Four-Dimensional Topological Insulators with Nodal-Line Boundary States

Conventional topological insulators and superconductors have topologically protected nodal points on their boundaries, and the recent interests in nodal-line semimetals only concerned bulk band structures. Here, we present a novel four-dimensional topological insulator protected by an anti-unitary reflection symmetry, whose boundary band has a single $PT$-symmetric nodal line with double topological charges. Inspired by the recent experimental realization of the four-dimensional quantum Hall effect, we also propose a cold-atom system which realizes the novel topological insulator with tunable parameters as extra dimensions.Comment: 5 pages and 3 figures for main text, 10 pages and 2 figures for supplemental materia

Machine Learning Phase Transition: An Iterative Proposal

We propose an iterative proposal to estimate critical points for statistical models based on configurations by combing machine-learning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by dimensionality-reduction techniques. Besides, this step not only provides labelled samples for the subsequent step but also is necessary for its application to novel statistical models. Secondly, making use of these samples as training set, neural networks are employed to assign labels to those samples between the phase boundaries in an iterative manner. Newly labelled samples would be put in the training set used in subsequent training and the phase boundaries would be updated as well. The average of the phase boundaries is expected to converge to the critical temperature in this proposal. In concrete examples, we implement this proposal to estimate the critical temperatures for two q-state Potts models with continuous and first order phase transitions. Linear and manifold dimensionality-reduction techniques are employed in the first step. Both a convolutional neural network and a bidirectional recurrent neural network with long short-term memory units perform well for two Potts models in the second step. The convergent behaviors of the estimations reflect the types of phase transitions. And the results indicate that our proposal may be used to explore phase transitions for new general statistical models.Comment: We focus on the iterative strategy but not the concrete tools like specific dimension-reduction techniques, CNN and BLSTM in this work. Other machine-learning tools with similar functions may be applied to new statistical models with this proposa

Topological photonic states in one-dimensional dimerized ultracold atomic chains

We study the topological optical states in one-dimensional (1D) dimerized ultracold atomic chains, as an extension of the Su-Schrieffer-Heeger (SSH) model. By taking the fully retarded near-field and far-field dipole-dipole interactions into account, we describe the system by an effective non-Hermitian Hamiltonian, vastly different from the Hermitian Hamiltonian of the conventional SSH model. We analytically calculate the complex bandstructures for infinitely long chains, and show that the topological invariant, i.e., the complex Zak phase, is still quantized and becomes nontrivial when the dimerization parameter $\beta>0.5$, despite the broken chiral symmetry and non-Hermiticity. We have verified the validity of the bulk-boundary correspondence for this non-Hermitian system by further analyzing the eigenstate distributions along with their inverse participation ratios (IPRs) for finite chains, where topologically protected edge states are unambiguously identified. We also reveal that such topological edge states are robust under symmetry-breaking disorders. For transverse eigenstates, we further discover the increase of localization length of topological edge states with the increase of lattice period due to the presence of strong far-field dipole-dipole interactions. Moreover, the ultra-strong scattering cross section and ultra-narrow linewidth of a single cold atom allow us to observe in more detail about topological states than in conventional systems, such as the frequency shift with respect to the single-atom resonance and the largely tunable bandgap. We envisage these topological photonic states can provide an efficient interface between light and matter.Comment: 13 pages 10 figures Comments are welcom

Role of Near-Field Interaction on Light Transport in Disordered Media

Understanding light-matter interaction in disordered photonic media allows people to manipulate light scattering and achieve exciting applications using seemingly scrambled media. As the concentration of scattering particles rises, they are inclined to step into near fields of each other in deep subwavelength scale. The fundamental physics involving the interplay between disorder and near-field interaction (NFI) is still not fully understood. We theoretically examine the role of NFI by analyzing the underlying multiple scattering mechanism. We find NFI leads to a stronger collective behavior involving more particles and widens the photonic pseudo-bandgap of disordered media. It also excites more weakly decayed longitudinal modes and results in higher local density of states. By introducing a sticky short-range order, we demonstrate the possibility of enhancing off-momentum-shell NFI of multiple scattering process. Our results have profound implications in understanding and harnessing nanoscale light-matter interaction for novel disordered photonic devices.Comment: 7 pages, 5 figures, plus a 9-page supplementary material, comments are welcom

Effect of Dependent Scattering on Light Absorption in Highly Scattering Random Media

The approximate nature of radiative transfer equation (RTE) leads to a bunch of considerations on the effect of "dependent scattering" in random media, especially particulate media composed of discrete scatterers, in the last a few decades, which usually indicates those deviations RTE (combined with ISA) lead to from experimental and exact numerical results due to electromagnetic wave interference. Here we theoretically and numerically demonstrate the effect of dependent scattering on absorption in disordered media consisting of highly scattering scatterers. By making comparison between the independent scattering approximation-radiative transfer equation (ISA-RTE) and the full-wave coupled dipole method (CDM), we find that deviations between the two methods increase as scatterer density in the media increases. The discrepancy also grows with optical thickness. To quantitatively take dependent scattering effect into account, we develop a theoretical model using quasi-crystalline approximation (QCA) to derive dependent-scattering corrected radiative properties, based on the path-integral diagrammatic technique in multiple scattering theory. The model results in a more reasonable agreement with numerical simulations. The present work has profound implications for the coherent scattering physics in random media with absorption, correctly modeling light absorptance in random media and interpreting the experimental observations in various applications for random media such as solar energy concentration, micro/nanofluids, structural color generation, etc.Comment: 30 pages, 8 figures, submitte

Coexistence of Superconductivity and Ferromagnetism in Dilute Co-doped La_{1.89} Ce_{0.11} Cu O_{4\pm\d} System

Thin films of the optimally electron-doped $T'$-phase superconductor La$_{1.89}$Ce$_{0.11}$CuO_{4\pm \d} are investigated by dilute Co doping, formed as La$_{1.89}$Ce$_{0.11}$(Cu$_{1-x}$Co$_{x}$)O_{4\pm\d} (LCCCO) with $x$ = 0.01 -- 0.05. The following results are obtained for the first time: for the whole dilute Co doping range, LCCCO thin films show long-range ferromagnetic ordering at the temperature range from 5 K to 300 K, which is likely due to the RKKY interaction; in the very dilute Co doping, $x$ = 0.01 and 0.02, the superconductivity is maitained, the system shows the coexistence of superconductivity and ferromagnetism in the CuO$_{2}$ plane. This may be based on the nature of the charge carriers in electron-doped high-$T_{c}$ cuprate superconductors.Comment: 5 pages, 4 figures, accepted for publication in Physical Review

Low-temperature thermal conductivity of antiferromagnetic S = 1/2 chain material CuCl_2⋅\cdot2((CH_3)_2SO)

We study the heat transport of S = 1/2 chain compound CuCl_2$\cdot$2((CH_3)_2SO) along the b axis (vertical to the chain direction) at very low temperatures. The zero-field thermal conductivity (\kappa) shows a distinct kink at about 0.9 K, which is related to the long-range antiferromagnetic (AF) transition. With applying magnetic field along the c axis, \kappa(H) curves also show distinct changes at the phase boundaries between the AF and the high-field disordered states. These results indicate a strong spin-phonon interaction and the magnetic excitations play a role in the b-axis heat transport as phonon scatterers.Comment: 3 pages, 3 figures, accepted for publication in J. Appl. Phys. (Proceedings of the 58th MMM Conference

A new approach for modelling mixed traffic flow with motorized vehicles and non-motorized vehicles based on cellular automaton model

In this study, we provide a novel approach for modelling the mixed traffic flow. The basic idea is to integrate models for nonmotorized vehicles (nm-vehicles) with models for motorized vehicles (m-vehicles). Based on the idea, a model for mix traffic flow is realized in in the following two steps. At a first step, the models that can be integrated should be chosen. The famous NaSch cellular automata (NCA) model for m-vehicles and the Burgur cellular automata (BCA) model for nm-vehicles are used in this paper, since the two models are similar and comparable. At a second step, we should study coupling rules between m-vehicles and nm-vehicles to represent their interaction. Special lane changing rules are designed for the coupling process. The proposed model is named as the combined cellular automata (CCA) model. The model is applied to a typical mixed traffic scenario, where a bus stop without special stop bay is set on nonmotorized lanes. The simulation results show that the model can describe both the interaction between the flow of nm-vehicles and m-vehicles and their characters.Comment: 20 pages, 5 figures, Submitted to Phys. Rev.

Low-temperature heat transport of Nd_{2-x}Ce_{x}CuO_{4} single crystals

We report a study of the Ce doping effect on the thermal conductivity (\kappa) of Nd_{2-x}Ce_{x}CuO_{4} (NCCO) at low temperatures down to 0.3 K and in magnetic fields up to 14 T. It is found that with Ce doping, the electronic thermal conductivity increases; at the same time, the a-axis field induced changes in \kappa(H), associated with the spin flop and spin polarization of Nd^{3+} sublattice, and the spin flop of Cu^{2+} sublattice, gradually disappear. These are clearly due to the electron doping and the destruction of the antiferromagnetic orders. In the superconducting NCCO with x = 0.14 and 0.18, although the electronic thermal conductivity shows sizable field dependencies with H // c, the paramagnetic scattering of phonons is still playing the dominant role in the heat transport, which is different from many other cuprates. In the lightly doped samples (x = 0.03 and 0.06), the low-T \kappa(H) isotherms with H // c show a step-like anomaly and is likely related to the spin/charge stripes.Comment: 10 pages, 7 figures, accepted for publication in Phys. Rev.

Low-temperature heat transport of the geometrically frustrated antiferromagnets R_2Ti_2O_7 (R = Gd and Er)

We report a systematic study on the low-temperature thermal conductivity (\kappa) of R_2Ti_2O_7 (R = Gd and Er) single crystals with different directions of magnetic field and heat current. It is found that the magnetic excitations mainly act as phonon scatterers rather than heat carriers, although these two materials have long-range magnetic orders at low temperatures. The low-T \kappa(H) isotherms of both compounds show rather complicated behaviors and have good correspondences with the magnetic transitions, where the \kappa(H) curves show drastic dip- or step-like changes. In comparison, the field dependencies of \kappa are more complicated in Gd_2Ti_2O_7, due to the complexity of its low-T phase diagram and field-induced magnetic transitions. These results demonstrate the significant coupling between spins and phonons in these materials and the ability of heat-transport properties probing the magnetic transitions.Comment: 9 pages, 6 figures, accepted for publication in Phys. Rev.