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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 

Incorporating relativistic physics into quantum tunneling can lead to exotic behavior such as perfect transmission through Klein tunneling. Here, we probed the tunneling properties of spin-momentum-locked relativistic fermions by designing and implementing a tunneling geometry that uses nanowires of the topological Kondo insulator candidate samarium hexaboride. The nanowires are attached to the end of scanning tunneling microscope tips and used to image the bicollinear stripe spin order in the antiferromagnet Fe_1.03Te with a Neel temperature of about 50 kelvin. The antiferromagnetic stripes become invisible above 10 kelvin concomitant with the suppression of the topological surface states in the tip. We further demonstrate that the direction of spin polarization is tied to the tunneling direction. Our technique establishes samarium hexaboride nanowires as ideal conduits for spin-polarized currents. 

Abstract The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of boundary states in the insulating gap is not always necessary since they can be hidden in the bulk energy bands, obscured by boundary artifacts of non-topological origin, or, in the case of higher-order topology, they can be gapped altogether. Recently, exotic defects of translation symmetry called partial dislocations have been proposed to trap gapless topological modes in some materials. Here we present experimental observations of partial-dislocation-induced topological modes in 2D and 3D insulators. We particularly focus on multipole higher-order topological insulators built from circuit-based resonator arrays, since crucially they are not sensitive to full dislocation defects, and they have a sublattice structure allowing for stacking faults and partial dislocations. 

Abstract Higher order topological insulators (HOTIs) are a new class of topological materials which host protected states at the corners or hinges of a crystal. HOTIs provide an intriguing alternative platform for helical and chiral edge states and Majorana modes, but there are very few known materials in this class. Recent studies have proposed Bi as a potential HOTI, however, its topological classification is not yet well accepted. In this work, we show that the (110) facets of Bi and BiSb alloys can be used to unequivocally establish the topology of these systems. Bi and Bi_0.92Sb_0.08(110) films were grown on silicon substrates using molecular beam epitaxy and studied by scanning tunneling spectroscopy. The surfaces manifest rectangular islands which show localized hinge states on three out of the four edges, consistent with the theory for the HOTI phase. This establishes Bi and Bi_0.92Sb_0.08as HOTIs, and raises questions about the topological classification of the full family of Bi_xSb_1−xalloys.