Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators

The ground state of translationally-invariant insulators comprise bands which can assume topologically distinct structures. There are few known examples where this distinction is enforced by a point-group symmetry alone. In this paper we show that 1D and 2D insulators with the simplest point-group symmetry - inversion - have a $Z^{\geq}$ classification. In 2D, we identify a relative winding number that is solely protected by inversion symmetry. By analysis of Berry phases, we show that this invariant has similarities with the first Chern class (of time-reversal breaking insulators), but is more closely analogous to the $Z_2$ invariant (of time-reversal invariant insulators). Implications of our work are discussed in holonomy, the geometric-phase theory of polarization, the theory of maximally-localized Wannier functions, and in the entanglement spectrum.Comment: The updated version is accepted in Physical Review

Mobility-Aware Caching for Content-Centric Wireless Networks: Modeling and Methodology

As mobile services are shifting from "connection-centric" communications to "content-centric" communications, content-centric wireless networking emerges as a promising paradigm to evolve the current network architecture. Caching popular content at the wireless edge, including base stations (BSs) and user terminals (UTs), provides an effective approach to alleviate the heavy burden on backhaul links, as well as lowering delays and deployment costs. In contrast to wired networks, a unique characteristic of content-centric wireless networks (CCWNs) is the mobility of mobile users. While it has rarely been considered by existing works in caching design, user mobility contains various helpful side information that can be exploited to improve caching efficiency at both BSs and UTs. In this paper, we present a general framework on mobility-aware caching in CCWNs. Key properties of user mobility patterns that are useful for content caching will be firstly identified, and then different design methodologies for mobility-aware caching will be proposed. Moreover, two design examples will be provided to illustrate the proposed framework in details, and interesting future research directions will be identified.Comment: 16 pages, 5 figures, to appear in IEEE Communications Magazin

Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry

We perform a complete classification of two-band \bk\cdot\mathbf{p} theories at band crossing points in 3D semimetals with $n$-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by $C_{4,6}$-protected double-Weyl nodes with quadratic in-plane (along $k_{x,y}$) dispersion or $C_6$-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr$_2$Se$_4$ and confirm it is a double-Weyl metal protected by $C_4$ symmetry. Furthermore, if the direction of the ferromagnetism is shifted away from the [001]- to the [111]-axis, the double-Weyl node splits into four single Weyl nodes, as dictated by the point group $S_6$ of that phase. Finally, we discuss experimentally relevant effects including splitting of multi-Weyl nodes by applying $C_n$ breaking strain and the surface Fermi arcs in these new semimetals.Comment: 4+ pages, 2 figures, 1 tabl

Backhaul-Aware Caching Placement for Wireless Networks

As the capacity demand of mobile applications keeps increasing, the backhaul network is becoming a bottleneck to support high quality of experience (QoE) in next-generation wireless networks. Content caching at base stations (BSs) is a promising approach to alleviate the backhaul burden and reduce user-perceived latency. In this paper, we consider a wireless caching network where all the BSs are connected to a central controller via backhaul links. In such a network, users can obtain the required data from candidate BSs if the data are pre-cached. Otherwise, the user data need to be first retrieved from the central controller to local BSs, which introduces extra delay over the backhaul. In order to reduce the download delay, the caching placement strategy needs to be optimized. We formulate such a design problem as the minimization of the average download delay over user requests, subject to the caching capacity constraint of each BS. Different from existing works, our model takes BS cooperation in the radio access into consideration and is fully aware of the propagation delay on the backhaul links. The design problem is a mixed integer programming problem and is highly complicated, and thus we relax the problem and propose a low-complexity algorithm. Simulation results will show that the proposed algorithm can effectively determine the near-optimal caching placement and provide significant performance gains over conventional caching placement strategies.Comment: 6 pages, 3 figures, accepted to IEEE Globecom, San Diego, CA, Dec. 201

Type-II Weyl Semimetals

Fermions in nature come in several types: Dirac, Majorana and Weyl are theoretically thought to form a complete list. Even though Majorana and Weyl fermions have for decades remained experimentally elusive, condensed matter has recently emerged as fertile ground for their discovery as low energy excitations of realistic materials. Here we show the existence of yet another particle - a new type of Weyl fermion - that emerges at the boundary between electron and hole pockets in a new type of Weyl semimetal phase of matter. This fermion was missed by Weyl in 1929 due to its breaking of the stringent Lorentz symmetry of high-energy physics. Lorentz invariance however is not present in condensed matter physics, and we predict that an established material, WTe$_2$, is an example of this novel type of topological semimetal hosting the new particle as a low energy excitation around a type-2 Weyl node. This node, although still a protected crossing, has an open, finite-density of states Fermi surface, likely resulting in a plethora physical properties very different from those of standard point-like Fermi surface Weyl points

Anomalous Phase Transition in Strained SrTiO3_3 Thin Films

We have studied the cubic to tetragonal phase transition in epitaxial SrTiO$_3$ films under various biaxial strain conditions using synchrotron X-ray diffraction. Measuring the superlattice peak associated with TiO$_6$ octahedra rotation in the low temperature tetragonal phase indicates the presence of a phase transition whose critical temperature is a strong function of strain, with T$_C$ as much as 50K above the corresponding bulk temperature. Surprisingly, the lattice constants evolve smoothly through the transition with no indication of a phase change. This signals an important change in the nature of the phase transition due to the epitaxy strain and substrate clamping effect. The internal degrees of freedom (TiO$_6$ rotations) have become uncoupled from the overall lattice shape.Comment: 4 pages, 3 figures, REVTeX

Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd3As2, KMgBi, and rutile-structure (β′-) PtO2