arXiv subjects
Publications and source records attributed to Biao Wang.
In 1982, Erdös and van Lint showed an estimate for the average of the ratio of the smallest and largest prime divisor of $n$. In this note, we apply C.H. Jia's method to give an estimate for the average of positive integer power of the ratio.
Emergent crystals are periodic alignment of "emergent particles", i.e., localized collective behavior of atoms or their charges/spins/orbits. These novel states of matter, widely observed in various systems, may deform under mechanical forces with elasticity strikingly different from that of the underlying material. However, their nonlinear and critical behaviors under strong fields are hitherto unclear. Here we theoretically study the nonlinear elasticity and structural transitions of skyrmion crystals (SkX) suffering uniaxial distortion by using three different methods. Under moderate tension, SkX behaves like a ductile material, with a negative crossover elastic stiffness and a negative emergent Poisson's ratio at appropriate conditions of magnetic field. Under strong straining, we observe at most six phase transitions, leading to appearance of four novel emergent crystals that are thermodynamically metastable. When subject to external loads, emergent crystals rotate globally, and their composing "particles" have unlimited deformability, which render their exotic polymorphism.
We investigate the maximal solid tubes around short simple geodesics in hyperbolic three-manifolds and how complex length of curves relate to closed, incompressible, least area minimal surfaces. As applications, we prove, there are some closed hyperbolic three-manifolds fibering over the circle which are not foliated by closed incompressible minimal surfaces diffeomorphic to the fiber. We also show, the existence of quasi-Fuchsian manifolds containing arbitrarily many embedded closed incompressible minimal surfaces. Our strategy is to prove main theorems under natural geometric conditions on the complex length of closed curves on a fibered hyperbolic three-manifold, then we find explicit examples where these conditions are satisfied via computer programs.
Using the strain-dependent effective Hamiltonian and the geometric phase, Droth et al. [Phys. Rev. B 94, 075404 (2016)] obtain an analytical expression for the electronic contribution to the piezoelectricity of planar hexagonal boron nitride (h -BN). Their analytical results of piezoelectric constants for h -BN are invalid because of the mistakes in constructing the adiabatic process of the piezoelectricity. In this comment, we reconstruct a proper adiabatic process for piezoelectricity and formulate a general Berry phase expression for the piezoelectric coefficients of two-dimensional piezoelectric crystals by means of the modern theory of polarization. The corrected analytical results of the piezoelectric constants are in complete consistency with the first-principles calculations and hence manifest the validity and generality of the Berry phase expression of piezoelectric coefficients.
The lack of inversion symmetry in semiconducting transition metal dichalcogenide monolayers (TMDMs) enables a considerable molecular-level intrinsic piezoelectricity, which opens prospects for atomically-thin piezotronics and optoelectronics. Here, based on the tight-binding (TB) approach and Berry phase polarization theory, we establish an atomic-scale TB theory for demonstrating piezoelectric physics in TMDMs. Using the TB piezoelectric theory, we predict their electronic Grüneisen parameters (EGP) which measure the electron-phonon couplings. By virtue of the constructed analytical piezoelectric model, we further reveal the correlation between the electronic contribution to piezoelectric coefficients and strain-induced pseudomagnetic gauge field (PMF). These predicted EGP and PMF for TMDMs are experimentally testable, and hence the TB piezoelectric model is an alternative theoretical framework for calculating electron-phonon interactions and PMF.
In bulk helimagnets, the presence of magnetic skyrmion lattices is always accompanied by a periodic stress field due to the intrinsic magnetoelastic coupling. The release of this nontrivial stress field at the surface causes a periodic displacement field, which characterizes a novel particle-like property of skyrmion: its surface configuration. Here, we derive the analytical solution of this displacement field for semi-infinite cubic helimagnets when skyrmions are present. For MnSi, we show that the skyrmion lattices have a bumpy surface configuration characterized by periodically arranged peaks with a characteristic height of about 10$^{-13}$ m. The pattern of the peaks can be controlled by varying the strength of the applied magnetic field. Moreover, we prove that the surface configuration varies together with the motion and deformation of the skyrmion lattices. As a result, the surface configuration can be tuned by application of electric current, mechanical loads, as well as any other form of external field which has an effect on the skyrmions.
Here we derive the linear constitutive equations governing the emergent elastic behavior of skX under applied mechanical forces as well as other effective fields. The linear coefficients appearing in the equations are expressed analytically in terms of the thermodynamic parameters describing the magnetoelastic interaction of the underlying chiral magnet. Through the deduction of equations, we clarify that two types of coupled deformation may occur for skX, that is the internal deformation, described by variation of the Fourier magnitudes, and the lattice deformation, described by the emergent elastic strains. We also find that besides mechanical loads, bias magnetic field, spatially periodic magnetic field, spatially periodic mechanical loads, and emergent stresses can all lead to deformation of the skX. When homogeneous stresses are applied only, the emergent elastic strains are linearly related to the elastic strains through the emergent strain ratio matrix λ. We calculate λ for the skX in bulk MnSi and discuss its variation with the temperature and magnetic field. In particular, we find that all components of λ are sensitive to variation of magnetic field b, such that they change sign as b increases. Moreover, as b approaches the critical magnetic field of the skX-ferromagnetic phase transition, the dominant components of λ diverges. The constitutive equations are of fundamental significance in emergent elasticity, a new area studying the variation of internal forces and deformation of emergent crystals and their relation when exposed to effective external fields.
A magnetic skyrmion is a spin whirl with topological protection and high mobility to electric current. Intrinsic magnetoelastic coupling in chiral magnets permits manipulation of magnetic skyrmions and their lattice using mechanical loads, which is essential for developing future spintronics devices. It is found in experiments that the stability and deformation of skyrmions are sensitive to stresses, while the appearance of magnetic skyrmions in turn has a significant effect on the mechanical properties of the underlying material. However, a theory which explains these related phenomena within a unified framework is not seen. Here we construct a thermodynamic model for B20 helimagnets incorporating a magnetoelastic functional with necessary higher order interactions derived by group theory. Within the model, we establish the methodology to calculate the phase diagram and equilibrium properties of helimagnets under coupled temperature-magneto-elastic field. Applying the model to bulk MnSi, we calculate the temperature-magnetic field phase diagram under stress-free condition and its variation when uniaxial compression is applied. We also calculate the variation of all the elastic constants with magnetic field. The results obtained agree quantitatively with corresponding experiments. Our model provides a reliable basis for further theoretical studies concerning any magnetoelastic related phenomena in chiral magnets.
The discovery of graphene and other two-dimensional (2-D) materials has stimulated a general interest in low-dimensional (low-D) materials. Whereas long time ago, Peierls and Landau's theoretical work demonstrated that any one- and two-dimensional materials could not exist in any finite temperature environment. Then, two basic issues became a central concern for many researchers: How can stable low-D materials exist? What kind of low-D materials are stable? Here, we establish an energy stability criterion for low-D materials, which seeks to provide a clear answer to these questions. For a certain kind of element, the stability of its specific low-D structure is determined by several derivatives of its interatomic potential. This atomistic-based approach is then applied to study any straight/planar, low-D, equal-bond-length elemental materials. We found that 1-D monatomic chains, 2-D honeycomb lattices, square lattices, and triangular lattices are the only four permissible structures, and the stability of these structures can only be understood by assuming multi-body interatomic potentials. Using this approach, the stable existence of graphene, silicene and germanene can be explained.
In this paper, we show that the catenoids and the Clifford minimal hypersurfaces are the only complete minimal hypersurfaces satisfying the Simons' equation (3.9) in the space forms.
Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of finite volume. We prove any closed immersed incompressible surface can be deformed to a closed immersed least area surface within its homotopy class in any cusped hyperbolic three-manifold. Our techniques highlight how special structures of these cusped hyperbolic three-manifolds prevent any least area minimal surface going too deep into the cusped region.
The analytical solution of the periodic elastic field in chiral magnets caused by presence of periodically distributed eigenstrains is obtained. For the skyrmion phase, both the periodic displacement field and the stress field are composed of three "triple-Q" structures with different wave numbers. We find that for increasing external magnetic field, one type of "triple-Q" displacement structure and stress structure undergo a configurational reversal, where the initial and the final field configuration share similar pattern but with opposite direction of all the field vectors. This result is enlightening for designing novel skyrmion-based data-storage devices and microwave applications. The solution obtained is of fundamental significance for understanding the emergent mechanical properties of skyrmions in chiral magnets.
In this paper, we study the stability of catenoids and helicoids in the hyperbolic $3$-space $\mathbb{H}^3$. (1) For a family of spherical minimal catenoids $\{\mathcal{C}_a\}_{a>0}$ in $\mathbb{H}^3$, there exist two constants $0 \bar{a}_c$.
A beam line is built after the IHEP RFQ for halo study. To determine transverse emittance and ellipse parameters of the RFQ output beam, beam size data obtained from the first two of 14 wire scanners are employed. By using the transfer matrix method and the least square method, a set of linear equations were set up and solved. The solutions were then applied as initial beam parameters in multi-particle simulations to check the method of calculation. It is shown that difference between the simulated RMS beam size and the measured one at the measurement location is less than 7%, which is acceptable in our experiments.
For a family of spherical minimal catenoids C_a in the hyperbolic 3-space, there exist two constants 0 =a_c, and (3) C_a is a least area minimal surface in the sense of Meeks-Yau if a>=a_l.
For a family of minimal helicoids H_a in the hyperbolic 3-space, there exists a constant a_c=2.17966 such that the following statements are true: (1) H_a is a globally stable minimal surface if 0<=a<=a_c, and (2) H_a is an unstable minimal surface with index one if a>a_c.
We propose a new type of the spin Seebeck effect (SSE) emerging from the Rashba spin-orbit coupling in asymmetric four-terminal electron systems. This system generates spin currents or spin voltages along the longitudinal direction parallel to the temperature gradient in the absence of magnetic fields. The remarkable result arises from the breaking of reflection symmetry along the transverse direction. In the meantime, the SSE along the transverse direction, so-called the spin Nernst effect, with spin currents or spin voltages perpendicular to the temperature gradient can be simultaneously realized in our system. We further find that it is possible to use the temperature differences between four leads to tune the spin Seebeck coefficients.
The various wireless networks have made the ambient radio frequency signals around the world. Wireless information and power transfer enables the devices to recycle energy from these ambient radio frequency signals and process information simultaneously. In this paper, we develop a wireless information and power transfer protocol in two-way amplify-and-forward relaying channels, where two sources exchange information via an energy harvesting relay node. The relay node collects energy from the received signals and uses it to provide the transmission power to forward the received signals. We analytically derive the exact expressions of the outage probability, the ergodic capacity and the finite-SNR diversity-multiplexing trade-off (DMT). Furthermore, the tight closed-form upper and lower bounds of the outage probability and the ergodic capacity are then developed. Moreover, the impact of the power splitting ratio is also evaluated and analyzed. Finally, we show that compared to the non-cooperative relaying scheme, the proposed protocol is a green solution to offer higher transmission rate and more reliable communication without consuming additional resource.