arXiv subjects
Publications and source records attributed to Xi Chen.
We proved that the union of rational curves is dense on a very general K3 surface and the union of elliptic curves is dense in the 1st jet space of a very general K3 surface, both in the strong topology.
A two-state spin system is specified by a 2 x 2 matrix A = {A_{0,0} A_{0,1}, A_{1,0} A_{1,1}} = {β1, 1 γ} where β, γ\ge 0. Given an input graph G=(V,E), the partition function Z_A(G) of a system is defined as Z_A(G) = \sum_{σ: V -> {0,1}} \prod_{(u,v) \in E} A_{σ(u), σ(v)} We prove inapproximability results for the partition function in the region specified by the non-uniqueness condition from phase transition for the Gibbs measure. More specifically, assuming NP \ne RP, for any fixed β, γin the unit square, there is no randomized polynomial-time algorithm that approximates Z_A(G) for d-regular graphs G with relative error ε= 10^{-4}, if d = Ω(Δ(β,γ)), where Δ(β,γ) > 1/(1-βγ) is the uniqueness threshold. Up to a constant factor, this hardness result confirms the conjecture that the uniqueness phase transition coincides with the transition from computational tractability to intractability for Z_A(G). We also show a matching inapproximability result for a region of parameters β, γoutside the unit square, and all our results generalize to partition functions with an external field.
We elucidate the existing controversies in the newly discovered K-doped iron selenide (KxFe2-ySe2-z) superconductors. The stoichiometric KFe2Se2 with \surd2\times\surd2 charge ordering was identified as the parent compound of KxFe2-ySe2-z superconductor using scanning tunneling microscopy and spectroscopy. The superconductivity is induced in KFe2Se2 by either Se vacancies or interacting with the anti-ferromagnetic K2Fe4Se5 compound. Totally four phases were found to exist in KxFe2-ySe2-z: parent compound KFe2Se2, superconducting KFe2Se2 with \surd2\times\surd5 charge ordering, superconducting KFe2Se2-z with Se vacancies and insulating K2Fe4Se5 with \surd5\times\surd5 Fe vacancy order. The phase separation takes place at the mesoscopic scale under standard molecular beam epitaxy condition.
We report a survey with the Purple Mountain Observatory (PMO) 13.7-m radio telescope for class I methanol masers from the 95 GHz (8_0 - 7_1 A^+) transition. The 214 target sources were selected by combining information from both the Spitzer GLIMPSE and 1.1 mm BGPS survey catalogs. The observed sources satisfy both the GLIMPSE mid-IR criteria of [3.6]-[4.5]>1.3, [3.6]-[5.8]>2.5, [3.6]-[8.0]>2.5 and 8.0 um magnitude less than 10, and also have an associated 1.1 mm BGPS source. Class I methanol maser emission was detected in 63 sources, corresponding to a detection rate of 29% for this survey. For the majority of detections (43), this is the first identification of a class I methanol maser associated with these sources. We show that the intensity of the class I methanol maser emission is not closely related to mid-IR intensity or the colors of the GLIMPSE point sources, however, it is closely correlated with properties (mass and beam-averaged column density) of the BGPS sources. Comparison of measures of star formation activity for the BGPS sources with and without class I methanol masers indicate that the sources with class I methanol masers usually have higher column density and larger flux density than those without them. Our results predict that the criteria log(S_{int})<-38.0+1.72log(N_{H_{2}}^{beam}) and log(N_{H_{2}}^{beam})>22.1, which utilizes both the integrated flux density (S_{int}) and beam-averaged column density (N_{H_{2}}^{beam}) of the BGPS sources, are very efficient for selecting sources likely to have an associated class I methanol maser. Our expectation is that searches using these criteria will detect 90% of the predicted number of class I methanol masers from the full BGPS catalog (~ 1000), and do so with a high detection efficiency (~75%).
The latest discovery of high temperature superconductivity signature in single-layer FeSe is significant because it is possible to break the superconducting critical temperature ceiling (maximum Tc~55 K) that has been stagnant since the discovery of Fe-based superconductivity in 2008. It also blows the superconductivity community by surprise because such a high Tc is unexpected in FeSe system with the bulk FeSe exhibiting a Tc at only 8 K at ambient pressure which can be enhanced to 38 K under high pressure. The Tc is still unusually high even considering the newly-discovered intercalated FeSe system A_xFe_{2-y}Se_2 (A=K, Cs, Rb and Tl) with a Tc at 32 K at ambient pressure and possible Tc near 48 K under high pressure. Particularly interesting is that such a high temperature superconductivity occurs in a single-layer FeSe system that is considered as a key building block of the Fe-based superconductors. Understanding the origin of high temperature superconductivity in such a strictly two-dimensional FeSe system is crucial to understanding the superconductivity mechanism in Fe-based superconductors in particular, and providing key insights on how to achieve high temperature superconductivity in general. Here we report distinct electronic structure associated with the single-layer FeSe superconductor. Its Fermi surface topology is different from other Fe-based superconductors; it consists only of electron pockets near the zone corner without indication of any Fermi surface around the zone center. Our observation of large and nearly isotropic superconducting gap in this strictly two-dimensional system rules out existence of node in the superconducting gap. These results have provided an unambiguous case that such a unique electronic structure is favorable for realizing high temperature superconductivity.
In the recent work by Song et al. [Science 332, 1410 (2011)], the scanning tunneling spectroscopy experiment in the stoichiometric FeSe reveals evidence for nodal superconductivity and strong anisotropy. The nodal structure can be explained with the extended s-wave pairing structure with the mixture of the $s_{x^2+y^2}$ and $s_{x^2y^2}$ pairing symmetries. We calculate the anisotropic vortex structure by using the self-consistent Bogoliubov-de Gennes mean-field theory. In considering the absence of magnetic ordering in the FeSe at the ambient pressure, orbital ordering is introduced, which breaks the $C_4$ lattice symmetry down to $C_2$, to explain the anisotropy in the vortex tunneling spectra.
We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, based on the l1/l2 mixed-norm penalty, and 2) graph-guided fusion penalty. For both types of penalties, due to their non-separability, developing an efficient optimization method has remained a challenging problem. In this paper, we propose a general optimization approach, called smoothing proximal gradient method, which can solve the structured sparse regression problems with a smooth convex loss and a wide spectrum of structured-sparsity-inducing penalties. Our approach is based on a general smoothing technique of Nesterov. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used interior-point method. Numerical results are reported to demonstrate the efficiency and scalability of the proposed method.
We consider a junction between surface $p$-type and surface $n$-type on an ideal topological insulator in which carrier type and density in two adjacent regions are locally controlled by composition graded doping or electrical gating. Such junction setting on topological insulators are fundamental for possible device application. A single gapless chiral edge state localized along the junction interface appears in the presence of an external magnetic field, and it can be probed by scanning tunneling microscopy and transport measurements. We propose to realize this topological \emph{p-n} junction in (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$, which has insulating bulk properties and a tunable surface state across the Dirac cone.
Searching for superconducting materials with high transition temperature (TC) is one of the most exciting and challenging fields in physics and materials science. Although superconductivity has been discovered for more than 100 years, the copper oxides are so far the only materials with TC above 77 K, the liquid nitrogen boiling point. Here we report an interface engineering method for dramatically raising the TC of superconducting films. We find that one unit-cell (UC) thick films of FeSe grown on SrTiO3 (STO) substrates by molecular beam epitaxy (MBE) show signatures of superconducting transition above 50 K by transport measurement. A superconducting gap as large as 20 meV of the 1 UC films observed by scanning tunneling microcopy (STM) suggests that the superconductivity could occur above 77 K. The occurrence of superconductivity is further supported by the presence of superconducting vortices under magnetic field. Our work not only demonstrates a powerful way for finding new superconductors and for raising TC, but also provides a well-defined platform for systematic study of the mechanism of unconventional superconductivity by using different superconducting materials and substrates.
Geometry, electronic structure, and magnetic properties of methylthiolate-stabilized Au$_{25}$L$_{18}$ and MnAu$_{24}$L$_{18}$ (L = SCH$_3$) clusters adsorbed on noble-metal (111) surfaces have been investigated by using spin-polarized density functional theory computations. The interaction between the cluster and the surface is found to be mediated by charge transfer mainly from or into the ligand monolayer. The electronic properties of the 13-atom metal core remain in all cases rather undisturbed as compared to the isolated clusters in gas phase. The Au$_{25}$L$_{18}$ cluster retains a clear HOMO - LUMO energy gap in the range of 0.7 eV to 1.0 eV depending on the surface. The ligand layer is able to decouple the electronic structure of the magnetic MnAu$_{24}$L$_{18}$ cluster from Au(111) surface, retaning a high local spin moment of close to 5 $μ_{B}$ arising from the spin-polarized Mn(3d) electrons. These computations imply that the thiolate monolayer-protected gold clusters may be used as promising building blocks with tunable energy gaps, tunneling barriers, and magnetic moments for applications in the area of electron and/or spin transport.
The Karman constant κ- widely used in atmospheric science and engineering turbulence modelling, and proposed by Prandtl in 1925 and von Karman in 1930 to describe the mean velocity of a turbulent wall-bounded flow - leads to a logarithmic profile in an overlap region near the wall. For over eighty years, its value was believed to be ~0.41. But more recently, many argue that it is not a constant, because of measured variations in different flows and at different Reynolds numbers (Re). Here, a multi-layer analytic theory is shown to lead to a re-interpretation of κas a global constant for both the overlap region and outer flow, and to yield a new method for its measurement. The newly determined value is 0.45 for both channel and pipe. It is shown that this new κ, together with other wall constants, yields a 99% accuracy in the prediction of mean velocity data at all points in high Re (up to 40 million) pipe flow. The theory also describes finite Re effect, and discovers a transition at the friction Re (i.e. Re_τ)=5000. An accurate model for the prediction of turbulent transport in canonical pipe and channel flows is achieved here, and we propose the model to be valid for a wide class of turbulent flows.
A Schrödinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes and dynamics. In contrast to this standard scenario, other relations are also possible, such as a common interaction-picture dynamical equation corresponding to several Schrödinger equations that represent different physics. This may enable us to design alternative and feasible experimental routes for operations that are a priori difficult or impossible to perform. The power of this concept is exemplified by engineering Hamiltonians that improve the performance or make realizable several shortcuts to adiabaticity.
Observations of ten Compact Symmetric Objects ({\rm CSO}) candidates have been made with the Very Long Baseline Array at 8.4 GHz in 2005 and with a combined Chinese and European VLBI array at 8.4 GHz in 2009. The 2009 observations incorporate for the first time the two new Chinese telescopes at Miyun and Kunming for international astrophysical observations. The observational data, in combination with archival VLBA data from previous epochs, have been used to derive the proper motions of the VLBI components. Because of the long time baseline of $\sim$16 years of the VLBI data sets, the expansion velocities of the hot spots can be measured at an accuracy as high as $\sim$1.3 $μ$as yr$^{-1}$. Six of the ten sources are identified as CSOs with a typical double or triple morphology on the basis of both spectral index maps and their mirror-symmetry of proper motions of the terminal hot spots. The compact double source J1324+4048 is also identified as a CSO candidate. Among the three remaining sources, J1756+5748 and J2312+3847 are identified as core-jet sources with proper motions of their jet components relating to systemic source expansion. The third source J0017+5312 is likely also a core-jet source, but a robust detection of a core is needed for an unambiguous identification. The kinematic ages of the CSOs derived from proper motions range from 300 to 2500 years. The kinematic age distribution of the CSOs confirm an overabundance of compact young CSOs with ages less than 500 years. CSOs with known kinematic ages may be used to study the dynamical evolution of extragalactic radio sources at early stages.
This paper has been withdrawn by the author
Three-dimensional (3D) topological insulators (TI) are novel quantum materials with insulating bulk and topologically protected metallic surfaces with Dirac-like band structure. The spin-helical Dirac surface states are expected to host exotic topological quantum effects and find applications in spintronics and quantum computation. The experimental realization of these ideas requires fabrication of versatile devices based on bulk-insulating TIs with tunable surface states. The main challenge facing the current TI materials exemplified by Bi2Se3 and Bi2Te3 is the significant bulk conduction, which remains unsolved despite extensive efforts involving nanostructuring, chemical doping and electrical gating. Here we report a novel approach for engineering the band structure of TIs by molecular beam epitaxy (MBE) growth of (Bi1-xSbx)2Te3 ternary compounds. Angle-resolved photoemission spectroscopy (ARPES) and transport measurements show that the topological surface states exist over the entire composition range of (Bi1-xSbx)2Te3 (x = 0 to 1), indicating the robustness of bulk Z2 topology. Most remarkably, the systematic band engineering leads to ideal TIs with truly insulating bulk and tunable surface state across the Dirac point that behave like one quarter of graphene. This work demonstrates a new route to achieving intrinsic quantum transport of the topological surface states and designing conceptually new TI devices with well-established semiconductor technology.
We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions, then we prove that #CSP(F) is solvable in polynomial time if all three conditions are satisfied; and is #P-hard otherwise. Our complexity dichotomy generalizes a long series of important results on counting problems: (a) the problem of counting graph homomorphisms is the special case when there is a single symmetric binary function in F; (b) the problem of counting directed graph homomorphisms is the special case when there is a single not-necessarily-symmetric binary function in F; and (c) the standard form of #CSP is when all functions in F take values in {0,1}.
We investigate electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice. It is found that such structure can possess a zero-$\bar{k}$ gap which exists in all Fibonacci sequences. Different from Bragg gap, zero-$\bar{k}$ gap associated with Dirac point is less sensitive to the incidence angle and lattice constants. The defect mode appeared inside the zero-$\bar{k}$ gap has a great effect on transmission, conductance and shot noise, which can be applicable to control the electron transport.
We report the experimental observation of Landau quantization of molecular beam epitaxy grown Sb2Te3 thin films by a low-temperature scanning tunneling microscope. Different from all the reported systems, the Landau quantization in Sb2Te3 topological insulator is not sensitive to the intrinsic substitutional defects in the films. As a result, a nearly perfect linear energy dispersion of surface states as 2D massless Dirac fermion system is achieved. We demonstrate that 4 quintuple layers are the thickness limit for Sb2Te3 thin film being a 3D topological insulator. The mechanism of the Landau level broadening is discussed in terms of enhanced quasiparticle lifetime.