We present a magneto-infrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe$_5$. We observe clear transitions between Landau levels and their further splitting under magnetic field. Both the sequence of transiti
ons and their field dependence follow quantitatively the relation expected for 3D emph{massless} Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe$_5$ is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides a direct and bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizeable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under current magnetic field configuration.
Three dimensional (3D) topological Dirac materials are under intensive study recently. The layered compound ZrTe$_5$ has been suggested to be one of them by transport and ARPES experiments. Here, we perform infrared reflectivity measurement to invest
igate the underlying physics of this material. The derived optical conductivity exhibits linear increasing with frequency below normal interband transitions, which provides the first optical spectroscopic proof of a 3D Dirac semimetal. Apart from that, the plasma edge shifts dramatically to lower energy upon temperature cooling, which might be associated with the consequence of lattice parameter shrinking. In addition, an extremely sharp peak shows up in the frequency dependent optical conductivity, indicating the presence of a Van Hove singularity in the joint density of state.
We performed an optical spectroscopy measurement on single crystals of $mathrm{Ba_2Ti_2Fe_2As_4O}$, which is a newly discovered superconductor showing a coexistence of superconductivity and density wave order. The study reveals a spectral change rela
ted to the formation density wave energy gap below $T_{DW}approx$125 K, leading to the removal of about half of the multiple Fermi surface sheets. The ratio of 2$Delta_{DW}$/$k_B T_{DW}approx$ 11.9 is considerably larger than the mean-field value based on the weak-coupling BCS theory. At the lowest temperature in the superconducting state, we observed opening of superconducting energy gaps $Delta_1(0) =3.4$ meV and $Delta_2(0)=7.9$ meV. The properties of superconducting state in $mathrm{Ba_2Ti_2Fe_2As_4O}$ are similar to that in $mathrm{BaFe_{1.85}Co_{0.15}As_2}$.
We present an optical spectroscopy study on P-doped CaFe$_2$As$_2$ which experiences a structural phase transition from tetragonal to collapsed tetragonal (cT) phase near 75 K. The measurement reveals a sudden reduction of low frequency spectral weig
ht and emergence of a new feature near 3200 cm (0.4 eV) in optical conductivity across the transition, indicating an abrupt reconstruction of band structure. The appearance of new feature is related to the interband transition arising from the sinking of hole bands near $Gamma$ point below Fermi level in the cT phase, as expected from the density function theory calculations in combination with the dynamical mean field theory. However, the reduction of Drude spectral weight is at variance with those calculations. The measurement also indicates an absence of the abnormal spectral weight transfer at high energy (near 0.5-0.7 eV) in the cT phase, suggesting a suppression of electron correlation effect.
We consider the following evolutionary Hamilton-Jacobi equation with initial condition: begin{equation*} begin{cases} partial_tu(x,t)+H(x,u(x,t),partial_xu(x,t))=0, u(x,0)=phi(x), end{cases} end{equation*} where $phi(x)in C(M,mathbb{R})$. Under some
assumptions on the convexity of $H(x,u,p)$ with respect to $p$ and the Osgood growth of $H(x,u,p)$ with respect to $u$, we establish an implicitly variational principle and provide an intrinsic relation between viscosity solutions and certain minimal characteristics. Moreover, we obtain a representation formula of the viscosity solution of the evolutionary Hamilton-Jacobi equation.
We present an optical spectroscopy study on F-substituted NdOBiS$_2$ superconducting single crystals grown using KCl/LiCl flux method. The measurement reveals a simple metallic response with a relatively low screened plasma edge near 5000 cm. The pla
sma frequency is estimated to be 2.1 eV, which is much smaller than the value expected from the first-principles calculations for an electron doping level of x=0.5, but very close to the value based on a doping level of 7$%$ of itinerant electrons per Bi site as determined by ARPES experiment. The energy scales of the interband transitions are also well reproduced by the first-principles calculations. The results suggest an absence of correlation effect in the compound, which essentially rules out the exotic pairing mechanism for superconductivity or scenario based on the strong electronic correlation effect. The study also reveals that the system is far from a CDW instability as being widely discussed for a doping level of x=0.5.
The power consumption of enormous network devices in data centers has emerged as a big concern to data center operators. Despite many traffic-engineering-based solutions, very little attention has been paid on performance-guaranteed energy saving sch
emes. In this paper, we propose a novel energy-saving model for data center networks by scheduling and routing deadline-constrained flows where the transmission of every flow has to be accomplished before a rigorous deadline, being the most critical requirement in production data center networks. Based on speed scaling and power-down energy saving strategies for network devices, we aim to explore the most energy efficient way of scheduling and routing flows on the network, as well as determining the transmission speed for every flow. We consider two genera
For an integrable Tonelli Hamiltonian with $d (dgeq 2)$ degrees of freedom, we show that all of the Lagrangian tori can be destroyed by analytic perturbations which are arbitrarily small in the $C^{d-delta}$ topology.
In this paper, we show that for exact area-preserving twist maps on annulus, the invariant circles with a given rotation number can be destroyed by arbitrarily small Gevrey-$alpha$ perturbations of the integrable generating function in the $C^r$ topology with $r<4-frac{2}{alpha}$, where $alpha>1$.
We report an optical spectroscopy study on the single crystal of Na$_2$Ti$_2$As$_2$O, a sister compound of superconductor BaTi$_2$Sb$_2$O. The study reveals unexpectedly two density wave phase transitions. The first transition at 320 K results in the
formation of a large energy gap and removes most part of the Fermi surfaces. But the compound remains metallic with residual itinerant carriers. Below 42 K, another density wave phase transition with smaller energy gap scale occurs and drives the compound into semiconducting ground state. These experiments thus enable us to shed light on the complex electronic structure in the titanium oxypnictides.
