Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect

Both topological crystalline insulators surfaces and graphene host multi-valley massless Dirac fermions which are not pinned to a high-symmetry point of the Brillouin zone. Strain couples to the low-energy electrons as a time-reversal invariant gauge field, leading to the formation of pseudo-Landau levels (PLL). Here we study periodic pseudo-magnetic fields originating from strain superlattices. We study the low-energy Dirac PLL spectrum induced by the strain superlattice and analyze the effect of various polarized states. Through self-consistent Hartree-Fock calculations we establish that, due to the strain superlattice and PLL electronic structure, a valley-ordered state spontaneously breaking time-reversal and realizing a quantum Hall phase is favored, while others are suppressed.Comment: 13 pages + 2 appendices, 9 figure

Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node

Motivated by the recent experiment indicating that superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing symmetry with rotational symmetry breaking, we study the general class of odd-parity superconductors with two-component order parameters in trigonal and hexagonal crystal systems. In the presence of strong spin-orbit interaction, we find two possible superconducting phases below $T_c$, a time-reversal-breaking (i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine their relative energetics from the gap function in momentum space. The nematic superconductor generally has a full quasi-particle gap, whereas the chiral superconductor with a three-dimensional (3D) Fermi surface has point nodes with lifted spin degeneracy, resulting in itinerant Majorana fermions in the bulk and topological Majorana arcs on the surface.Comment: 4+ pages, 2 figures; 20 pages suppl mat + 4 figures; published versio

Three-Dimensional Majorana Fermions in Chiral Superconductors

Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-non-degenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum $J$ formed by Bloch electrons with angular momentum $j$ in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the non-unitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions, and find that the nuclear magnetic resonance (NMR) spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface that form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs$_4$Sb$_{12}$ and related materials as promising candidates for non-unitary chiral superconductors hosting three-dimensional Majorana fermions.Comment: 12 pages, 3 figures + appendices; published versio

Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene

Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory shades light on the recent observation of rotational symmetry breaking in the superconducting state of twisted bilayer graphene

Dynamic characteristics and processing of fillers in polyurethane elastomers for vibration damping applications

Polyurethane elastomers have the potential of being used to reduce vibrational noise in many engineering applications. The performance of the elastomer is directly related to matching the nature of the mechanical loss characteristics to the frequency and temperature dependence of the source of the vibration. Materials with a broad frequency response and good mechanical properties are desirable for situations were load bearing and isolation becomes an issue. Because automobile, and other related vehicles operate over a broad temperature range, it is desirable for the damping characteristics of the elastomer to ideally be independent of temperature and frequency. In practice, this is not possible and the creation of materials with a broad spectrum response is desirable. In this paper, the effects of various fillers on the breadth and temperature dependence of the vibration damping characteristics of a filled and crosslinked polyurethane elastomer are explored. The fillers studied are wollastonite, barium sulphate and talc. These materials have different shapes, sizes and surface chemistry and undergo different types of interaction with the matrix. The vibration damping characteristics were further varied by the use of a crosslinking agent. Data presented on the rheological characteristics indicate the strength of the filler-polyol interactions. Dielectric relaxation and dynamic mechanical thermal analysis demonstrate the way in which changes in the type of filler, concentration and amount of crosslinker lead to changes in the location and breadth of the energy dissipation process in these elastomers. The vibration damping characteristics of a selected material are presented to demonstrate the potential of these materials

Digital twin-enabled human-robot collaborative teaming towards sustainable and healthy built environments

Development of sustainable and healthy built environments (SHBE) is highly advocated to achieve collective societal good. Part of the pathway to SHBE is the engagement of robots to manage the ever-complex facilities for tasks such as inspection and disinfection. However, despite the increasing advancements of robot intelligence, it is still “mission impossible” for robots to independently undertake such open-ended problems as facility management, calling for a need to “team up” the robots with humans. Leveraging digital twin's ability to capture real-time data and inform decision-making via dynamic simulation, this study aims to develop a human-robot teaming framework for facility management to achieve sustainability and healthiness in the built environments. A digital twin-enabled prototype system is developed based on the framework. Case studies showed that the framework can safely and efficiently incorporate robotics into facility management tasks (e.g., patrolling, inspection, and cleaning) by allowing humans to plan, oversee, manage, and cooperate with the robot via the digital twin's bi-directional mechanism. The study lays out a high-level framework, under which purposeful efforts can be made to unlock digital twin's full potential in collaborating humans and robots in facility management towards SHBE