k − space. It is intriguing that the first-order perturbation of the orbit and spin angular momentum coupling is the major source of the MAE due to the specific one-dimensional band structure. The transverse Rashba effect and the strong perpendicular magnetization hosted simultaneously by the proposed centrosymmetric antiferromagnet lock the up- (or down-) spin quantization direction (SQD) to the backward (or forward) movement, and the SQD is related to the chirality of the AFM structure. This finding offers a magnetic approach to a high coherency spin propagation in one-dimensionality, and open a new door to manipulating spin transportation in graphene nanoribbon-based spintronics.

Effective continuum model of twisted bilayer GeSe and origin of the emerging one-dimensional mode

The electric structure of twisted bilayer GeSe, which shows a rectangular moir\'{e} pattern, is analyzed using a $\bm{k}\cdot\bm{p}$ type effective continuum model. The effective model is constructed on the basis of the the local approximation method, where the local lattice structure of a twisted bilayer system is approximated by its untwisted bilayer with parallel displacement, and the required parameters are fixed with the help of the first-principles method. By inspecting the twist angle dependence of the physical properties, we reveal a relation between the effective potential under moir\'{e} pattern and the alignment of the Ge atoms, and also the resultant one-dimensional flat band, where the band is flattened stronger in a specific direction than the perpendicular direction. Due to the relatively large effective mass of the original monolayers, the flat band with its band width as small as a few meV appear in a relatively large angle. This gives us an opportunity to explore the dimensional crossover in the twisted bilayer platform.

Magnetic states of the quasi-one-dimensional iron chalcogenide Ba2FeS3

Quasi-one-dimensional iron-based ladders and chains, with the $3d$ iron electronic density $n=6$, are attracting considerable attention. Recently, a new iron chain system ${\mathrm{Ba}}_{2}{\mathrm{FeS}}_{3}$, also with $n=6$, was prepared under high-pressure and high-temperature conditions. Here the magnetic and electronic phase diagrams are theoretically studied for this quasi-one-dimensional compound. Based on first-principles calculations, a strongly anisotropic one-dimensional electronic band behavior near the Fermi level was observed. In addition, a three-orbital electronic Hubbard model for this chain was constructed. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group (DMRG) method, we studied the ground-state phase diagram. A robust staggered $\ensuremath{\uparrow}\text{\ensuremath{-}}\ensuremath{\downarrow}\text{\ensuremath{-}}\ensuremath{\uparrow}\text{\ensuremath{-}}\ensuremath{\downarrow}$ AFM region was unveiled in the chain direction, consistent with our density functional theory (DFT) calculations. Furthermore, at intermediate Hubbard $U$ coupling strengths, this system was found to display an orbital selective Mott phase (OSMP) with one localized orbital and two itinerant metallic orbitals. At very large $U/W$ $(W=\mathrm{bandwidth})$, the system displays Mott insulator characteristics, with two orbitals half-filled and one doubly occupied. Our results for high pressure ${\mathrm{Ba}}_{2}{\mathrm{FeS}}_{3}$ provide guidance to experimentalists and theorists working on this one-dimensional iron chalcogenide chain material.

Entanglement clustering for ground-stateable quantum many-body states

Despite their fundamental importance in dictating the quantum mechanical properties of a system, ground states of many-body local quantum Hamiltonians form a set of measure zero in the many-body Hilbert space. Hence determining whether a given many-body quantum state is ground-stateable is a challenging task. Here we propose an unsupervised machine learning approach, dubbed the Entanglement Clustering ("EntanCl"), to separate out ground-stateable wave functions from those that must be excited state wave functions using entanglement structure information. EntanCl uses snapshots of an ensemble of swap operators as input and projects this high dimensional data to two-dimensions, preserving important topological features of the data associated with distinct entanglement structure using the uniform manifold approximation and projection (UMAP). The projected data is then clustered using K-means clustering with $k=2$. By applying EntanCl to two examples, a one-dimensional band insulator and the two-dimensional toric code, we demonstrate that EntanCl can successfully separate ground states from excited states with high computational efficiency. Being independent of a Hamiltonian and associated energy estimates, EntanCl offers a new paradigm for addressing quantum many-body wave functions in a computationally efficient manner.

Simple formulas of directional amplification from non-Bloch band theory

Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to finding the roots of a simple algebraic equation. As an application, our formulation provides the desirable formulas for the defining quantities, the gain and directionality, of directional amplification. Thus our formulas provide an efficient guide for designing directional amplifiers.

Enhanced circular dichroism of sparse nanoobjects by localized superchiral optical field

The spectroscopic methods of circular dichroism (CD) is commonly used in analysing the chirality of molecules, which plays an important role in pharmaceutical compounds. However, the current methods require high sample density due to the weak CD effect of natural material, making it challenging to detect the signal of individual chiral molecule. In this work, we propose a technique to enhance CD signal of individual chiral molecule with the use of superchiral optical field, which is acquired by focusing a twisted radially polarized vortex onto a one-dimensional photonic band gap structure. Through adjusting the topological charge and the focusing angle of the illumination, a deep subwavelength optical field with full width at half maxima (FWHM) of 0.02λ and 22.4-fold superchirality factor enhancement can be generated. In addition, we demonstrate that up to 20-fold CD enhancement can be obtained by introducing 2 nm on-resonant chiral molecule into the superchiral optical field. This finding will have widely potential applications in CD spectroscopy and superresolution imaging for sparse subdiffraction chiral objects.

Magnetic higher-order nodal lines

Nodal lines, as one-dimensional band degeneracies in momentum space, usually feature a linear energy splitting. Here, we propose the concept of magnetic higher-order nodal lines, which are nodal lines with higher-order energy splitting and realized in magnetic systems with broken time reversal symmetry. We provide sufficient symmetry conditions for stabilizing magnetic quadratic and cubic nodal lines, based on which concrete lattice models are constructed to demonstrate their existence. Unlike its counterpart in nonmagnetic systems, the magnetic quadratic nodal line can exist as the only band degeneracy at the Fermi level. We show that these nodal lines can be accompanied by torus surface states, which form a surface band that span over the whole surface Brillouin zone. Under symmetry breaking, these magnetic nodal lines can be transformed into a variety of interesting topological states, such as three-dimensional quantum anomalous Hall insulator, multiple linear nodal lines, and magnetic triple-Weyl semimetal. The three-dimensional quantum anomalous Hall insulator features a Hall conductivity $\sigma_{xy}$ quantized in unit of $e^2/(hd)$ where $d$ is the lattice constant normal to the $x$-$y$ plane. Our work reveals previously unknown topological states, and offers guidance to search for them in realistic material systems.

The density of states of 1D random band matrices via a supersymmetric transfer operator

Recently,M. and T. Shcherbina proved a pointwise semicircle law for the density of states of one-dimensional Gaussian band matrices of large bandwidth. The main step of their proof is a new method to study the spectral properties of non-self-adjoint operators in the semiclassical regime. The method is applied to a transfer operator constructed from the supersymmetric integral representation for the density of states. We present a simpler proof of a slightly upgraded version of the semicircle law, which requires only standard semiclassical arguments and some peculiar elementary computations. The simplification is due to the use of supersymmetry, which manifests itself in the commutation between the transfer operator and a family of transformations of superspace, and was applied earlier in the context of band matrices by Constantinescu. Other versions of this supersymmetry have been a crucial ingredient in the study of the localization–delocalization transition by theoretical physicists.

Design Method of Notch Filter Based on One-dimensional Photonic Crystal Band Structure

Design Method of Notch Filter Based on One-dimensional Photonic Crystal Band Structure

Surface modes in plasmonic stubbed structures

We present an analytical and numerical study about the existence of surface localized modes, known as Tamm states, in a one-dimensional (1D) comb-like plasmonic band gap structure. Surface plasmon polaritons (SPPs) waveguides with coupled resonators have been widely studied in recent years, because of their potential applications in highly integrated optical circuits. The system studied here is composed of an infinite 1D waveguide, along which stubs of length d1 are grafted periodically with spacing period d2. The analytical study has been performed by means of the Green’s function method which allows the calculation of the dispersion relations of the bulk, surface states of the plasmonic structure and the transmission coefficient. The band structure, as well as the transmission spectrum exhibit passbands separated by stopbands. The surface modes inside the gaps of the semi-infinite structure can be introduced by a defect at its surface. The analytical results are confirmed by numerical simulation using finite element method via Comsol Multiphysics software. These structures can be used to realize highly sensitive plasmonic sensors.

Characterization of photonic band resonators for DNP NMR of thin film samples at 7 T magnetic field

Polarization of nuclear spins via Dynamic Nuclear Polarization (DNP) relies on generating sufficiently high mm-wave B1e fields over the sample, which could be achieved by developing suitable resonance structures. Recently, we have introduced one-dimensional photonic band gap (1D PBG) resonators for DNP and reported on prototype devices operating at ca. 200 GHz electron resonance frequency. Here we systematically compare the performance of five (5) PBG resonators constructed from various alternating dielectric layers by monitoring the DNP effect on natural-abundance 13C spins in synthetic diamond microparticles embedded into a commercial polyester-based lapping film of just 3 mil (76 μm) thickness. An odd-numbered configuration of dielectric layers for 1D PBG resonator was introduced to achieve further B1e enhancements. Among the PBG configurations tested, combinations of high-ε perovskite LiTaO3 together with AlN as well as AlN with optical quartz wafers have resulted in ca. 40 to over 50- fold gains in the average mm-wave power over the sample vs. the mirror-only configuration. The results are rationalized in terms of the electromagnetic energy distribution inside the resonators obtained analytically and from COMSOL simulations. It was found that average of B1e2 over the sample strongly depends on the arrangement of the dielectric layers that are the closest to the sample, which favors odd-numbered PBG resonator configurations for their use in DNP.

The Zeeman, spin-orbit, and quantum spin Hall interactions in anisotropic and low-dimensional conductors

To construct a microscopic theory of electrons and holes in anisotropic conductors that self-consistently treats their band effective mass anisotropy with their interactions with applied electric and magnetic fields, the Dirac equation is extended for an electron or hole in an orthorhombically-anisotropic conduction band. Its covariance is established both by a modified version of the Klemm–Clem transformations to a space in which it is isotropic, and also in its fully anisotropic form by making the most general proper and improper Lorentz transformations, proving its validity in both the relativistic and non-relativistic limits. The appropriate Foldy–Wouthuysen transformations are extended to expand about the non-relativistic Hamiltonian limit to fourth order in the inverse of the particle’s Einstein rest energy. The results have important consequences for magnetic measurements of many classes of clean anisotropic semiconductors, metals, and superconductors. In all of these cases, the Zeeman interaction is found to depend strongly upon the effective mass anisotropy. When an electron or hole is traveling in an atomically thin one-dimensional conduction band, its Zeeman, spin–orbit, and quantum spin Hall interactions are vanishingly small. Accurate expressions for the Zeeman, spin–orbit and quantum spin Hall interactions for two-dimensional conductors are provided.

Homogeneous superconducting gap in DyBa2Cu3O7−δ synthesized by oxide molecular beam epitaxy

Much of what is known about high-temperature cuprate superconductors stems from studies based on two surface analytical tools, angle-resolved photoemission spectroscopy (ARPES) and spectroscopic imaging scanning tunneling microscopy (SI-STM). A question of general interest is whether and when the surface properties probed by ARPES and SI-STM are representative of the intrinsic properties of bulk materials. We find this question is prominent in thin films of a rarely studied cuprate DBCO. We synthesize DBCO films by oxide molecular beam epitaxy and study them by in situ ARPES and SI-STM. Both ARPES and SI-STM show that the surface DBCO layer is different from the bulk of the film. It is heavily underdoped, while the doping level in the bulk is close to optimal doping evidenced by bulk-sensitive mutual inductance measurements. ARPES shows the typical electronic structure of a heavily underdoped CuO2 plane and two sets of one-dimensional bands originating from the CuO chains with one of them gapped. SI-STM reveals two different energy scales in the local density of states, with one corresponding to the superconductivity and the other one to the pseudogap. While the pseudogap shows large variations over the length scale of a few nanometers, the superconducting gap is very homogeneous. This indicates that the pseudogap and superconductivity are of different origins.

Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect.

The charge-density-wave (CDW) mechanism of the 3D quantum Hall effect has been observed recently in ZrTe_{5} [Tang etal., Nature 569, 537 (2019)10.1038/s41586-019-1180-9]. Different from previous cases, the CDW forms on a one-dimensional (1D) band of Landau levels, which strongly depends on the magnetic field. However, its theory is still lacking. We develop a theory for the CDW mechanism of 3D quantum Hall effect. The theory can capture the main features in the experiments. We find a magnetic field induced second-order phase transition to the CDW phase. We find that electron-phonon interactions, rather than electron-electron interactions, dominate the order parameter. We extract the electron-phonon coupling constant from the non-Ohmic I-V relation. We point out a commensurate-incommensurate CDW crossover in the experiment. More importantly, our theory explores a rare case, in which a magnetic field can induce an order-parameter phase transition in one direction but a topological phase transition in other two directions, both depend on one magnetic field.

Multicriticality in a one-dimensional topological band insulator

A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in the ground-state energy in the thermodynamic limit implies a QPT. Here we report on a finding that challenges this assertion. As a case study we take a phase diagram of a one-dimensional band insulator with spin-orbit coupled electrons, supporting trivial and topological gapped phases separated by intersecting critical surfaces. The intersections define multicritical lines across which the ground-state energy becomes nonanalytical, concurrent with a closing of the band gap, but with no phase transition taking place.