Topological structure of Gauss-Bonnet-Chern theorem and -branes

By making use of the φ-mapping topological current theory, this paper shows that the Gauss-Bonnet-Chern density (the Euler-Poincaré characteristic χ(M) density) can be expressed in terms of a smooth vector field φ and take the form of δ(φ), which means that only the zeros of φ contribute to χ(M). This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of -branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi -branes.     

Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn4N epitaxial films with perpendicular magnetic anisotropy

Epitaxial Mn$_{4}$N films with different thicknesses were fabricated by facing-target reactive sputtering and their anomalous Hall effect (AHE) is investigated systematically. The Hall resistivity shows a reversed magnetic hysteresis loop with the magnetic field. The magnitude of the anomalous Hall resistivity sharply decreases with decreasing temperature from 300 K to 150 K. The AHE scaling law in Mn$_{4}$N films is influenced by the temperature-dependent magnetization, carrier concentration and interfacial scattering. Different scaling laws are used to distinguish the various contributions of AHE mechanisms. The scaling exponent $\gamma > 2$ for the conventional scaling in Mn$_{4}$N films could be attributed to the residual resistivity $\rho_{xx0}$. The longitudinal conductivity $\sigma_{xx}$ falls into the dirty regime. The scaling of $\rho_{\rm AH}=\alpha \rho_{xx0} +b\rho_{xx}^{n}$ is used to separate out the temperature-independent $\rho_{xx0}$ from extrinsic contribution. Moreover, the relationship between $\rho_{\rm AH}$ and $\rho_{xx}$ is fitted by the proper scaling to clarify the contributions from extrinsic and intrinsic mechanisms of AHE, which demonstrates that the dominant mechanism of AHE in the Mn$_{4}$N films can be ascribed to the competition between skew scattering, side jump and the intrinsic mechanisms.     

Enhancement of spin-orbit torque efficiency by tailoring interfacial spin-orbit coupling in Pt-based magnetic multilayers

We study inserting Co layer thickness-dependent spin transport and spin-orbit torques (SOTs) in the Pt/Co/Py trilayers by spin-torque ferromagnetic resonance. The interfacial perpendicular magnetic anisotropy (IPMA) energy density ($K_{\rm s}= 2.7 $ erg/cm$^{2}$, 1 erg = 10$^{-7}$ J), which is dominated by interfacial spin-orbit coupling (ISOC) in the Pt/Co interface, total effective spin-mixing conductance $(G_{\mathrm{eff,tot}}^{\mathrm{\uparrow \downarrow }}=\mathrm{0.42\times }{10}^{15} \mathrm{\Omega }^{-1}\cdot\mathrm{m}^{-2}$) and two-magnon scattering ($\beta_{\mathrm{TMS}}= 0.46 {\mathrm{nm}}^{2}$) are first characterized, and the damping-like torque ($\xi_{\mathrm{DL}}= 0.103$) and field-like torque ($\xi _{\mathrm{FL}}=-0.017$) efficiencies are also calculated quantitatively by varying the thickness of the inserting Co layer. The significant enhancement of $\xi_{\mathrm{DL}}$ and $\xi_{\mathrm{FL}}$ in Pt/Co/Py than Pt/Py bilayer system originates from the interfacial Rashba-Edelstein effect due to the strong ISOC between Co-3d and Pt-5d orbitals at the Pt/Co interface. Additionally, we find a considerable out-of-plane spin polarization SOT, which is ascribed to the spin anomalous Hall effect and possible spin precession effect due to IPMA-induced perpendicular magnetization at the Pt/Co interface. Our results demonstrate that the ISOC of the Pt/Co interface plays a vital role in spin transport and SOTs-generation. Our finds offer an alternative approach to improve the conventional SOTs efficiencies and generate unconventional SOTs with out-of-plane spin polarization to develop low power Pt-based spintronic via tailoring the Pt/FM interface.     

Optical study on topological superconductor candidate Sr-doped Bi2Se3

Utilizing infrared spectroscopy, we study the charge dynamics of the topological superconductor candidate Sr$_x$Bi$_2$Se$_3$. The frequency-dependent reflectivity $R(\omega$) demonstrates metallic feature and the scattering rate of the free carriers decreases with temperature decreasing. The plasma edge shows a slight blue shift upon cooling, similar to the behavior of Cu$_x$Bi$_2$Se$_3$. As the carrier concentration $n$ obtained by Hall resistivity increases slightly with the decreasing temperature, the effective mass is proved to increase as well, which is in contrast with that of Cu$_x$Bi$_2$Se$_3$.We also perform the ultrafast pump-probe study on the Sr$_{0.2}$Bi$_2$Se$_3$ compounds. Resembling its parent compound Bi$_2$Se$_3$, three distinct relaxation processes are found to contribute to the transient reflectivity. However, the deduced relaxation times are quite different. In addition, the electron-optical-phonon coupling constant is identified to be $\lambda = 0.88$.     

Effect of substrate temperature on the growth and properties of boron-doped microcrystalline silicon films

Highly conductive boron-doped hydrogenated microcrystalline silicon (\mu c-Si:H) films are prepared by very high frequency plasma enhanced chemical vapour deposition (VHF PECVD) at the substrate temperatures $T_{\rm S})$ ranging from 90$^\circ$C to 270$^\circ$C. The effects of $T_{\rm S}$ on the growth and properties of the films are investigated. Results indicate that the growth rate, the electrical (dark conductivity, carrier concentration and Hall mobility) and structural (crystallinity and grain size) properties are all strongly dependent on $T_{\rm S}$. As $T_{\rm S}$ increases, it is observed that 1) the growth rate initially increases and then arrives at a maximum value of 13.3 nm/min at $T_{\rm S}$=210$^\circ$C, 2) the crystalline volume fraction ($X_{\rm c})$ and the grain size increase initially, then reach their maximum values at $T_{\rm S}$=140$^\circ$C, and finally decrease, 3) the dark conductivity ($\sigma _{\rm d})$, carrier concentration and Hall mobility have a similar dependence on $T_{\rm S}$ and arrive at their maximum values at $T_{\rm S}$=190$^\circ$C. In addition, it is also observed that at a lower substrate temperature $T_{\rm S}$, a higher dopant concentration is required in order to obtain a maximum $\sigma _{\rm d}$.     

Self-assembled nanocrystalline CdSe thin films

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidots located on the sites of the square lattice. In such a system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.     

Topology of a parity-time symmetric non-Hermitian rhombic lattice

We investigate the topological properties of a trimerized parity–time(PT)symmetric non-Hermitian rhombic lattice.Although the system is PT-symmetric,the topology is not inherited from the Hermitian lattice;in contrast,the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices.The bulk–boundary correspondence is valid and the Bloch bulk captures the band topology.Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach.In addition,the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice.Our findings reveal the topological properties of the??PT-symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases.     

Thermal and mechanical characterizations of asubstrate-free focal plane array

We propose a substrate-free focal plane array (FPA) in this paper. The solid substrate is completely removed, and the microcantilevers extend from a supporting frame. Using finite element analysis, the thermal and mechanical characterizations of the substrate-free FPA are presented. Because of the large decrease in thermal conductance, the supporting frame is temperature dependent, which brings out a unique feature: the lower the thermal conductance of the supporting frame is, the higher the energy conversion efficiency in the substrate-free FPA will be. The results from the finite element analyses are consistent with our measurements: two types of substrate-free FPAs with pixel sizes of 200× 200 and 60× 60~μ m² are implemented in the proposed infrared detector. The noise equivalent temperature difference (NETD) values are experimentally measured to be 520 and 300~mK respectively. Further refinements are considered in various aspects, and the substrate-free FPA with a pixel size of 30× 30~μ m² has a potential of achieving an NETD value of 10~mK.     

Nondissipative spin Hall effect via quantized edge transport

The spin Hall effect in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings is studied numerically. Integer quantized spin Hall conductance is obtained at the zero Rashba coupling limit when electron Fermi energy lies in the energy gap created by the intrinsic spin-orbit coupling, in agreement with recent theoretical prediction. While nonzero Rashba coupling destroys electron spin conservation, the spin Hall conductance is found to remain near the quantized value, being insensitive to disorder scattering, until the energy gap collapses with increasing the Rashba coupling. We further show that the charge transport through counterpropagating spin-polarized edge channels is well quantized, which is associated with a topological invariant of the system.     

A gauge theory for two-band model of Chern insulators and induced topological defects

In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_xy=e²/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.     

Quantum Hall effect in kagomé lattices under staggered magnetic field

The interplay of staggered magnetic field (SMF) and uniform magnetic field (UMF) on the quantum Hall effect (QHE) in kagomé lattices is investigated in the weak UMF limit. The topological band gaps coming from SMF are robust against UMF although the extended bands split into a series of Landau levels. With SMF applied, in the unconventional QHE region, one plateau of Hall conductance becomes wider and the others are compressed. Meanwhile, one of the two series of integer Hall plateaus splits and the resulting two series of Hall plateaus still exhibit the integer behavior. The Hall conductance varies with SMF step by step with the step height being e(2)/h or 2e(2)/h according to the QHE being conventional or unconventional. In the transitional regions, redistribution of Chern numbers happens even in the weak UMF limit.     

Transmission of electron through an Aharonov－Bohm interferometer with a quantum dot in Coulomb blockade regime

We calculate conductance of an Aharonov－Bohm (AB) interferometer for which a single-level quantum dot in the Coulomb blockade regime is embedded in one of its arms. Using the Schr?dinger equations and taking into account the Coulomb interaction on the dot, we calculate conductance G as a function of flux φ threaded through the ring and as a function of gate voltage V applied to the dot. It is found that the AB oscillations of G(φ) depend on the particle occupation on the dot, controlled by V. If the system is closed, there is no loss of particles, G(φ) is periodic and G(φ)=G(-φ), satisfying the Onsager relation. In this case G(φ) can reach its maximum value, 2e^2/h, at the resonance. When the system is open, one has G(φ)≠G(-φ), G(φ) yields a phase shift which depends on the loss rate of electrons in this open system.     

Quantum spin Hall effect

The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e/4pi). The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.     

Phase diagram for quantum hall bilayers at nu=1

We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at a total filling factor nu=1, based on exact numerical calculations of the topological Chern number matrix and the (interlayer) superfluid density. We find three phases: a quantized Hall state with pseudospin superfluidity, a quantized Hall state with pseudospin "gauge-glass" order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau, and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.     

Topology of a <Superscript>3</Superscript>He-A Film on a Corrugated Graphene Substrate

A thin film of superfluid ³He on a corrugated graphene substrate represents topological matter with a smooth disorder. It is possible that the atomically smooth disorder produced by the corrugated graphene does not destroy the superfluidity even in a very thin film, where the system can be considered as quasi two-dimensional topological material. This will allow us to study the effect of disorder on different classes of the 2 + 1 topological materials: the chiral ³He-A with intrinsic quantum Hall effect and the time reversal invariant planar phase with intrinsic spin quantum Hall effect. In the limit of smooth disorder, the system can be considered as a Chern mosaic, i.e., a collection of domains with different values of Chern numbers. In this limit, the quantization of the Hall conductance is determined by the percolated domain, while the density of the fermionic states is determined by the edge modes on the boundaries of the finite domains. This system can be useful for the general consideration of disorder in the topological matter.     

Bloch electrons in a magnetic field: Topology of quantum states and transport

Quantum states and Hall conductances of electrons in n-type heterojunctions and holes in p-type heterojunctions in a field of a lateral superlattice and a perpendicular magnetic field were studied. It is shown that the energy spectrum of magnetic subbands in a periodic potential without inversion center is not symmetric about the reversal of the quasi-momentum sign. The properties of wave functions and the related topological invariants determining the Hall conductance were examined. The method of calculating the magnetic Bloch states of holes was developed on the basis of the Luttinger Hamiltonian, allowing the spin and spin-orbit interactions to be taken into account in this problem. The Hall conductance quantization law was determined for 2D holes in a periodic superlattice potential.     

The invisible Majorana bound state at the helical edge

The presence of a Majorana bound state in condensed matter systems is often associated to a zero bias peak in conductance measurements. Here, we analyze a system were this paradigm is violated. A Majorana bound state is always present at the interface between a quantum spin Hall system that is magnetically gapped and a quantum spin Hall system gapped by proximity induced s-wave superconductivity. However, the linear conductance could be either zero or non-zero and quantized depending on the energy and length scales of the barriers. The transition between the two values is reminiscent of the topological phase transition in proximitized spin–orbit coupled quantum wires in the presence of an applied magnetic field. We interpret the behavior of the conductance in terms of scattering states at both zero and non-zero energy.     

二维三角格点系统中的拓扑陈数

利用紧束缚模型对二维三角周期格点中各能带的陈数分布进行研究.通过严格对角化方法得到体系能量本征值和对应的本征态，再利用Kubo公式计算出量子化的霍尔电导、态密度及各扩展态对应的陈数.在傅里叶变换下将哈密顿量转换到k空间从而得到体系的能谱分布.研究表明：次近邻格点之间的跳跃积分t'的不同取值影响体系各能带对应的陈数分布，计算得到当t'=1/2时体系三个能带从低到高对应的陈数分布为{-4，5，-1}，t'=-1/2时其对应陈数分布变化为{2，-4，2}，而t'=±1/4时对应的陈数分布都为{2，-1，-1}.同时发现：能谱帯隙的宽度和对应霍尔平台的宽度一致，并且k空间的能带越平坦，其对应的在霍尔电导跳跃处的态密度峰就越高越尖锐，而该处霍尔电导跳跃就越陡峭.     

Manipulation of intrinsic quantum anomalous Hall effect in two-dimensional MoYN2CSCl MXene

Quantum anomalous Hall effect (QAHE) is an innovative topological spintronic phenomenon with dissipationless chiral edge states and attracts rapidly increasing attention. However, it has only been observed in few materials in experiments. Here, according to the first-principles calculations, we report that the MXene MoYN$_{2}$CSCl shows a topologically nontrivial band gap of 37.3~meV, possessing QAHE with a Chern number of $C = 1$, which is induced by band inversion between $ {\rm d}_{xz}$ and ${\rm d}_{yz}$ orbitals. Also, the topological phase transition for the MoYN$_{2}$CSCl can be realized via strain or by turning the magnetization direction. Remarkably, MoYN$_{2}$CSCl shows the nodal-line semimetal state dependent on the electron correlation $U$. Our findings add an experimentally accessible and tunable member to the QAHE family, which stands a chance of enriching the applications in spintronics.     

Saturating the unitarity bound in AdS/CFT(AdS)

Journal of High Energy Physics - Generalized Bogomolny equations are encountered in the localization of the topological $ \mathcal{N} = 4\;{\text{SYM}} $ theory. The boundary conditions for...