Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators

We study the bulk-edge correspondence in topological insulators by taking Fu-Kane spin pumping model as an example. We show that the Kane-Mele invariant in this model is Z2 invariant modulo the spectral flow of a single-parameter family of 1+1-dimensional Dirac operators with a global boundary condition induced by the Kramers degeneracy of the system. This spectral flow is defined as an integer which counts the difference between the number of eigenvalues of the Dirac operator family that flow from negative to non-negative and the number of eigenvalues that flow from non-negative to negative. Since the bulk states of the insulator are completely gapped and the ground state is assumed being no more degenerate except the Kramers, they do not contribute to the spectral flow and only edge states contribute to. The parity of the number of the Kramers pairs of gapless edge states is exactly the same as that of the spectral flow. This reveals the origin of the edge-bulk correspondence, i.e., why the edge states can be used to characterize the topological insulators. Furthermore, the spectral flow is related to the reduced eta-invariant and thus counts both the discrete ground state degeneracy and the continuous gapless excitations, which distinguishes the topological insulator from the conventional band insulator even if the edge states open a gap due to a strong interaction between edge modes. We emphasize that these results are also valid even for a weak disordered and/or weak interacting system. The higher spectral flow to categorize the higher-dimensional topological insulators are expected.Comment: 9 page, accepted for publication in Nucl Phys

Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene

The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally FQHE has been observed in high mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.Comment: 17 pages, 13 figure

Influence of Intrinsic Electronic Properties on Light Transmission through Subwavelength Holes on Gold and MgB2 Thin Films

We show how intrinsic material properties modify light transmission through subwavelength hole arrays on thin metallic films in the THz regime. We compare the temperature-dependent transmittance of Au films and MgB$_{2}$ films. The experimental data is consistent with analytical calculations, and is attributed to the temperature change of the conductivity of both films. The transmission versus conductivity is interpreted within the open resonator model when taking the skin depth into consideration. We also show that the efficiency of this temperature control depends on the ratio of the transmission peak frequency to the superconducting energy gap in MgB$_{2}$ films.Comment: 6 pages, 6 figure

Experimental demonstration of the topological surface states protected by the time-reversal symmetry

We report direct imaging of standing waves of the nontrivial surface states of topological insulator Bi$_2$Te$_3$ by using a low temperature scanning tunneling microscope. The interference fringes are caused by the scattering of the topological states off Ag impurities and step edges on the Bi$_2$Te$_3$(111) surface. By studying the voltage-dependent standing wave patterns, we determine the energy dispersion $E(k)$, which confirms the Dirac cone structure of the topological states. We further show that, very different from the conventional surface states, the backscattering of the topological states by nonmagnetic impurities is completely suppressed. The absence of backscattering is a spectacular manifestation of the time-reversal symmetry, which offers a direct proof of the topological nature of the surface states

Sensing Home: A Cost-Effective Design for Smart Home via Heterogeneous Wireless Networks

The aging population has inspired the marketing of advanced real time devices for home health care, more and more wearable devices and mobile applications, which have emerged in this field. However, to properly collect behavior information, accurately recognize human activities, and deploy the whole system in a real living environment is a challenging task. In this paper, we propose a feasible wireless-based solution to deploy a data collection scheme, activity recognition model, feedback control and mobile integration via heterogeneous networks. We compared and found a suitable algorithm that can be run on cost-efficient embedded devices. Specifically, we use the Super Set Transformation method to map the raw data into a sparse binary matrix. Furthermore, designed front-end devices of low power consumption gather the living data of the habitant via ZigBee to reduce the burden of wiring work. Finally, we evaluated our approach and show it can achieve a theoretical time-slice accuracy of 98%. The mapping solution we propose is compatible with more wearable devices and mobile apps

The Effect of the Displacement Amplitude on the Fretting Wear of GCr15 Steel with a TiC Coating

In the present paper, the effect of mechanical ball milling time on the fretting wear of GCr15 steel balls at different displacement amplitudes is investigated. TiC powder coating was fabricated on the surface of GCr15 steel balls using various process times, and the fretting wear tests were conducted on an AISI 52100 steel disk with the applied force of 80 N. Additionally, various displacement amplitudes (10 μm, 20 μm, and 60 μm) were selected. Specimen attributes and wear scars were characterized using an inverted metallographic microscope, a microhardness tester, an X-ray diffractometry analyzer, a white light interferometer, and a scanning electron microscope. The results showed that thick and continuous coatings could be obtained at the milling time of 18 h. The specimens processed for a longer milling time demonstrated better fretting wear resistance, which we attribute to higher microhardness of the surface layer. The coefficient of friction and wear volume of specimens at each different displacement amplitude significantly decreased with increasing milling time. As the displacement amplitude increased, the three fretting states were: partial slip coordinated by elastic deformation; partial slip state coordinated by plastic deformation; and gross slip condition. Our observations indicate that mechanical ball milling could be an efficient approach to improve the fretting wear resistance of GCr15 steel balls

Improvement of the high-temperature oxidation resistance of 254SMo using ultrasonic strengthening grinding

This paper used ultrasonic strengthening grinding (USGP) to process 254SMo welded joints. The mechanical properties of processed and unmachined samples of welded joints, including grain size, dislocation, microhardness, residual stress, and high-temperature oxidation resistance at 900 °C, were investigated. The results indicate that the grains of the processed samples exhibit significant refinement and a high dislocation density and that the maximum microhardness and residual compressive stress are 392.5 HV0.3 and −633.44 MPa, respectively. In addition, the processed sample exhibits excellent oxidation at high temperatures. At 900 °C, the mass gain of the USGP-processed sample is reduced by 47.5 % compared to its mass gain prior to processing. These results highlight the potential of this method in improving the high-temperature resistance of various mechanical components, particularly those made from special materials

Micromorphology, Microstructure, and Wear Behavior of AISI 1045 Steels Irregular Texture Fabricated by Ultrasonic Strengthening Grinding Process

In this study, the tribological properties of three AISI 1045 steel samples were investigated. Two samples were treated with ultrasonic shot peening (USP) and ultrasonic strengthening grinding process (USGP), respectively, while the other one was only treated with a polishing process. Sample properties, such as surface morphology, roughness, microhardness, elastic modulus, frictional coefficient, and phase structures were analyzed. Results show that the sample treated with USGP had the best tribological properties. It realized the highest surface roughness, microhardness, and elastic modulus. Compared with a polished sample, the roughness of the sample treated with USGP increased by 157%, and the microhardness and elastic modulus improved by 32.8% and 21.3%, respectively. Additionally, USGP provided an average frictional coefficient of 0.4, decreasing approximately 45% compared to polishing. The possible mechanisms of USGP surface texturing were discussed. The findings denote that USGP could be an efficient approach to improve the fatigue life of some mechanical components