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1. Non-equilibrium states and interactions in the topological insulator and topological crystalline insulator phases of NaCd4As3

   https://doi.org/10.1063/4.0000273  

   Kafle, Tika R; Zhang, Yingchao; Wang, Yi-yan; Shi, Xun; Li, Na; Sapkota, Richa; Thurston, Jeremy; You, Wenjing; Gao, Shunye; Dong, Qingxin; et al (January 2025, Structural Dynamics)

   Topological materials are of great interest because they can support metallic edge or surface states that are robust against perturbations, with the potential for technological applications. Here, we experimentally explore the light-induced non-equilibrium properties of two distinct topological phases in NaCd4As3: a topological crystalline insulator (TCI) phase and a topological insulator (TI) phase. This material has surface states that are protected by mirror symmetry in the TCI phase at room temperature, while it undergoes a structural phase transition to a TI phase below 200 K. After exciting the TI phase by an ultrafast laser pulse, we observe a leading band edge shift of >150 meV that slowly builds up and reaches a maximum after ∼0.6 ps and that persists for ∼8 ps. The slow rise time of the excited electron population and electron temperature suggests that the electronic and structural orders are strongly coupled in this TI phase. It also suggests that the directly excited electronic states and the probed electronic states are weakly coupled. Both couplings are likely due to a partial relaxation of the lattice distortion, which is known to be associated with the TI phase. In contrast, no distinct excited state is observed in the TCI phase immediately or after photoexcitation, which we attribute to the low density of states and phase space available near the Fermi level. Our results show how ultrafast laser excitation can reveal the distinct excited states and interactions in phase-rich topological materials. 

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2. Nonsymmorphic symmetry-protected band crossings in a square-net metal PtPb4

   https://doi.org/10.1038/s41535-022-00441-x  

   Wu, Han; Hallas, Alannah M.; Cai, Xiaochan; Huang, Jianwei; Oh, Ji Seop; Loganathan, Vaideesh; Weiland, Ashley; McCandless, Gregory T.; Chan, Julia Y.; Mo, Sung-Kwan; et al (December 2022, npj Quantum Materials)

   Abstract Topological semimetals with symmetry-protected band crossings have emerged as a rich landscape to explore intriguing electronic phenomena. Nonsymmorphic symmetries in particular have been shown to play an important role in protecting the crossings along a line (rather than a point) in momentum space. Here we report experimental and theoretical evidence for Dirac nodal line crossings along the Brillouin zone boundaries in PtPb 4 , arising from the nonsymmorphic symmetry of its crystal structure. Interestingly, while the nodal lines would remain gapless in the absence of spin–orbit coupling (SOC), the SOC, in this case, plays a detrimental role to topology by lifting the band degeneracy everywhere except at a set of isolated points. Nevertheless, the nodal line is observed to have a bandwidth much smaller than that found in density functional theory (DFT). Our findings reveal PtPb 4 to be a material system with narrow crossings approximately protected by nonsymmorphic crystalline symmetries. 

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3. Recent advancements in the study of intrinsic magnetic topological insulators and magnetic Weyl semimetals

   https://doi.org/10.1063/5.0015328  

   Ning, Wei; Mao, Zhiqiang (September 2020, APL Materials)

   The studies of topological insulators (TI) and topological semimetals have been at frontiers of condensed matter physics and material science. Both classes of materials are characterized by robust surface states created by the topology of the bulk band structures and exhibit exotic transport properties. When magnetism is present in topological materials and breaks the time-reversal symmetry, more exotic quantum phenomena can be generated, e.g., quantum anomalous Hall effect (QAHE), axion insulator, and large intrinsic AHE. In this research update, we briefly summarize the recent research progress in magnetic topological materials, including intrinsic magnetic TI and magnetic Weyl semimetals. 

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4. Spin-resolved topology and partial axion angles in three-dimensional insulators

   https://doi.org/10.1038/s41467-024-44762-w  

   Lin, Kuan-Sen; Palumbo, Giandomenico; Guo, Zhaopeng; Hwang, Yoonseok; Blackburn, Jeremy; Shoemaker, Daniel P.; Mahmood, Fahad; Wang, Zhijun; Fiete, Gregory A.; Wieder, Benjamin J.; et al (January 2024, Nature Communications)

   Abstract Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($${{{{{{{\mathcal{T}}}}}}}}$$ $T$-) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and$${{{{{{{\mathcal{T}}}}}}}}$$ $T$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate thatβ-MoTe₂realizes a spin-Weyl state and thatα-BiBr hosts both 3D QSHI and T-DAXI regimes. 

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5. Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

   https://doi.org/10.1038/s41467-020-14443-5  

   Wieder, Benjamin J.; Wang, Zhijun; Cano, Jennifer; Dai, Xi; Schoop, Leslie M.; Bradlyn, Barry; Bernevig, B. Andrei (January 2020, Nature Communications)

   Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of ans–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd₃As₂, KMgBi, and rutile-structure ($$ \beta ^{\prime} $$ ${\beta }^{\prime }$-) PtO₂. 

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