Vanishing Bulk Research Articles

Hermitian and non-hermitian higher-order topological states in mechanical metamaterials

Higher-order topological insulators exhibit clear hierarchical boundary states, providing an amazing platform for robust wave manipulations in mechanical or acoustic systems. Recently, this theory has been extended to non-Hermiticity-induced higher-order topology, which enables actively controllable topological transport. Nevertheless, most related studies focus on the non-Hermitian quadrupole topology, associated with the coexistence of negative and positive couplings to constitute a π-flux lattice, which hindered the realizations in classical wave systems. Here, we propose a novel tight-binding model without negative couplings, which supports non-Hermiticity-induced higher-order topological states. In the Hermitian case, the middle band gaps host the vanishing bulk polarization and the associated topology is dependent only upon the associated edge polarization. By introducing the external loss as non-Hermitian components, we reveal that therein the trivial structures can also host topological corner states, featured by the quantized nonzero edge polarizations in the biorthogonal basis. Furthermore, such a topological phase transition induced by non-Hermiticity can be realized for almost all of our lattices, except for the isotropic case where the middle band gaps never open. Basing on the theoretical design, we map the lattice models into the mechanical metamaterials to access the analogous higher-order topology in the elastic wave systems for both Hermitian and non-Hermitian physics. The simulated band structures match well with theoretical solutions. And the robust higher-order topological states are also identified. Our work paves the way to implement the non-Hermitian higher-order topology and offers the possibility for wave manipulations in non-Hermitian systems.

Towards a theory of surface orbital magnetization

The theory of bulk orbital magnetization has been formulated both in reciprocal space based on Berry curvature and related quantities, and in real space in terms of the spatial average of a quantum mechanical local marker. Here we consider a three-dimensional antiferromagnetic material having a vanishing bulk but a nonzero surface orbital magnetization. We ask whether the surface-normal component of the surface magnetization is well defined, and if so, how to compute it. As the physical observable corresponding to this quantity, we identify the macroscopic current running along a hinge shared by two facets. However, the hinge current only constrains the difference of the surface magnetizations on the adjoined facets, leaving a potential ambiguity. By performing a symmetry analysis, we find that only crystals exhibiting a pseudoscalar symmetry admit well-defined magnetizations at their surfaces at the classical level. We then explore the possibility of computing surface magnetization via a coarse-graining procedure applied to a quantum local marker. We show that multiple expressions for the local marker exist, and apply constraints to filter out potentially meaningful candidates. Using several tight-binding models as our theoretical test bed and several potential markers, we compute surface magnetizations for slab geometries and compare their predictions with explicit calculations of the macroscopic hinge currents of rod geometries. We find that only a particular form of the marker consistently predicts the correct hinge currents.

Glide symmetry protected higher-order topological insulators from semimetals with butterfly-like nodal lines

Most topological insulators (TIs) discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the gapped topological insulator phases and the gapless TSMs. Recently, we have discovered a family of TSMs in time-reversal invariant spinless systems, which host butterfly-like nodal-lines (NLs) consisting of a pair of identical concentric intersecting coplanar ellipses (CICE). In this Communication, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a {{mathbb{Z}}}_{4} = 2 topological crystalline insulator (TCI), by including substantial SOC. We demonstrate that in three space groups (i.e., Pbam (No.55), P4/mbm (No.127), and P42/mbc (No.135)), the TCI supports a fourfold Dirac fermion on the (001) surface protected by two glide symmetries, which originates from the intertwined drumhead surface states of the CICE NLs. The higher order topology is further demonstrated by the emergence of one-dimensional helical hinge states, indicating the discovery of a higher order topological insulator protected by a glide symmetry.

Three-Dimensional Higher-Order Topological Insulator Protected by Cubic Symmetry

Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently under active investigation, only a few studies explore the physics of the three-dimensional higher-order topological insulators. Here we propose a three-dimensional structure with cubic symmetry exhibiting vanishing bulk polarization but nonzero corner charge and hosting a zero-dimensional corner state mediated by the long-range interactions. We trace the evolution of the corner state with the next-nearest-neighbor coupling strength and prove the topological origin of the corner mode calculating the associated topological invariants. Our results thus reveal the potential of long-range couplings for the formation of three-dimensional higher-order topological phases.

General corner charge formula in two-dimensional Cn -symmetric higher-order topological insulators

In this paper, we derive a general formula for the quantized fractional corner charge in two-dimensional ${C}_{n}$-symmetric higher-order topological insulators. We assume that the electronic states can be described by the Wannier functions and that the edges are charge neutral, but we do not assume vanishing bulk electric polarization. We expand the scope of the corner charge formula obtained in previous works by considering more general surface conditions, such as surfaces with higher Miller index and surfaces with surface reconstruction. Our theory is applicable even when the electronic states are largely modulated near system boundaries. It also applies to insulators with nonvanishing bulk polarization, and we find that in such cases the value of the corner charge depends on the surface termination even for the same bulk crystal with ${C}_{3}$ or ${C}_{4}$ symmetry, via a difference in the Wyckoff position of the center of the ${C}_{n}$-symmetric crystal.

Fractional chiral hinge insulator

We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two non-interacting second order topological insulators with chiral hinge modes at half filling. We use large-scale variational Monte Carlo computations to characterize the model states via the entanglement entropy and charge-spin-fluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge $c=1$ and Luttinger parameter $K=1/2$, like the edge modes of a Laughlin $1/2$ state. By changing the boundary conditions for the underlying fermions, we investigate the topological degeneracy of the FCHI. Within the range of the numerically accessible system sizes, we observe a non-trivial topological degeneracy. A more numerically pristine characterization of the bulk topology is provided by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host a two-dimensional topological order with a TEE per surface compatible with half that of a Laughlin $1/2$ state, a value that cannot be obtained from topological quantum field theory.

Frequency‐Dependent P Wave Anisotropy Due to Wave‐Induced Fluid Flow and Elastic Scattering in a Fluid‐Saturated Porous Medium With Aligned Fractures

AbstractSeismic anisotropy is an important attribute for fracture detection and characterization. If fracture size is comparable to the wavelength or fluid diffusion length, the P wave anisotropy is frequency dependent. By solving the Biot's equations of dynamic poroelasticity and using the Foldy approximation, we investigate the frequency‐dependent P wave anisotropy in a fluid‐saturated porous rock with a set of aligned penny‐shaped fractures. This approach includes the effects of both wave‐induced fluid flow (WIFF) and elastic scattering on P wave anisotropy. The results show that the velocity and attenuation anisotropy in the WIFF and elastic scattering regimes have quite different features and are affected by various factors. In particular, the background permeability and fluid viscosity primarily affect the frequency‐dependent anisotropy caused by WIFF. The fracture geometry (radius and thickness) and fracture density have significant effects on both WIFF and elastic scattering‐induced frequency‐dependent anisotropy. The fluid bulk modulus also affects the frequency‐dependent anisotropy. With the vanishing fluid bulk modulus, the frequency dependency vanishes in the WIFF regime but is the largest in the elastic scattering regime. Predictions of the model agree with previous models in all known limiting cases. Comparison with experimental data shows that WIFF and elastic scattering are important causes for frequency‐dependent P wave anisotropy, and our model is capable to account for these effects.

Thermally Triggered Vanishing Bulk Polyoxymethylene for Transient Electronics

Transient materials capable of disappearing rapidly and completely are critical for transient electronics. End-capped polyoxymethylene (POM) has excellent mechanical properties and thermal stability. However, research concerning the inherent thermal instability of POM without end-capping to obtain transient rather than stable materials, has never been reported. Here, POM without end-capping is proposed as a novel thermally triggered transient solid material that can vanish rapidly by undergoing conversion to a volatile gas, and a chemical vapor deposition method is developed to obtain a smooth POM substrate from the synthesized POM powder. Experimental and theoretical analysis was employed to reveal the mechanism whereby the POM substrate formed and vanished. A Cr/Au/SiO2/Cu memristor device, which was successfully deposited on the POM substrate by physical vapor deposition, exhibits bipolar resistive switching, suggesting that the POM substrate is suitable for use in electrical devices. Thermal triggering causes the POM substrate to vanish as the memristor disintegrates, confirming excellent transient performance. The deposited bulk POM material can completely vanish by thermally triggered depolymerization, and is suitable for physically transient substrates and packaging materials, demonstrating great prospects for application in transient electronics for information security.

Low damping magnetic properties and perpendicular magnetic anisotropy in the Heusler alloy Fe1.5CoGe

We present a study of the dynamic magnetic properties of TiN-buffered epitaxial thin films of the Heusler alloy Fe1.5CoGe. Thickness series annealed at different temperatures are prepared and the magnetic damping is measured, a lowest value of α = 2.18 × 10−3 is obtained. The perpendicular magnetic anisotropy properties in Fe1.5CoGe/MgO are also characterized. The evolution of the interfacial perpendicular anisotropy constant KS⊥ with the annealing temperature is shown and compared with the widely used CoFeB/MgO interface. A large volume contribution to the perpendicular anisotropy of (4.3 ± 0.5) × 105 J/m3 is also found, in contrast with vanishing bulk contribution in common Co- and Fe-based Heusler alloys.

Homogeneous melting near the superheat limit of hard-sphere crystals.

A defect-free crystal can be superheated into a metastable state above its melting point and eventually melts via homogeneous nucleation. Further increasing the temperature leads to the metastable crystal becoming unstable and melting catastrophically once beyond its superheat limit. The homogeneous melting is not well studied near the superheat limit and this limit is difficult to measure accurately, even for the simplest model of hard-sphere crystals. Here our molecular-dynamics simulations identify its superheat limit at volume fraction φlimit = 0.494 ± 0.003, which is higher than the previous theoretical estimations. We found that the hard-sphere crystal at the superheat limit does not satisfy Born's melting criterion, but has a vanishing bulk modulus, i.e. a spinodal instability, which preempts other thermodynamic or mechanical instabilities. At the strong superheating regime, the nucleation deviates from the assumptions in the classical nucleation theory. In contrast to crystallization which often develops nuclei with various intermediate structures, the melting of face-centered cubic (fcc) hard-sphere crystal does not produce intermediate structures such as body-centered cubic (bcc) crystallites although bcc is more stable than fcc at the strong superheating regime. Moreover, we found that the time evolutions of the order parameters and the pressure all exhibit a compressed exponential function, in contrast to the stretched exponential relaxation of supercooled liquids. The compressed exponential functions have the same exponent, which poses a new challenge to theory.

Constraining the phantom braneworld model from cosmic structure sizes

We consider the phantom braneworld model in the context of the maximum turn around radius, $R_{\rm TA,max}$, of a stable, spherical cosmic structure with a given mass. The maximum turn around radius is the point where the attraction due to the central inhomogeneity gets balanced with the repulsion of the ambient dark energy, beyond which a structure cannot hold any mass, thereby giving the maximum upper bound on the size of a stable structure. In this work we derive an analytical expression of $R_{\rm TA,max}$ for this model using cosmological scalar perturbation theory. Using this we numerically constrain the parameter space, including a bulk cosmological constant and the Weyl fluid, from the mass versus observed size data for some nearby, non-virial cosmic structures. We use different values of the matter density parameter $\Omega_m$, both larger and smaller than that of the $\Lambda{\rm CDM}$, as the input in our analysis. We show in particular, that a) with a vanishing bulk cosmological constant the predicted upper bound is always greater than what is actually observed; similar conclusion holds if the bulk cosmological constant is negative b) if it is positive, the predicted maximum size can go considerably below than what is actually observed and owing to the involved nature of the field equations, it leads to interesting constraints on not only the bulk cosmological constant itself but on the whole parameter space of the theory.

Local equilibrium solutions in simple anisotropic cosmological models, as described by relativistic fluid dynamics

We test the physical relevance of the full and the truncated versions of the Israel–Stewart (IS) theory of irreversible thermodynamics in a cosmological setting. Using a dynamical systems method, we determine the asymptotic future of plane symmetric Bianchi type I spacetimes with a viscous mathematical fluid, keeping track of the magnitude of the relative dissipative fluxes, which determines the applicability of the IS theory. We consider the situations where the dissipative mechanisms of shear and bulk viscosity are involved separately and simultaneously. It is demonstrated that the only case in the given model when the fluid asymptotically approaches local thermal equilibrium, and the underlying assumptions of the IS theory are therefore not violated, is that of a dissipative fluid with vanishing bulk viscosity. The truncated IS equations for shear viscosity are found to produce solutions which manifest pathological dynamical features and, in addition, to be strongly sensitive to the choice of initial conditions. Since these features are observed already in the case of an oversimplified mathematical fluid model, we have no reason to assume that the truncation of the IS transport equations will produce relevant results for physically more realistic fluids. The possible role of bulk and shear viscosity in cosmological evolution is also discussed.

Stability and anomalous entropic elasticity of subisostatic random-bond networks.

We study the elasticity of thermalized spring networks under an applied bulk strain. The networks considered are subisostatic random-bond networks that, in the athermal limit, are known to have vanishing bulk and linear shear moduli at zero bulk strain. Above a bulk strain threshold, however, these networks become rigid, although surprisingly the shear modulus remains zero until a second, higher, strain threshold. We find that thermal fluctuations stabilize all networks below the rigidity transition, resulting in systems with both finite bulk and shear moduli. Our results show a T(0.66) temperature dependence of the moduli in the region below the bulk strain threshold, resulting in networks with anomalously high rigidity as compared to ordinary entropic elasticity. Furthermore, we find a second regime of anomalous temperature scaling for the shear modulus at its zero-temperature rigidity point, where it scales as T(0.5), behavior that is absent for the bulk modulus since its athermal rigidity transition is discontinuous.

Unusual spin correlations in a nanomagnet

We show how atomic-scale exchange phenomena can be controlled and exploited in nanoscale itinerant magnets to substantially improve magnetic properties. Cluster-deposition experiments, first-principle simulations, and analytical calculations are used to demonstrate the effect in Co2Si nanoclusters, which have average sizes varying from about 0.6 to 29.5 nm. The cluster-deposited nanoparticles exhibit average magnetic moments of up to 0.70 μB/Co at 10 K and 0.49 μB/Co at 300 K with appreciable magnetocrystalline anisotropies, in sharp contrast to the nearly vanishing bulk magnetization. The underlying spin correlations and associated cluster-size dependence of the magnetization are explained by a surface induced ferromagnetic spin polarization with a decay length of the order of 1 nm, much larger than the nearest-neighbor interatomic distance in the alloy.

Bulk viscosity in holographic Lifshitz hydrodynamics

We compute the bulk viscosity in holographic models dual to theories with Lifshitz scaling and/or hyperscaling violation, using a generalization of the bulk viscosity formula derived in arXiv:1103.1657 from the null focusing equation. We find that only a class of models with massive vector fields are truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other holographic models with scalars and/or massless vector fields we find a universal formula in terms of the dynamical exponent and the hyperscaling violation exponent.

Onsager Relations in a Two-Dimensional Electron Gas with Spin-Orbit Coupling

Theory predicts for the two-dimensional electron gas with only a Rashba spin-orbit interaction a vanishing spin Hall conductivity and at the same time a finite inverse spin Hall effect. We show how these seemingly contradictory results are compatible with the Onsager relations: The latter do hold for spin and particle (charge) currents in the two-dimensional electron gas, although (i) their form depends on the experimental setup and (ii) a vanishing bulk spin Hall conductivity does not necessarily imply a vanishing spin Hall effect. We also discuss the situation in which extrinsic spin orbit from impurities is present and the bulk spin Hall conductivity can be different from zero.

Holographic charged fluid with anomalous current at finite cutoff surface in Einstein-Maxwell gravity

The holographic charged fluid with anomalous current in Einstein-Maxwell gravity has been generalized from the infinite boundary to the finite cutoff surface by using the gravity/fluid correspondence. After perturbing the boosted Reissner-Nordstrom (RN)-AdS black brane solution of the Einstein-Maxwell gravity with the Chern-Simons term, we obtain the first order perturbative gravitational and Maxwell solutions, and calculate the stress tensor and charged current of the dual fluid at finite cutoff surfaces which contains undetermined parameters after demanding regularity condition at the future horizon. We adopt the Dirichlet boundary condition and impose the Landau frame to fix these parameters, finally obtain the dependence of transport coefficients in the dual stress tensor and charged current on the arbitrary radical cutoff $r_c$. We find that the dual fluid is not conformal, but it has vanishing bulk viscosity, and the shear viscosity to entropy density ratio is universally $1/4\pi$. Other transport coefficients of the dual current turns out to be cutoff-dependent. In particular, the chiral vortical conductivity expressed in terms of thermodynamic quantities takes the same form as that of the dual fluid at the asymptotic AdS boundary, and the chiral magnetic conductivity receives a cutoff-dependent correction which vanishes at the infinite boundary.

Searching for perfect fluids: quantum viscosity in a universal Fermi gas

We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏn is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.

Higher-derivative gravity in brane world models

We investigate brane world models in higher-derivative gravity theories where thegravitational Lagrangian is an arbitrary function of the Ricci scalar. Making use of theconformal equivalence of such gravity models and Einstein–Hilbert gravity with a scalarfield, we deduce the main features of higher-derivative gravity brane worlds. Wesolve for a gravity model that has corrections quadratic in the Ricci scalar andfind it is possible to have a vanishing bulk cosmological constant. An analysis oftensor and scalar perturbations shows that gravity is localized on the brane, theNewtonian limit is recovered and the brane–bulk system appears to be stabilized.

Stable, time-dependent, exact solutions for brane models with a bulk scalar field

We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a non-trivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflationary, time-dependent solutions of the 3D scale factor on the brane. We also derive the constraints necessary for the stability of these solutions under time-dependent perturbations of the radion field, and we demonstrate the existence of phenomenologically interesting, stable solutions with a positive cosmological constant on the brane.