Phase portraits of Bernoulli quadratic polynomial differential systems

In this paper we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincaré disk of Bernoulli quadratic polynomial differential systems in R2

Study of stability of relativistic ideal Bose-Einstein condensates

A relativistic complex scalar boson field at finite temperature $T$ is examined below its critical Bose-Einstein condensation temperature. It is shown that at the same $T$ the state with antibosons has higher entropy, lower Helmholtz free energy and higher pressure than the state without antibosons, but the same Gibbs free energy as it should. This implies that the configuration without antibosons is metastable. Results are generalized for arbitrary $d$ spatial dimensions.Comment: Accepted for publication in Phys.Lett.

Critical dynamics in the 2d classical XY-model: a spin dynamics study

Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the classical three component XY-model (i.e. the anisotropic limit of an easy-plane Heisenberg ferromagnet), on square lattices of size up to 192^2, for several temperatures below, at, and above T_KT. The temporal evolution of spin configurations was determined numerically from coupled equations of motion for individual spins by a fourth order predictor-corrector method, with initial spin configurations generated by a hybrid Monte Carlo algorithm. The neutron scattering function S(q,omega) was calculated from the resultant space-time displaced spin-spin correlation function. Pronounced spin-wave peaks were found both in the in-plane and the out-of-plane scattering function over a wide range of temperatures. The in-plane scattering function S^xx also has a large number of clear but weak additional peaks, which we interpret to come from two-spin-wave scattering. In addition, we observed a small central peak in S^xx, even at temperatures well below the phase transition. We used dynamic finite size scaling theory to extract the dynamic critical exponent z. We find z=1.00(4) for all T <= T_KT, in excellent agreement with theoretical predictions, although the shape of S(q,omega) is not well described by current theory.Comment: 31 pages, LaTex, 13 figures (38 subfigures) included as eps-files, needs psfig, 260 K

Strain-induced partially flat band, helical snake states, and interface superconductivity in topological crystalline insulators

Topological crystalline insulators in IV-VI compounds host novel topological surface states consisting of multi-valley massless Dirac fermions at low energy. Here we show that strain generically acts as an effective gauge field on these Dirac fermions and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict the realization of this phenomenon in IV-VI semiconductor heterostructures, due to a naturally occurring misfit dislocation array at the interface that produces a periodically varying strain field. Remarkably, the zero-energy Landau orbitals form a flat band in the vicinity of the Dirac point, and coexist with a network of snake states at higher energy. We propose that the high density of states of this flat band gives rise to interface superconductivity observed in IV-VI semiconductor multilayers at unusually high temperatures, with non-BCS behavior. Our work demonstrates a new route to altering macroscopic electronic properties to achieve a partially flat band, and paves the way for realizing novel correlated states of matter.Comment: Accepted by Nature Physic

Device-Compatible Chiroptical Surfaces through Self-Assembly of Enantiopure Allenes

Chiroptical methods have been proven to be superior compared to their achiral counterparts for the structural elucidation of many compounds. To expand the use of chiroptical systems to everyday applications, the development of functional materials exhibiting intense chiroptical responses is essential. Particularly, tailored and robust interfaces compatible with standard device operation conditions are required. Herein, we present the design and synthesis of chiral allenes and their use for the functionalization of gold surfaces. The self-assembly results in a monolayer-thin room-temperature-stable upstanding chiral architecture as ascertained by ellipsometry, X-ray photoelectron spectroscopy, and near-edge X-ray absorption fine structure. Moreover, these nanostructures anchored to device-compatible substrates feature intense chiroptical second harmonic generation. Both straightforward preparation of the device-compatible interfaces along with their chiroptical nature provide major prospects for everyday applications

Device-Compatible Chiroptical Surfaces through Self-Assembly of Enantiopure Allenes

Chiroptical methods have been proven to be superior compared to their achiral counterparts for the structural elucidation of many compounds. To expand the use of chiroptical systems to everyday applications, the development of functional materials exhibiting intense chiroptical responses is essential. Particularly, tailored and robust interfaces compatible with standard device operation conditions are required. Herein, we present the design and synthesis of chiral allenes and their use for the functionalization of gold surfaces. The self-assembly results in a monolayer-thin room-temperature-stable upstanding chiral architecture as ascertained by ellipsometry, X-ray photoelectron spectroscopy, and near-edge X-ray absorption fine structure. Moreover, these nanostructures anchored to device-compatible substrates feature intense chiroptical second harmonic generation. Both straightforward preparation of the device-compatible interfaces along with their chiroptical nature provide major prospects for everyday applications.</p