arXiv subjects

Tao Hou

Publications and source records attributed to Tao Hou.

At least 37 records · Page 2Linked to original sources

arXiv2023

Topological chiral kagome lattice

Chirality, a fundamental structural property of crystals, can induce many unique topological quantum phenomena. In kagome lattice, unconventional transports have been reported under tantalizing chiral charge order. Here, we show how by deforming the kagome lattice to obtain a three-dimensional (3D) chiral kagome lattice in which the key band features of the non-chiral 2D kagome lattice - flat energy bands, van Hove singularities (VHSs), and degeneracies - remain robust in both the $k_z$ = 0 and $π$ planes in momentum space. Given the handedness of our kagome lattice, degenerate momentum points possess quantized Chern numbers, ushering in the realization of Weyl fermions. Our 3D chiral kagome lattice surprisingly exhibits 1D behavior on its surface, where topological surface Fermi arc states connecting Weyl fermions are dispersive in one momentum direction and flat in the other direction. These 1D Fermi arcs open up unique possibilities for generating unconventional non-local transport phenomena at the interfaces of domains with different handedness, and the associated enhanced conductance as the separation of the leads on the surface is increased. Employing first-principles calculations, we investigate in-depth the electronic and phononic structures of representative materials within the ten space groups that can support topological chiral kagome lattices. Our study opens a new research direction that integrates the advantages of structural chirality with those of a kagome lattice and thus provides a new materials platform for exploring unique aspects of correlated topological physics in chiral lattices.

cond-mat.mtrl-sci↗

arXiv2023

Intertwining of magnetism and charge ordering in kagome FeGe

Recent experiments report a charge density wave (CDW) in the antiferromagnet FeGe, but the nature of the charge ordering and the associated structural distortion remains elusive. We discuss the structural and electronic properties of FeGe. Our proposed ground state phase accurately captures atomic topographies acquired by scanning tunneling microscopy. We show that the 2$\times$2$\times$1 CDW likely results from the Fermi surface nesting of hexagonal-prism-shaped kagome states. FeGe is found to exhibit distortions in the positions of the Ge atoms instead of the Fe atoms in the kagome layers. Using in-depth first-principles calculations and analytical modeling, we demonstrate that this unconventional distortion is driven by the intertwining of magnetic exchange coupling and CDW interactions in this kagome material. Movement of Ge atoms from their pristine positions also enhances the magnetic moment of the Fe kagome layers. Our study indicates that magnetic kagome lattices provide a material candidate for exploring the effects of strong electronic correlations on the ground state and their implications for transport, magnetic, and optical responses in materials.

cond-mat.mtrl-sci↗

arXiv2023

Revisiting Graph Persistence for Updates and Efficiency

It is well known that ordinary persistence on graphs can be computed more efficiently than the general persistence. Recently, it has been shown that zigzag persistence on graphs also exhibits similar behavior. Motivated by these results, we revisit graph persistence and propose efficient algorithms especially for local updates on filtrations, similar to what is done in ordinary persistence for computing the vineyard. We show that, for a filtration of length $m$, (i) switches (transpositions) in ordinary graph persistence can be done in $O(\log m)$ time; (ii) zigzag persistence on graphs can be computed in $O(m\log m)$ time, which improves a recent $O(m\log^4n)$ time algorithm assuming $n$, the size of the union of all graphs in the filtration, satisfies $n\inΩ({m^\varepsilon})$ for any fixed $0<\varepsilon<1$; (iii) open-closed, closed-open, and closed-closed bars in dimension $0$ for graph zigzag persistence can be updated in $O(\log m)$ time, whereas the open-open bars in dimension $0$ and closed-closed bars in dimension $1$ can be done in $O(\sqrt{m}\,\log m)$ time.

cs.CG↗

arXiv2022

Vortex-induced Shear Polaritons

Hyperbolic shear polaritons (HShPs) emerge with widespread attention as a new class of polariton modes with broken symmetry due to shear lattices. In this letter, we find a new mechanism of generating HShPs. When utilizing vortex waves as excitation sources of hyperbolic materials without off-diagonal elements, HShPs will appear. In addition, this asymmetric HShPs can be recovered as symmetric modes away from the source, with a critical transition mode between the left-skewed and right-skewed HShPs, via tuning the magnitude of the off-diagonal imaginary component and controlling the topological charge of vortex source. It is worth mentioning that we explore the influence of parity of topological charges on the field distribution and demonstrate these exotic phenomena from numerical and analytical perspectives. Our results will promote new opportunities for both HShPs and vortex waves, widening the horizon for various hyperbolic materials based on vortex sources and offering a new degree of freedom to control various kinds of polaritons.

physics.optics↗

arXiv2022

Updating Barcodes and Representatives for Zigzag Persistence

Computing persistence over changing filtrations give rise to a stack of 2D persistence diagrams where the birth-death points are connected by the so-called `vines'. We consider computing these vines over changing filtrations for zigzag persistence. We observe that eight atomic operations are sufficient for changing one zigzag filtration to another and provide update algorithms for each of them. Six of these operations that have some analogues to one or multiple transpositions in the non-zigzag case can be executed as efficiently as their non-zigzag counterparts. This approach takes advantage of a recently discovered algorithm for computing zigzag barcodes by converting a zigzag filtration to a non-zigzag one and then connecting barcodes of the two with a bijection. The remaining two atomic operations do not have a strict analogue in the non-zigzag case. For them, we propose algorithms based on explicit maintenance of representatives (homology cycles) which can be useful in their own rights for applications requiring explicit updates of representatives.

cs.CG↗

arXiv2022

Layer Zero-Line Modes in Antiferromagnetic Topological Insulators

Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators MnBi$_2$Te$_4$, where we find that the topological zero-line modes (ZLMs) appear along the domain walls. Here, we theoretically demonstrate that these ZLMs are layer-dependent in MnBi$_2$Te$_4$ multilayers. For domain walls with out-of-plane ferromagnetism, we find that ZLMs are equally distributed in the odd-number layers. When domain walls possess in-plane magnetization, the ZLMs can also exist in even-number layers due to in-plane mirror-symmetry breaking. Moreover, the conductive channels are mainly distributed in the outermost layers with increasing layer thickness. Our findings lay out a strategy in manipulating ZLMs and also can be utilized to distinguish the corresponding magnetic structures.

cond-mat.mes-hall↗

arXiv2022

Fast Computation of Zigzag Persistence

Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes considerably more time than the standard persistence. We propose an algorithm called FastZigzag which narrows this efficiency gap. Our main result is that an input simplex-wise zigzag filtration can be converted to a cell-wise non-zigzag filtration of a $Δ$-complex with the same length, where the cells are copies of the input simplices. This conversion step in FastZigzag incurs very little cost. Furthermore, the barcode of the original filtration can be easily read from the barcode of the new cell-wise filtration because the conversion embodies a series of diamond switches known in topological data analysis. This seemingly simple observation opens up the vast possibilities for improving the computation of zigzag persistence because any efficient algorithm/software for standard persistence can now be applied to computing zigzag persistence. Our experiment shows that this indeed achieves substantial performance gain over the existing state-of-the-art softwares.

cs.CG↗

arXiv2021

On Association between Absolute and Relative Zigzag Persistence

Duality results connecting persistence modules for absolute and relative homology provides a fundamental understanding into persistence theory. In this paper, we study similar associations in the context of zigzag persistence. Our main finding is a weak duality for the so-called non-repetitive zigzag filtrations in which a simplex is never added again after being deleted. The technique used to prove the duality for non-zigzag persistence does not extend straightforwardly to our case. Accordingly, taking a different route, we prove the weak duality by converting a non-repetitive filtration to an up-down filtration by a sequence of diamond switches. We then show an application of the weak duality result which gives a near-linear algorithm for computing the $p$-th and a subset of the $(p-1)$-th persistence for a non-repetitive zigzag filtration of a simplicial $p$-manifold. Utilizing the fact that a non-repetitive filtration admits an up-down filtration as its canonical form, we further reduce the problem of computing zigzag persistence for non-repetitive filtrations to the problem of computing standard persistence for which several efficient implementations exist. Our experiment shows that this achieves substantial performance gain. Our study also identifies repetitive filtrations as instances that fundamentally distinguish zigzag persistence from the standard persistence.

cs.CG↗

arXiv2021

Topological Filtering for 3D Microstructure Segmentation

Tomography is a widely used tool for analyzing microstructures in three dimensions (3D). The analysis, however, faces difficulty because the constituent materials produce similar grey-scale values. Sometimes, this prompts the image segmentation process to assign a pixel/voxel to the wrong phase (active material or pore). Consequently, errors are introduced in the microstructure characteristics calculation. In this work, we develop a filtering algorithm called PerSplat based on topological persistence (a technique used in topological data analysis) to improve segmentation quality. One problem faced when evaluating filtering algorithms is that real image data in general are not equipped with the `ground truth' for the microstructure characteristics. For this study, we construct synthetic images for which the ground-truth values are known. On the synthetic images, we compare the pore tortuosity and Minkowski functionals (volume and surface area) computed with our PerSplat filter and other methods such as total variation (TV) and non-local means (NL-means). Moreover, on a real 3D image, we visually compare the segmentation results provided by our filter against TV and NL-means. The experimental results indicate that PerSplat provides a significant improvement in segmentation quality.

cond-mat.mtrl-sci↗

arXiv2021

Physical Origin of Current Partition at a Topological Trifurcation

In gated bilayer graphene, topological zero-line modes (ZLMs) appear along lines separating regions with opposite valley Hall topologies. Although it is experimentally difficult to design the electric gates to realize ZLMs due to the extremely challenging techniques, twisted bilayer graphene provides a natural platform to produce ZLMs in the presence of uniform electric field. In this Letter, we develop a set of wavepacket dynamics, which can be utilized to characterize various gapless edge modes and can quantitatively reproduce the electronic transport properties at topological intersections. To our surprise, in the minimally twisted bilayer graphene where a topological trifurcation intersection naturally arises, we show that the counterintuitive current partition (i.e., the direct transport propagation) originates from the microscopic mechanism "bypass jump". Our method can be applied to understand the microscopic pictures of the electronic transport features of all kinds of topological states.

cond-mat.mes-hall↗

arXiv2021

Computing Zigzag Persistence on Graphs in Near-Linear Time

Graphs model real-world circumstances in many applications where they may constantly change to capture the dynamic behavior of the phenomena. Topological persistence which provides a set of birth and death pairs for the topological features is one instrument for analyzing such changing graph data. However, standard persistent homology defined over a growing space cannot always capture such a dynamic process unless shrinking with deletions is also allowed. Hence, zigzag persistence which incorporates both insertions and deletions of simplices is more appropriate in such a setting. Unlike standard persistence which admits nearly linear-time algorithms for graphs, such results for the zigzag version improving the general $O(m^ω)$ time complexity are not known, where $ω< 2.37286$ is the matrix multiplication exponent. In this paper, we propose algorithms for zigzag persistence on graphs which run in near-linear time. Specifically, given a filtration with $m$ additions and deletions on a graph with $n$ vertices and edges, the algorithm for $0$-dimension runs in $O(m\log^2 n+m\log m)$ time and the algorithm for 1-dimension runs in $O(m\log^4 n)$ time. The algorithm for $0$-dimension draws upon another algorithm designed originally for pairing critical points of Morse functions on $2$-manifolds. The algorithm for $1$-dimension pairs a negative edge with the earliest positive edge so that a $1$-cycle containing both edges resides in all intermediate graphs. Both algorithms achieve the claimed time complexity via dynamic graph data structures proposed by Holm et al. In the end, using Alexander duality, we extend the algorithm for $0$-dimension to compute the $(p-1)$-dimensional zigzag persistence for $\mathbb{R}^p$-embedded complexes in $O(m\log^2 n+m\log m+n\log n)$ time.

cs.CG↗

arXiv2020

Valley-Current Splitter in Minimally Twisted Bilayer Graphene

We study the electronic transport properties at the intersection of three topological zero-lines as the elementary current partition node that arises in minimally twisted bilayer graphene. Unlike the partition laws of two intersecting zero-lines, we find that (i) the incoming current can be partitioned into both left-right adjacent topological channels and that (ii) the forward-propagating current is nonzero. By tuning the Fermi energy from the charge-neutrality point to a band edge, the currents partitioned into the three outgoing channels become nearly equal. Moreover, we find that current partition node can be designed as a perfect valley filter and energy splitter controlled by electric gating. By changing the relative electric field magnitude, the intersection of three topological zero-lines can transform smoothly into a single zero line, and the current partition can be controlled precisely. We explore the available methods for modulating this device systematically by changing the Fermi energy, the energy gap size, and the size of central gapless region. The current partition is also influenced by magnetic fields and the system size. Our results provide a microscopic depiction of the electronic transport properties around a unit cell of minimally twisted bilayer graphene and have far-reaching implications in the design of electron-beam splitters and interferometer devices.

cond-mat.mes-hall↗

arXiv2020

Metallic Network of Topological Domain Walls

We study the electronic and transport properties of a network of domain walls between insulating domains with opposite valley Chern numbers. We find that the network is semi-metallic with Dirac dispersion near the charge neutrality point and the corresponding electronic states distribute along the domain walls. Near the charge neutrality point, we find quantized conductance in nanoribbon with sawtooth domain wall edges that propagates along the boundaries and is robust against weak disorder. For a trident edged ribbon, we find a small energy gap due to the finite size effect making the nanoribbon an insulator. When the Fermi energy is away from charge neutrality point, all domain walls contribute to the conduction of current. Our results provide a comprehensive analysis of the electronic transport properties in a topological domain wall network that not only agrees qualitatively with experiments on marginally twisted bilayer graphene under a perpendicular electric field, but also can provide useful insights for designing low-power topological quantum devices.

cond-mat.mes-hall↗

arXiv2020

Approaching Three-Dimensional Quantum Hall effect in Bulk HfTe5

The discovery of quantum Hall effect in two-dimensional (2D) electronic systems inspired the topological classifications of electronic systems1,2. By stacking 2D quantum Hall effects with interlayer coupling much weaker than the Landau level spacing, quasi-2D quantum Hall effects have been experimentally observed3~7, due to the similar physical origin of the 2D counterpart. Recently, in a real 3D electronic gas system where the interlayer coupling is much stronger than the Landau level spacing, 3D quantum Hall effect has been observed in ZrTe58. In this Letter, we report the electronic transport features of its sister bulk material, i.e., HfTe5, under external magnetic field. We observe a series of plateaus in Hall resistance \r{ho}xy as magnetic field increases until it reaches the quantum limit at 1~2 Tesla. At the plateau regions, the longitudinal resistance \r{ho}xx exhibits local minima. Although \r{ho}xx is still nonzero, its value becomes much smaller than \r{ho}xy at the last few plateaus. By mapping the Fermi surface via measuring the Shubonikov-de Haas oscillation, we find that the strength of Hall plateau is proportional to the Fermi wavelength, suggesting that its formation may be attributed to the gap opening from the interaction driven Fermi surface instability. By comparing the bulk band structures of ZrTe5 and HfTe5, we find that there exists an extra pocket near the Fermi level of HfTe5, which may lead to the finite but nonzero longitudinal conductance.

cond-mat.mtrl-sci↗

arXiv2020

Computing Minimal Persistent Cycles: Polynomial and Hard Cases

Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing minimal 1-dimensional persistent cycles (persistent 1-cycles) for finite intervals is NP-hard while the same for infinite intervals is polynomially tractable. In this paper, we address this problem for general dimensions with $\mathbb{Z}_2$ coefficients. In addition to proving that it is NP-hard to compute minimal persistent d-cycles (d>1) for both types of intervals given arbitrary simplicial complexes, we identify two interesting cases which are polynomially tractable. These two cases assume the complex to be a certain generalization of manifolds which we term as weak pseudomanifolds. For finite intervals from the d-th persistence diagram of a weak (d+1)-pseudomanifold, we utilize the fact that persistent cycles of such intervals are null-homologous and reduce the problem to a minimal cut problem. Since the same problem for infinite intervals is NP-hard, we further assume the weak (d+1)-pseudomanifold to be embedded in $\mathbb{R}^{d+1}$ so that the complex has a natural dual graph structure and the problem reduces to a minimal cut problem. Experiments with both algorithms on scientific data indicate that the minimal persistent cycles capture various significant features of the data.

cs.CG↗

arXiv2019

Finite-Size Effects in the Dynamic Conductivity and Faraday Effect of Quantum Anomalous Hall Insulators

We theoretically study the finite-size effects in the dynamical response of a quantum anomalous Hall insulator in the disk geometry. Semi-analytic and numerical results are obtained for the wavefunctions and energies of the disk within a continuum Dirac Hamiltonian description subject to a topological infinite mass boundary condition. Using the Kubo formula, we obtain the frequency-dependent longitudinal and Hall conductivities and find that optical transitions between edge states contribute dominantly to the real part of the dynamic Hall conductivity for frequency values both within and beyond the bulk band gap. We also find that the topological infinite mass boundary condition changes the low-frequency Hall conductivity to $ e^2/h $ in a finite-size system from the well-known value $ e^2/2h $ in an extended system. The magneto-optical Faraday rotation is then studied as a function of frequency for the setup of a quantum anomalous Hall insulator mounted on a dielectric substrate, showing both finite-size effects of the disk and Fabry-Pérot resonances due to the substrate. Our work demonstrates the important role played by the boundary condition in the topological properties of finite-size systems through its effects on the electronic wavefunctions.

cond-mat.mes-hall↗

arXiv2019

Quantum Anomalous Hall Effect by Coupling Heavy Atomic Layers with CrI$_{3}$

We explored the possibility of realizing quantum anomalous Hall effect by placing heavy-element atomic layer on top of monolayer CrI$_{3}$ with a natural cleavage surface and broken time-reversal symmetry. We showed that CrI$_{3}$/X (X = Bi, Sb, or As) systems can open up a sizable bulk gap to harbour quantum anomalous Hall effect, e.g., CrI$_{3}$/Bi is a natural magnetic insulator with a bulk gap of 30~meV, which can be further enlarged via strain engineering or adjusting spin orientations. We also found that the ferromagnetic properties (magnetic anisotropic energy and Curie temperature) of pristine CrI$_{3}$ can be further improved due to the presence of heavy atomic layers, and the spin orientation can be utilized as a useful knob to tune the band structure and Fermi level of CrI$_{3}$/Bi system. The topological nature, together with the enhanced ferromagnetism, can unlock new potential applications for CrI$_{3}$-based materials in spintronics and electronics.

cond-mat.mtrl-sci↗

arXiv2019

Nonmagnetic-Doping Induced Quantum Anomalous Hall Effect in Topological Insulators

Quantum anomalous Hall effect (QAHE) has been experimentally observed in magnetically doped topological insulators. However, ultra-low temperature (usually below 300 mK), which is mainly attributed to inhomogeneous magnetic doping, becomes a daunting challenge for potential applications. Here, a \textit{nonmagnetic}-doping strategy is proposed to produce ferromagnetism and realize QAHE in topological insulators. We numerically demonstrated that magnetic moments can be induced by nitrogen or carbon substitution in Bi$_2$Se$_3$, Bi$_2$Te$_3$, and Sb$_2$Te$_3$, but only nitrogen-doped Sb$_2$Te$_3$ exhibits long-range ferromagnetism and preserve large bulk band gap. We further show that its corresponding thin-film can harbor QAHE at temperatures of 17-29 Kelvin, which is two orders of magnitude higher than the typical temperatures in similar systems. Our proposed \textit{nonmagnetic} doping scheme may shed new light in experimental realization of high-temperature QAHE in topological insulators.

cond-mat.mtrl-sci↗