Partial Gap Research Articles

Charge Density Waves and the Hidden Nesting of Purple Bronze K_{0.9}Mo_{6}O_{17}.

We introduce the first multiorbital effective tight-binding model to describe the effect of electron-electron interactions in this system. Upon fixing all the effective hopping parameters in the normal state against an abinitio band structure, and with only the overall scale of the interactions as the sole adjustable parameter, we find that a self-consistent Hartree-Fock solution reproduces extremely well the experimental behavior of the charge density wave (CDW) order parameter in the full range 0<T<T_{c}, as well as the precise reciprocal space locations of the partial gap opening and Fermi arc development. The interaction strengths extracted from fitting to the experimental CDW gap are consistent with those derived from an independent Stoner-type analysis.

Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction

We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin–orbit (SO) interaction in a magnetic field, using a combination of matrix product state and bosonization techniques. Quantum wires with strong Rashba SO interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with SO interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at k = 0 and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton–antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.

Investigation on Variable Guide Vane (VGV) Unsteady Flow Characteristic of Axial Turbine

An investigation is conducted on the unsteady flow characteristic of a variable turbine guide vane. Subsequently, an analysis is performed on the unsteady flow characteristic under three situations, namely, no gap, partial gap, and full gap at the endwall of a variable guide vane. Investigation result demonstrates that an obvious leakage flow will occur when a partial gap or a full gap is present at the endwall of a variable turbine guide vane. Such leakage flow will cause turbine grade loss to deteriorate. The periodic unsteady effect will be evident when the running rotor blades cut through the leakage flow. Pressure and temperature pulsations will both be higher when the gap at the endwall is full compared with when it is partial.

Sound transmission loss characteristics of sandwich panels with a truss lattice core.

Sandwich panels are extensively used in constructional, naval, and aerospace structures due to the high stiffness and strength-to-weight ratios. In contrast, the sound transmission properties are adversely influenced by the low effective mass. Phase velocity matching of structural waves propagating within the panel and the incident pressure waves from the fluid medium leads to coincidence effects resulting in reduced impedance and high sound transmission. Truss-like lattice cores with porous microarchitecture and reduced inter panel connectivity offer the potential to satisfy the conflicting structural and vibroacoustic response requirements. This study combines Bloch-wave analysis and the finite element method to understand wave propagation and hence sound transmission in sandwich panels with a truss lattice core. Three dimensional coupled fluid-structure finite element simulations are conducted to compare the performance of a representative set of lattice core topologies. Potential advantages of sandwich structures with a lattice core are identified. The significance of partial band gaps is evident in the sound transmission loss characteristics of the panels studied. This work demonstrates that, even without optimization, significant enhancements in sound transmission loss performance can be achieved in truss lattice core sandwich panels compared to a traditional sandwich panel employing a honeycomb core under constant mass constraint.

Finite-temperature conductance of strongly interacting quantum wire with a nuclear spin order

We study the temperature dependence of the electrical conductance of a clean strongly interacting quantum wire in the presence of a helical nuclear spin order. The nuclear spin helix opens a temperature-dependent partial gap in the electron spectrum. Using a bosonization framework we describe the gapped electron modes by sine-Gordon-like kinks. We predict an internal resistivity caused by an Ohmic-like friction these kinks experience via interacting with gapless excitations. As a result, the conductance rises from $G=e^2/h$ at temperatures below the critical temperature when nuclear spins are fully polarized to $G=2e^2/h$ at higher temperatures when the order is destroyed, featuring a relatively wide plateau in the intermediate regime. The theoretical results are compared with the experimental data for GaAs quantum wires obtained recently by Scheller et al. [Phys. Rev. Lett. 112, 066801 (2014)].

On acoustic wave beaming in two-dimensional structural lattices

We discuss directional energy flow, often referred to as wave beaming, in two-dimensional periodic truss lattices under infinitesimal harmonic excitation. While the phenomenon of directional wave guiding is well-known and commonly treated in the context of dispersion relations, the theoretical and computational tools to predict beaming are limited, which is why a fundamental understanding for complex lattices is incomplete. Here, we present a new strategy to identify partial band gaps and wave beaming in a simple fashion, covering wide frequency ranges and distinguishing in-plane and out-of-plane vibrational modes in lattices composed of linear elastic Euler-Bernoulli beams. By calculating group velocities that provide insight into the frequency-dependent directional energy flow, we show that dispersion surfaces overlap in frequency and beaming direction, elucidating the need to consider multiple surfaces when predicting global system response – in contrast to many prior approaches that focused on the lowest surface(s) individually. These concepts are demonstrated for three examples of two-dimensional structural lattices (of rectangular, sheared, and hexagonal architecture), for each of which we study the influence of geometry on wave dispersion. Direct numerical simulations validate directional energy flow predictions, demonstrate directional frequency dispersion, and highlight conventional dispersion analysis limitations.

Spin-orbit coupling in quasi-one-dimensional Wigner crystals

We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D Wigner crystal can move in the transverse direction, SOC cannot be gauged away in contrast to the pure 1D case. We show that for weak SOC, a partial gap in the spectrum opens at certain ratios between density of electrons and the inverse Rashba length. We present how the low-energy branch of charge degrees of freedom deviates due to SOC from its usual linear dependence at small wave vectors. In the case of strong SOC, we show that spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian any more, and that instead the ground state of neighboring electrons is mostly a triplet state. We present a new spin sector Hamiltonian and discuss the spectrum of Wigner crystal in this limit.

Vibrational band structure of nanoscale phononic crystals

AbstractThe vibrational properties of two‐dimensional phononic crystals are studied with large‐scale molecular dynamics simulations and finite element method calculation. The vibrational band structure derived from the molecular dynamics simulations shows the existence of partial acoustic band gaps along the –M direction. The band structure is in excellent agreement with the results from the finite element model, proving that molecular dynamics simulations can be used to study the vibrational properties of such complex systems. An analysis of the structure of the vibrational modes reveals how the acoustic modes deviate from the homogeneous bulk behavior for shorter wavelengths and hints toward a decoupling of vibrations in the phononic crystal.

Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials

The elastic wave propagation is investigated in a beam lattice material characterized by a square periodic cell with anti-tetrachiral microstructure. With reference to the Floquet-Bloch spectrum, focus is made on the band structure enrichments and modifications which can be achieved by equipping the cellular microstructure with tunable local resonators. By virtue of its composite mechanical nature, the so-built inertial meta-material gains enhanced capacities of passive frequency-band filtering. Indeed the number, placement and properties of the inertial resonators can be designed to open, shift and enlarge the band gaps between one or more pairs of consecutive branches in the frequency spectrum. In order to improve the meta-material performance, several nonlinear optimization problems are formulated. The largest among the band gap amplitudes in the low-frequency range is selected as suited objective function. Proper inequality constraints are introduced to restrict the admissible solutions within a compact set of mechanical and geometric parameters, including only physically realistic properties of both the lattice and the resonators. The optimization problems related to full and partial band gaps are solved by using a globally convergent version of the numerical method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique. The optimal solutions are numerically computed, discussed and compared from the qualitative and quantitative viewpoints, bringing to light the limits and potential of the meta-material performance. The clearest trends emerging from the numerical analyses are pointed out and interpreted from the physical viewpoint. Finally, some specific recommendations about the microstructural design of the meta-material are synthesized.

Helical gaps in interacting Rashba wires at low electron densities

Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap ("helical gap") in the energy spectrum of noninteracting or weakly interacting one-dimensional quantum wires. By comparing kinetic energy and Coulomb energy we show that this gap opening typically occurs at low electron densities where the Coulomb energy dominates. To address this strongly correlated limit, we investigate Rashba wires using Wigner crystal theory. We find that the helical gap exists even in the limit of strong interactions but its dependence on electron density differs significantly from the weakly interacting case. In particular, we find that the critical magnetic field for opening the gap becomes an oscillatory function of electron density. This changes strongly the expected signature of the helical gap in conductance measurements.

Complete band gaps including non-local effects occur only in the relaxed micromorphic model

In this paper, we substantiate the claim implicitly made in previous works that the relaxed micromorphic model is the only linear, isotropic, reversibly elastic, nonlocal generalized continuum model able to describe complete band-gaps on a phenomenological level. To this end, we recapitulate the response of the standard Mindlin–Eringen micromorphic model with the full micro-distortion gradient ∇P, the relaxed micromorphic model depending only on the CurlP of the micro-distortion P, and a variant of the standard micromorphic model, in which the curvature depends only on the divergence DivP of the micro distortion. The Div-model has size-effects, but the dispersion analysis for plane waves shows the incapability of that model to even produce a partial band gap. Combining the curvature to depend quadratically on DivP and CurlP shows that such a model is similar to the standard Mindlin–Eringen model, which can eventually show only a partial band gap.

Two-Step Fixed-Point Proximity Algorithms for Multi-block Separable Convex Problems

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that the classic alternating direction method of multipliers (ADMM) for the problem is not necessarily convergent. However, it is observed that ADMM outperforms numerically many of its variants with guaranteed theoretical convergence. The goal of this paper is to develop convergent and computationally efficient algorithms for solving multi-block separable convex problems. We first characterize the solutions of the optimization problems by proximity operators of the convex functions involved in their objective function. We then design a two-step fixed-point iterative scheme for solving these problems based on the characterization. We further prove convergence of the iterative scheme and show that it has O(1/k) convergence rate in the ergodic sense and the sense of the partial primal-dual gap, where k denotes the iteration number. Moreover, we derive specific two-step fixed-point proximity algorithms (2SFPPA) from the proposed iterative scheme and establish their global convergence. Numerical experiments for solving the sparse MRI problem demonstrate the numerical efficiency of the proposed 2SFPPA.

Waveform-preserved unidirectional acoustic transmission based on impedance-matched acoustic metasurface and phononic crystal

The waveform distortion happens in most of the unidirectional acoustic transmission (UAT) devices proposed before. In this paper, a novel type of waveform-preserved UAT device composed of an impedance-matched acoustic metasurface (AMS) and a phononic crystal (PC) structure is proposed and numerically investigated. The acoustic pressure field distributions and transmittance are calculated by using the finite element method. The subwavelength AMS that can modulate the wavefront of the transmitted wave at will is designed and the band structure of the PC structure is calculated and analyzed. The sound pressure field distributions demonstrate that the unidirectional acoustic transmission can be realized by the proposed UAT device without changing the waveforms of the output waves, which is the distinctive feature compared with the previous UAT devices. The physical mechanism of the unidirectional acoustic transmission is discussed by analyzing the refraction angle changes and partial band gap map. The calculated transmission spectra show that the UAT device is valid within a relatively broad frequency range. The simulation results agree well with the theoretical predictions. The proposed UAT device provides a good reference for designing waveform-preserved UAT devices and has potential applications in many fields, such as medical ultrasound, acoustic rectifiers, and noise insulation.

Analysis of magneto-optical properties for three-dimensional photonic crystals in high-symmetry arrangement doped by metamaterials and uniaxial materials

Abstract In this paper, we use a modified plane wave expansion (PWE) method to investigate the properties of photonic band gaps (PBGs) for the extraordinary mode in the three-dimensional (3D) photonic crystals (PCs) which are composed of the anisotropic dielectric (the uniaxial materials) spheres immersed in the homogeneous metamaterials (epsilon-negative materials) background with high-symmetry (body-centered-cubic) lattices, as the magneto-optical Voigt effects are considered. The equations for calculating the PBGs in the first irreducible Brillouin zone are theoretically derived. It is numerically illustrated that the anisotropic PBGs and two flattened band regions can be achieved. The influences of the ordinary-refractive index, extraordinary-refractive index, filling factor of dielectric spheres, electronic plasma frequency and cyclotron frequency on the magneto-optical properties of such 3D PCs also are studied in detail, respectively, and some corresponding physical explanations are given. The numerical results demonstrate that the anisotropy can open partial band gaps in the proposed PCs, and the complete PBGs can be obtained compared with the conventional PCs only containing the isotropic material with similar structures. The bandwidths of PBGs can be tuned by introducing the epsilon-negative materials into such PCs containing the uniaxial materials. The anisotropic PBGs can be manipulated by the parameters as mentioned above. As the proposed PCs with high-symmetry lattices, the complete PBGs can be obtained by introducing the uniaxial materials.

Two distinct superconducting phases in LiFeAs.

A non-trivial temperature evolution of superconductivity including a temperature-induced phase transition between two superconducting phases or even a time-reversal symmetry breaking order parameter is in principle expected in multiband superconductors such as iron-pnictides. Here we present scanning tunnelling spectroscopy data of LiFeAs which reveal two distinct superconducting phases: at = 18 K a partial superconducting gap opens, evidenced by subtle, yet clear features in the tunnelling spectra, i.e. particle-hole symmetric coherence peak and dip-hump structures. At Tc = 16 K, these features substantiate dramatically and become characteristic of full superconductivity. Remarkably, the distance between the dip-hump structures and the coherence peaks remains practically constant in the whole temperature regimeT ≤ . This rules out the connection of the dip-hump structures to an antiferromagnetic spin resonance.

Engineering Electronic Structure of a Two-Dimensional Topological Insulator Bi(111) Bilayer on Sb Nanofilms by Quantum Confinement Effect.

We report on the fabrication of a two-dimensional topological insulator Bi(111) bilayer on Sb nanofilms via a sequential molecular beam epitaxy growth technique. Our angle-resolved photoemission measurements demonstrate the evolution of the electronic band structure of the heterostructure as a function of the film thickness and reveal the existence of a two-dimensional spinful massless electron gas within the top Bi bilayer. Interestingly, our first-principles calculation extrapolating the observed band structure shows that, by tuning down the thickness of the supporting Sb films into the quantum dimension regime, a pair of isolated topological edge states emerges in a partial energy gap at 0.32 eV above the Fermi level as a consequence of quantum confinement effect. Our results and methodology of fabricating nanoscale heterostructures establish the Bi bilayer/Sb heterostructure as a platform of great potential for both ultra-low-energy-cost electronics and surface-based spintronics.

Two mechanisms for dust gap opening in protoplanetary discs

Abstract We identify two distinct physical mechanisms for dust gap opening by embedded planets in protoplanetary discs based on the symmetry of the drag-induced motion around the planet: (I) a mechanism where low-mass planets, that do not disturb the gas, open gaps in dust by tidal torques assisted by drag in the inner disc, but resisted by drag in the outer disc; and (II) the usual, drag-assisted, mechanism where higher mass planets create pressure maxima in the gas disc, which the drag torque then acts to evacuate further in the dust. The first mechanism produces gaps in dust but not gas, while the second produces partial or total gas gaps which are deeper in the dust phase. Dust gaps do not necessarily indicate gas gaps.

Change of carrier density at the pseudogap critical point of a cuprate superconductor.

The pseudogap is a partial gap in the electronic density of states that opens in the normal (non-superconducting) state of cuprate superconductors and whose origin is a long-standing puzzle. Its connection to the Mott insulator phase at low doping (hole concentration, p) remains ambiguous and its relation to the charge order that reconstructs the Fermi surface at intermediate doping is still unclear. Here we use measurements of the Hall coefficient in magnetic fields up to 88 tesla to show that Fermi-surface reconstruction by charge order in the cuprate YBa2Cu3Oy ends sharply at a critical doping p = 0.16 that is distinctly lower than the pseudogap critical point p* = 0.19 (ref. 11). This shows that the pseudogap and charge order are separate phenomena. We find that the change in carrier density n from n = 1 + p in the conventional metal at high doping (ref. 12) to n = p at low doping (ref. 13) starts at the pseudogap critical point. This shows that the pseudogap and the antiferromagnetic Mott insulator are linked.

Wave propagation in 3D viscoelastic auxetic and textile materials by homogenized continuum micropolar models

We analyze in this contribution the impact of wave damping on the dispersion features of 3D viscoelastic periodic structures, which are modeled as Kelvin–Voigt viscoelastic beam-lattices. The band diagram structure and damping ratio are computed for different repetitive structures, based on the micropolar viscoelastic response of the effective medium obtained by the homogenization of the initially discrete lattice architecture. The employed methodology is herewith exemplified for the cases of the 3D hexagon structure, which shows negative Poisson’s ratio for reentrant configurations, and the 2D plain weave textile structure. The dispersion relations and damping ratio are obtained by inserting an harmonic plane waves Ansatz into the dynamical equations of motion of the obtained effective viscoelastic anisotropic continuum. The 3D reentrant hexagon is an auxetic metamaterial showing excellent wave absorption capabilities, as reflected by the high incidence of partial band gaps. The textile plain weave structure shows a complete band gap for low frequencies. Comparing the frequency band structure of the effective continuum with that obtained by Floquet–Bloch analysis extended to a 3D context shows that the wave propagation characteristics can be directly obtained from the homogenized continuum at low frequencies.

Electronic structure of the titanium-based oxypnictide superconductorBa0.95Na0.05Ti2Sb2Oand direct observation of its charge density wave order

${\mathrm{Ba}}_{0.95}{\mathrm{Na}}_{0.05}{\mathrm{Ti}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$ is a titanium-based oxypnictide superconductor with possible density wave order. We have performed high-resolution angle-resolved photoemission spectroscopy and scanning tunneling microscopy (STM) studies on ${\mathrm{Ba}}_{0.95}{\mathrm{Na}}_{0.05}{\mathrm{Ti}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$. Our STM studies find a charge density wave (CDW) order with the wave vector of ($\ensuremath{\pi}, \ensuremath{\pi}$). The electronic structure shows both multiorbital and three-dimensional nature, consistent with the theoretical calculations. The observed Fermi surfaces are well nested along the ($\ensuremath{\pi}, \ensuremath{\pi}$) direction, which might drive the CDW transition. Likely due to the weak strength of the CDW order, we do not observe a leading-edge gap. Instead, we observe an overall spectral weight enhancement with decreasing temperature, but the rate of this enhancement is abruptly reduced or diminished in the CDW state, suggesting the suppression of spectral weight or opening of a partial CDW gap. Our results give a comprehensive picture of the electronic structure and direct observation of the CDW order in ${\mathrm{Ba}}_{0.95}{\mathrm{Na}}_{0.05}{\mathrm{Ti}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$.