Trivial Regions Research Articles

Band structure of the one-dimensional spin–orbit-coupled Su–Schrieffer–Heeger lattice with [formula omitted]-symmetric onsite imaginary potentials

Energy band structures of one-dimensional non-Hermitian spin–orbit-coupled Su–Schrieffer–Heeger (SSH) model are theoretically investigated, by introducing imaginary potentials with gain and loss effects. It is found that the imaginary potentials can promote the occurrence of PT-symmetry breaking. In the topologically-nontrivial regions, the different imaginary parts of the edge-state energies leads to the different localization degrees of such states. Moreover, gapless phase regions arise between the topologically-nontrivial and -trivial regions, in which edge states are allowed to survive. Therefore, these results are helpful to understand the band-structural and topological properties of PT-symmetric non-Hermitian systems.

Topology optimization of a second-order phononic topological insulator with dual-band corner states

Second-order phononic topological insulators (SPTIs) with topologically protected corner states offer unique routes for the realization of steering elastic waves in lower-dimension regime with robustness. However, prevailing SPTIs only host corner states within a single bandgap, restricting applications of SPTIs in multiband domain. Here, we design four new types of SPTIs with the customized dual-bandgap which supports dual-band corner states. The dual-bandgap is created by simultaneously maximizing the minimum imaginary parts of wave vectors at two desired frequencies via topology optimization. Topological trivial and nontrivial unit cells (UCs), sharing the dual-bandgap, are configured by selecting UCs from the same optimized phononic crystals (PCs) in different ways. The dual-band topological corner states are observed at the corner between the trivial and nontrivial regions. The developed four SPTIs with customized dual-band operating frequencies pave the way for multiband communications and manipulation of elastic waves with enhanced robustness.

Real-potential-driven anti--symmetry breaking in non-Hermitian Su–Schrieffer–Heeger model

Non-Hermitian Hamiltonians with anti- symmetry show distinct discrepancies compared to -symmetric systems. Here we investigate the non-Hermitian Su–Schrieffer–Heeger (SSH) model and reveal the interplay between anti- symmetry and different topological phases, in which the anti- symmetry is triggered by introducing real chemical potential and imaginary nearest-neighbor hopping. Three types of anti--symmetric SSH models with different on-site configurations are investigated, and the effect of each on-site configuration on the energy spectrum of system is analyzed and discussed. We find that the type of on-site configuration affects the energy spectrum of the same topological region significantly and each on-site configuration has distinguishable impacts on the energy spectra of different topological regions. Moreover, the spontaneous anti--symmetry-breaking transitions undergone in both of the topologically trivial and nontrivial regions are also clarified. Furthermore, we address the corresponding eigenstates of some specific eigenvalues and some interesting localized phenomena are observed. Our results enrich the study of non-Hermitian topological phases and broaden the understanding of anti--symmetric systems.

Experimental demonstration of a reconfigurable acoustic second-order topological insulator using condensed soda cans array

Traditional topological insulators support the topologically protected boundary states that are one dimension lower than the system itself. Recently, higher-order topological insulators have received increasing attention in the field of acoustic wave manipulation due to their unique bulk-boundary correspondence principle, hosting both gapped edge states and in-gap corner states simultaneously. However, for most of the topological acoustic systems, the lack of reconfigurability and the inevitable outer trivial regions with considerable thickness restrict the potential applications of acoustic topological insulators. Here, we experimentally demonstrate a reconfigurable condensed acoustic second-order topological insulator in free space by using subwavelength soda cans whose side length is significantly reduced to 1.89 times of the corresponding wavelength. The topological nontrivial phase is introduced through tunably modulating the interval between cans. Without the typically required outer trivial regions, we observe the topological corner states at the corner of the finite structures in both simulations and experiments. Furthermore, the robustness against the defects induced by dislocations and deformations is discussed. We foresee that the proposal may facilitate the application potentials of topological acoustics in low-frequency sound manipulations.

Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these states in the near- and far-field using a semi-analytical model. We provide the conditions under which directionality was observed and show that it is source position dependent. By probing with circularly-polarised magnetic dipoles out of the plane, we first characterise modes along the interface in terms of the enhancement of source emissions due to the metasurface. We then excite from the far-field with non-zero orbital angular momentum beams. The position-dependent directionality holds true for all classical wave systems with a breathing honeycomb lattice. Our results show that a metasurface in combination with a chiral two-dimensional material, could be used to guide light effectively on the nanoscale.

Topological Anderson insulators in two-dimensional non-Hermitian disordered systems

The interplay among topology, disorder, and non-Hermiticity can induce some exotic topological and localization phenomena. Here we investigate this interplay in a two-dimensional non-Hermitian disordered Chern-insulator model with two typical kinds of non-Hermiticities, the nonreciprocal hopping and on-site gain-and-loss effects. The topological phase diagrams are obtained by numerically calculating two topological invariants in the real space, which are the disorder-averaged open-bulk Chern number and the generalized Bott index, respectively. We reveal that the nonreciprocal hopping (the gain-and-loss effect) can enlarge (reduce) the topological regions and the topological Anderson insulators induced by disorders can exist under both kinds of non-Hermiticities. Furthermore, we study the localization properties of the system in the topologically nontrivial and trivial regions by using the inverse participation ratio and the expansion of single particle density distribution.

Imaging quantum spin Hall edges in monolayer WTe2.

A two-dimensional (2D) topological insulator exhibits the quantum spin Hall (QSH) effect, in which topologically protected conducting channels exist at the sample edges. Experimental signatures of the QSH effect have recently been reported in an atomically thin material, monolayer WTe2. Here, we directly image the local conductivity of monolayer WTe2 using microwave impedance microscopy, establishing beyond doubt that conduction is indeed strongly localized to the physical edges at temperatures up to 77 K and above. The edge conductivity shows no gap as a function of gate voltage, and is suppressed by magnetic field as expected. We observe additional conducting features which can be explained by edge states following boundaries between topologically trivial and nontrivial regions. These observations will be critical for interpreting and improving the properties of devices incorporating WTe2. Meanwhile, they reveal the robustness of the QSH channels and the potential to engineer them in the monolayer material platform.

Valley selecting current partition at zero-line mode of quantum anomalous Hall topologies

Topologically protected zero-line modes appear at the interface between two regions of the monolayer graphene in quantum anomalous Hall phase with different Chern number. In the presence of staggered sublattice potential, the band gaps of the two valleys become different, and the phase diagram defined by the Chern number has an additional regime of topologically trivial phase. The interface between the topologically trivial and non-trivial regions hosts zero-line mode in only one valley. By tuning the exchange field, three types of interface that host zero-line modes in selected valley(s) are formed. The nano-devices consisted of Y-shape junctions of the three types of interface exhibit the functions of valley splitting, merging or filtering for the incident currents.

The nontrivial topological phases of indirect excitons in semiconductor coupled quantum wells

Motivated by the experimental realization of two-dimensional electrostatic lattices for indirect excitons using patterned interdigitated electrodes [M. Remeika et al., Appl. Phys. Lett. 100, 061103 (2012)] and the observation of spin currents governed by spin-orbit interaction and controlled by an applied magnetic field in a coherent gas of indirect excitons [A. A. High et al., Phys. Rev. Lett. 110, 246403 (2013)], we investigate in details the nontrivial topological phases of indirect excitons in a one-dimensional dimerized lattice, known as Su-Schrieffer-Heeger model. The studies focus on the interplay between the spin-orbit coupling of electrons and holes and Zeeman field. We find that a uniform (staggered) perpendicular Zeeman field can turn trivial regions into nontrivial through a topological phase transition. In the nontrivial region of the band, a pair of zero-energy boundary states can survive due to the protection of time-reversal, particle-hole, chiral, and inversion symmetries. The topological class of the system is BDI and can be characterized by Z index. The winding number is used to distinguish the different topological regions of a band. We justify how the topological edge states can be realized by applying a Zeeman field in x -direction to balance the splitting of bright state and dark state, and discuss the exciton polarization degree of the edge states.

Electrically controlled crossover between 2π and 4π Josephson effects through topologically confined channels in silicene

We propose a tunable topological Josephson junction in silicene where electrostatic gates could switch between a trivial and a topological junction. These aspects are a consequence of a tunable phase transition of the topologically confined valley-chiral states from a spin-degenerate to a spin-helical regime. We calculate the Andreev bound states in such a junction analytically using a low-energy approximation to the tight-binding model of silicene in proximity to s-wave superconductors as well as numerically in the short- and long-junction regime and in the presence of intervalley scattering. Combining topologically trivial and non-trivial regions, we show how intervalley scattering can be effectively switched on and off within the Josephson junction. This constitutes a topological Josephson junction with an electrically tunable quasiparticle poisoning source.

Sliding and Dry Friction: Prandtl-Tomlinson Athermal Model Revisited

The microscopic origin of friction has been the goal of several theoretical studies in the last decades. Depending on the investigated systems or models, on the simulation techniques or conditions, different and somewhat contradictory results have been found, even when using the same model. In this contribution, we address this apparent paradox in a well-known case, the Prandtl-Tomlinson model at zero temperature, studying the force-velocity relation for a wide range of velocities not previously presented. Including much more data density for the non trivial regions, we are able to shed light on this problem and at the same time, provide new insight in the use of the paradigmatic Tomlinson model for the secular problem of friction laws.

A structure-aware axis-aligned grid deformation approach for robust image retargeting

Content-based image retargeting is a technique that resizes an input image to a given target resolution while minimizing distortions of important objects caused by aspect ratio variations. Conventional approaches have shared a similar methodology which aims to preserve salient regions as much as possible while allowing distortions of less important regions. Those methods have shown satisfactory results for input images whose objects are distinct and backgrounds are monotonous. However, their performance is not always guaranteed for images containing structural components such as straight lines, which are prone to be distorted after resizing and sensitive to human visual perception. In this paper, we propose a structure-aware axis-aligned grid deformation approach for robust image retargeting. Based on axis-aligned grid, our method finds the optimal grid for target image by quadratic optimization represented by two objective functions. The first one is the As-similar-as-possible (ASAP) energy function, which aims to preserve important regions while allowing distortions of trivial regions. The second one is the Adaptive Laplacian regularization (ALR) energy function, which aims to relieve structural distortions. Those two energy functions are combined into single quadratic optimization model ensuring the global convexity and solved by a quadratic programming solver for finding the optimal grid. Experimental results show that our method is robust to structural distortions while achieving the basic purpose of content-based image retargeting. For objective comparisons with other methods, we have provided objective evaluation scores by using a recent state-of-the-art image retargeting quality assessment scheme.

Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice

We study theoretically the interplay effect of Zeeman field and modulated spin-orbit coupling on topological properties of a one-dimensional dimerized lattice, known as Su-Schrieffer-Heeger model. We find that in the weak (strong) modulated spin-orbit coupling regime, trivial regions or nontrivial ones with two pairs of zero-energy states can be turned into nontrivial regions by applying a uniform (staggered) perpendicular Zeeman field through a topological phase transition. Furthermore, the resulting nontrivial phase hosting a pair of zero-energy boundary states can survive within a certain range of the perpendicular Zeeman field magnitude. Due to the effective time-reversal, particle-hole, chiral, and inversion symmetries, in the presence of either uniform or staggered perpendicular Zeeman field, the topological class of the system is BDI which can be characterized by $\mathbbm{Z}$ index. We also examine the robustness of the nontrivial phase by breaking the underlying symmetries giving rise that inversion symmetry plays an important role.

Topological phase boundary in a generalized Kitaev model**Project supported by the National Basic Research Program of China (Grant No. 2012CB921704).

We study the effects of the next-nearest-neighbor hopping and nearest-neighbor interactions on topological phases in a one-dimensional generalized Kitaev model. In the noninteracting case, we define a topological number and calculate exactly the phase diagram of the system. With addition of the next-nearest-neighbor hopping, the change of phase boundary between the topological and trivial regions can be described by an effective shift of the chemical potential. In the interacting case, we obtain the entanglement spectrum, the degeneracies of which correspond to the topological edge modes, by using the infinite time-evolving block decimation method. The results show that the interactions change the phase boundary as adding an effective chemical potential which can be explained by the change of the average number of particles.

Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons.

Thermodynamic properties of chiral spin liquids are investigated for a variant of the Kitaev model defined on a decorated honeycomb lattice. Using the quantum MonteCarlo simulation, we find that the model exhibits a finite-temperature phase transition associated with the time reversal symmetry breaking, in both topologically trivial and nontrivial regions. Numerical results for the Chern number and the thermal Hall conductivity indicate that the phase transition changes from a continuous to a discontinuous transition as we vary the coupling constants to reach the non-Abelian phase coming from the Abelian phase of the model. In addition, we find as a diagnostic of the chiral spin liquids, successive crossovers with multistage entropy release above the critical temperature, which indicates that the hierarchical fractionalization of a quantum spin occurs differently between the two regions.

Topological pumping in class-Dsuperconducting wires

We study adiabatic pumping at a normal metal/class-$D$ superconductor hybrid interface when superconductivity is induced through the proximity effect in a spin-orbit coupled nanowire in the presence of a tilted Zeeman field. When the induced order parameter in the nanowire is nonuniform, the phase diagram has isolated trivial regions surrounded by topological ones. We show that in this case the pumped charge is quantized in units of the elementary charge $e$ and has a topological nature.

Multiscale roughness measure for color image segmentation

Color image segmentation is always an important technique in image processing system. Highly precise segmentation with low computation complexity can be achieved through roughness measurement which approximate the color histogram based on rough set theory. However, due to the imprecise description of neighborhood similarity, the existing roughness measure tends to over-focus on the trivial homogeneous regions but is not accurate enough to measure the color homogeneity. This paper aims to construct a multiscale roughness measure through simulating the human vision. We apply the theories of linear scale-space and rough sets to generate the hierarchical roughness of color distribution under multiple scales. This multiscale roughness can tolerate the disturbance of trivial regions and also can provide the multilevel homogeneity representation in vision, which therefore produces precise and intuitive segmentation results. Furthermore, we propose roughness entropy for scale selection. The optimal scale for segmentation is decided by the entropy variation. The proposed method shows the encouraging performance in the experiments based on Berkeley segmentation database.

Majorana Fermions in Equilibrium and in Driven Cold-Atom Quantum Wires

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.

Development of morphological technique for segmentation of anatomical objects in abdominal MRI

In this paper, a morphological technique for the segmentation of abdominal organs in magnetic resonance imaging (MRI) images is proposed based on watershed segmentation. New morphological based preprocessing and post-processing techniques are developed to reduce oversegmentation by means of removing and merging spurious segments. The preprocessing aims at removing trivial regions as well as background noise by combining thresholding, morphological smoothing, Gaussian smoothing and morphological edge detection. To obtain a more concise region representation, the watershed segmented image is post-processed, where a region adjacency list is built for the region merging process that produces the final segments. To control the merging process, a similarity function is defined, whence the most similar neighbouring regions are merged. The proposed technique produces effective and significant results in successfully segmenting various anatomical objects in axial MRI images of the abdomen, as it is shown in this paper.

Vegetation field spectrum denoising via lifting wavelet transform

Field spectrum pretreatment experiments were carried out, and denoising numerical experiment via lifting wavelet transform (LWT) was designed, and several famous test signals including blocks, bumps, heavy sine and doppler were processed via LWT in these experiment. And the field spectrum was processed via LWT. Experiments proved that S NRG-to-S NRN curves have similar feature and they all have a peak. And SNRG of almost all employed wavelets have higher value with S NRN between 0 and 20 dB. When signal is at high S NR, the SNRG is very little, and the M SED of denoised signal became little by little. LWT is more suite to denoise the low S NR or heavy noise contaminated signals. Bior4.4 have wider S NRN interval for denoising comparing with other five wavelets, including haar, db6, sym6, bior2.2 and bior3.3. Original field spectrum is processed by 3 stage liftings based on bior4.4 to denoise the trivial noise-contaminated regions. On processing the water band signal, logarithm transform is firstly taken. And then the spectrum is denoised via LWT based on bior4.4. The results show that an excellent denoised spectrum can be get, especially between 350 nm and 1 800 nm, and between 1 960 nm to 2 500 nm. While there is still a bump around 1 900 nm, this maybe due to the spectrum machine’s limited precision.