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1. 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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2. Band Representations and Topological Quantum Chemistry

   https://doi.org/10.1146/annurev-conmatphys-041720-124134  

   Cano, Jennifer; Bradlyn, Barry (March 2021, Annual Review of Condensed Matter Physics)

   null (Ed.)

   In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space. Next, we introduce the concept of a band representation, which quantifies the symmetry of topologically trivial band structures. By combining band representations with symmetry constraints on the connectivity of bands in momentum space, we show how topologically nontrivial bands can be cataloged and classified. We present several examples of new topological phases discovered using this paradigm and conclude with an outlook toward future developments. 

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3. Observation of the topological Anderson insulator in disordered atomic wires

   https://doi.org/10.1126/science.aat3406  

   Meier, Eric J.; An, Fangzhao Alex; Dauphin, Alexandre; Maffei, Maria; Massignan, Pietro; Hughes, Taylor L.; Gadway, Bryce (October 2018, Science)

   Topology and disorder have a rich combined influence on quantum transport. To probe their interplay, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. Measuring the bulk evolution of a topological indicator after a sudden quench, we observed the topological Anderson insulator phase, in which added disorder drives the band structure of a wire from topologically trivial to nontrivial. In addition, we observed the robustness of topologically nontrivial wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform may enable realizations of strongly interacting topological fluids. 

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4. Anomalous Crystalline-Electromagnetic Responses in Semimetals

   https://doi.org/10.1103/PhysRevX.14.041060  

   Hirsbrunner, Mark R; Dubinkin, Oleg; Burnell, F J; Hughes, Taylor L (December 2024, Physical Review X)

   We present a unifying framework that allows us to study the mixed crystalline-electromagnetic responses of topological semimetals in spatial dimensions up to $D=3$through dimensional augmentation and reduction procedures. We show how this framework illuminates relations between the previously known topological semimetals and use it to identify a new class of quadrupolar nodal line semimetals for which we construct a lattice tight-binding Hamiltonian. We further utilize this framework to quantify a variety of mixed crystalline-electromagnetic responses, including several that have not previously been explored in existing literature, and show that the corresponding coefficients are universally proportional to weighted momentum-energy multipole moments of the nodal points (or lines) of the semimetal. We introduce lattice gauge fields that couple to the crystal momentum and describe how tools including the gradient expansion procedure, dimensional reduction, compactification, and the Kubo formula can be used to systematically derive these responses and their coefficients. We further substantiate these findings through analytical physical arguments, microscopic calculations, and explicit numerical simulations employing tight-binding models. Published by the American Physical Society2024 

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5. Fragility of surface states in topological superfluid 3He

   https://doi.org/10.1038/s41467-021-21831-y  

   Heikkinen, P. J.; Casey, A.; Levitin, L. V.; Rojas, X.; Vorontsov, A.; Sharma, P.; Zhelev, N.; Parpia, J. M.; Saunders, J. (December 2021, Nature Communications)

   null (Ed.)

   Abstract Superfluid 3 He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superfluids and superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid 3 He within a cavity of height D comparable to the Cooper pair diameter ξ 0 . We precisely determine the superfluid transition temperature T c and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasiclassical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of T c , corresponding to an increased density of low energy bound states. 

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