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Probabilistic mixture models are recognized as effective tools for unsupervised outlier detection owing to their interpretability and global characteristics. Among these, Dirichlet process mixture models stand out as a strong alternative to conventional finite mixture models for both clustering and outlier detection tasks. Unlike finite mixture models, Dirichlet process mixtures are infinite mixture models that automatically determine the number of mixture components based on the data. Despite their advantages, the adoption of Dirichlet process mixture models for unsupervised outlier detection has been limited by challenges related to computational inefficiency and sensitivity to outliers in the construction of outlier detectors. Additionally, Dirichlet process Gaussian mixtures struggle to effectively model non-Gaussian data with discrete or binary features. To address these challenges, we propose a novel outlier detection method that utilizes ensembles of Dirichlet process Gaussian mixtures. This unsupervised algorithm employs random subspace and subsampling ensembles to ensure efficient computation and improve the robustness of the outlier detector. The ensemble approach further improves the suitability of the proposed method for detecting outliers in non-Gaussian data. Furthermore, our method uses variational inference for Dirichlet process mixtures, which ensures both efficient and rapid computation. Empirical analyses using benchmark datasets demonstrate that our method outperforms existing approaches in unsupervised outlier detection.

Chiral exact flat bands (FBs) at charge neutrality have attracted much recent interest, presenting an intriguing condensed-matter system to realize exact many-body phenomena, as specifically shown in "magic angle" twisted bilayer graphene for superconductivity and triangulene-based superatomic graphene for excitonic condensation. Yet, no generic physical model to realize such FBs has been developed. Here we present a new mathematical theorem, called bipartite double cover (BDC) theorem, and prove that the BDC of line-graph (LG) lattices hosts at least two chiral exact FBs of opposite chirality, i.e., yin-yang FBs, centered-around/at charge neutrality (E = 0) akin to the "chiral limit" of twisted bilayer graphene. We illustrate this theorem by mapping it exactly onto tight-binding lattice models of the BDC of LGs of hexagonal lattice for strong topological and of triangular lattice for fragile topological FBs, respectively. Moreover, we use orbital design principle to realize such exotic yin-yang FBs in non-BDC lattices to instigate their real material discovery. This work not only enables the search for exact chiral FBs at zero energy beyond moir\'e heterostructures, but also opens the door to discovering quantum semiconductor features with FB-enabled strongly correlated carriers.

SrAs$_3$ is a unique nodal-line semimetal that contains only a single nodal ring in the Brillouin zone, uninterrupted by any trivial bands near the Fermi energy. We performed axis-resolved optical reflection measurements on SrAs$_3$ and observed that the optical conductivity exhibits flat absorption up to 129 meV in both the radial and axial directions, confirming the robustness of the universal power-law behavior of the nodal ring. Furthermore, in conjunction with model and first-principles calculations, the axis-resolved optical conductivity unveiled fundamental properties beyond the flat absorption, including the overlap energy of the topological bands, the spin-orbit coupling gap along the nodal ring, and the geometric properties of the nodal ring such as the average ring radius, ring ellipticity, and velocity anisotropy. In addition, our temperature-dependent measurements revealed a spectral weight transfer between intraband and interband transitions, indicating a possible violation of the optical sum rule within the measured energy range., Comment: 6 pages, 4 figures + supplemental material (22 pages, 10 figures)

Recently there has been intense interest in Kagome metals, which are expected to host flat bands (FBs). However, the observed FBs are non-ideal as they are not flat over the whole 2D Brillouin zone and overlap strongly with other bands. Most critically, the theoretical conditions for the existence of ideal FB in Kagome metals, beyond the simplest Kagome lattice model, are unknown. Here, based on tight-binding model analyses of the interplay between d-orbital symmetry and underlying Kagome lattice symmetry, we establish such conditions. We show that for a pure transition-metal (TM) Kagome lattice, only dz2 orbital gives rise to a FB; while dxy, dx2-y2, dxz, and dyz orbitals do not. The condition for the latter four orbitals to produce a FB is to rotate them so that they will conform with the underlying Kagome lattice symmetry. Interestingly, the lattice having rotated dxy (dxz) and dx2-y2 (dyz) orbitals leads to a FB of opposite chirality sitting above and below the Dirac bands, respectively. For intercalated TM Kagome lattices, the Kagome-hexagonal intercalation exhibits always a FB, while the case for the Kagome-trigonal intercalation is conditional. Another condition to isolate the FB arising from individual d-orbitals is to increase the crystal field splitting, such as in Kagome metals of layered metalorganic frameworks., Comment: 12 pages, 3figures

The antiferromagnetic topological insulator MnBi2Te4 (MBT) exhibits an ideal platform to study exotic topological phenomena and magnetic properties. The transport signatures of magnetic phase transitions in the MBT family materials have been well-studied. However, their mechanical properties and magneto-mechanical coupling have not been well-explored. We use nanoelectromechanical systems to study the intrinsic magnetism in MBT thin flakes via their magnetostrictive coupling. We investigate mechanical resonance signatures of magnetic phase transitions from antiferromagnetic (AFM) to canted antiferromagnetic (cAFM) to ferromagnetic (FM) phases versus magnetic field at different temperatures. The spin-flop transitions in MBT are revealed by frequency shifts of mechanical resonance. With temperatures going above TN, the transitions disappear in the resonance frequency map, consistent with transport measurements. We use a magnetostrictive model to correlate the frequency shifts with the spin-canting states. Our work demonstrates a technique to study magnetic phase transitions, magnetization and magnetoelastic properties of the magnetic topological insulator.

We study topological phase transitions in tetragonal NaZnSb$_{1-x}$Bi$_x$, driven by the chemical composition $x$. Notably, we examine mirror Chern numbers that change without symmetry indicators. First-principles calculations are performed to show that NaZnSb$_{1-x}$Bi$_x$ experiences consecutive topological phase transitions, diagnosed by the strong $\mathbb Z_{2}$ topological index $\nu_{0}$ and two mirror Chern numbers $\mu_{x}$ and $\mu_{xy}$. As the chemical composition $x$ increases, the topological invariants ($\mu_{x}\mu_{xy}\nu_{0}$) change from $(000)$, $(020)$, $(220)$, to $(111)$ at $x$ = 0.15, 0.20, and 0.53, respectively. A simplified low-energy effective model is developed to examine the mirror Chern number changes, highlighting the central role of spectator Dirac fermions in avoiding symmetry indicators. Our findings suggest that NaZnSb$_{1-x}$Bi$_{x}$ can be an exciting testbed for the exploration of the interplay between the topology and symmetry.

In this article, we review the recent progress in the study of topological phases in systems with space-time inversion symmetry $I_{\text{ST}}$. $I_{\text{ST}}$ is an anti-unitary symmetry which is local in momentum space and satisfies $I_{\text{ST}}^2=1$ such as $PT$ or $C_{2}T$ symmetry where $P$, $T$, $C_2$ indicate inversion, time-reversal, and two-fold rotation symmetries, respectively. Under $I_{\text{ST}}$, the Hamiltonian and the Bloch wave function can be constrained to be real-valued, which makes the Berry curvature and the Chern number to vanish. In this class of systems, gapped band structures of real wave functions can be topologically distinguished by Stiefel-Whitney numbers instead. The first and second Stiefel-Whitney numbers $w_1$ and $w_2$, respectively, are the corresponding invariants in 1D and 2D, which are equivalent to the quantized Berry phase and the $Z_2$ monopole charge, respectively. We first describe the topological phases characterized by the first Stiefel-Whitney number, including 1D topological insulators with quantized charge polarization, 2D Dirac semimetals, and 3D nodal line semimetals. Next we review how the second Stiefel-Whitney class characterizes the 3D nodal line semimetals carrying a $Z_{2}$ monopole charge. In particular, we explain how the second Stiefel-Whitney number $w_2$, the $Z_{2}$ monopole charge, and the linking number between nodal lines are related. Finally, we review the properties of 2D and 3D topological insulators characterized by the nontrivial second Stiefel Whitney class., Comment: A review article; 17 pages, 12 figures; suggestions and comments are highly appreciated

Dirac line node (DLN) semimetals are a class of topological semimetals that feature band-crossing lines in momentum space. We study the type-I and type-II classification of DLN semimetals by developing a criterion that determines the type using band velocities. Using first-principles calculations, we also predict that Na3N under an epitaxial tensile strain realizes a type-II DLN semimetal with vanishing spin-orbit coupling (SOC), characterized by the Berry phase that is Z2-quantized in the presence of inversion and time-reversal symmetries. The surface energy spectrum is calculated to demonstrate the topological phase, and the type-II nature is demonstrated by calculating the band velocities. We also develop a tight-binding model and a low-energy effective Hamiltonian that describe the low-energy electronic structure of strained Na3N. The occurrence of a DLN in Na3N under strain is captured in the optical conductivity, which we propose as a means to experimentally confirm the type-II class of the DLN semimetal., Comment: 14 pages, 9 figure

Previous experimental work has shown high-frequency Poisson-distributed trains of combined excitatory and inhibitory conductance- and current-based synaptic inputs reduce amplitude of subthreshold oscillations of SCs. In this paper, we investigate the mechanism underlying these phenomena in the context of the model. More specially, we studied the effects of both conductance- and current-based synaptic inputs at various maximal conductance values on a SC model. Our numerical simulations show that conductance-based synaptic inputs reduce the amplitude of SC's subthreshold oscillations for low enough value of the maximal synaptic conductance value but amplify these oscillations at a higher range. These results contrast with the experimental results.

We study the band topology and the associated linking structure of topological semimetals with nodal lines carrying $Z_{2}$ monopole charges, which can be realized in three-dimensional systems invariant under the combination of inversion $P$ and time reversal $T$ when spin-orbit coupling is negligible. In contrast to the well-known $PT$-symmetric nodal lines protected only by $\pi$ Berry phase in which a single nodal line can exist, the nodal lines with $Z_{2}$ monopole charges should always exist in pairs. We show that a pair of nodal lines with $Z_{2}$ monopole charges is created by a {\it double band inversion} (DBI) process, and that the resulting nodal lines are always {\it linked by another nodal line} formed between the two topmost occupied bands. It is shown that both the linking structure and the $Z_{2}$ monopole charge are the manifestation of the nontrivial band topology characterized by the {\it second Stiefel-Whitney class}, which can be read off from the Wilson loop spectrum. We show that the second Stiefel-Whitney class can serve as a well-defined topological invariant of a $PT$-invariant two-dimensional (2D) insulator in the absence of Berry phase. Based on this, we propose that pair creation and annihilation of nodal lines with $Z_{2}$ monopole charges can mediate a topological phase transition between a normal insulator and a three-dimensional weak Stiefel-Whitney insulator (3D weak SWI). Moreover, using first-principles calculations, we predict ABC-stacked graphdiyne as a nodal line semimetal (NLSM) with $Z_{2}$ monopole charges having the linking structure. Finally, we develop a formula for computing the second Stiefel-Whitney class based on parity eigenvalues at inversion invariant momenta, which is used to prove the quantized bulk magnetoelectric response of NLSMs with $Z_2$ monopole charges under a $T$-breaking perturbation., Comment: 4+28 pages, 3+17 figures