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We report the growth of high quality bulk crystals, through crystallization from molten Sn flux, of the predicted ferromagnetic Weyl metal ZrCo2−x Sn with the L21 Heusler phase structure. The concentration of Co vacancies in the single crystals is found to be dependent on the initial concentration of Co in the flux. The saturation magnetization increases approximately linearly with decreasing Co deficiency and the ferromagnetic transition temperature changes significantly. p-type carrier conduction and an anomalous Hall effect are observed. The calculated electronic density of states of ZrCo2−x Sn shows a significant change in minority and majority spin state occupancies and a shift in the Fermi level with Co deficiency.

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions. We employed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. By mapping the quasiparticle interference and emerging Landau levels at high magnetic field in Dirac semimetals Cd$_3$As$_2$ and Na$_3$Bi, we observed extended Dirac-like bulk electronic bands. Quasiparticle interference imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface-projected Weyl nodes.

We review a class of translational-invariant insulators without spin–orbit coupling, as may be realized in intrinsically spinless systems, e.g., photonic crystals and ultra-cold atoms. Some of these insulators have no time-reversal symmetry as well, i.e., the relevant symmetries are purely crystalline. Nevertheless, topological phases exist which are distinguished by their robust surface modes. To describe these phases, we introduce the notions of (a) a halved-mirror chirality: an integer invariant which characterizes half-mirror planes in the 3D Brillouin zone, and (b) a bent Chern number: the traditional Thouless–Kohmoto–Nightingale–Nijs invariant generalized to bent 2D manifolds. Like other well-known topological phases, their band topology is unveiled by the crystalline analog of Berry phases, i.e., parallel transport across certain non-contractible loops in the Brillouin zone. We also identify certain topological phases without any robust surface modes—they are uniquely distinguished by parallel transport along bent loops, whose shapes are determined by the symmetry group. Finally, we describe the Weyl semimetallic phase that intermediates two distinct, gapped phases.

We develop a local spin model to explain the rich magnetic structures in the iron-based superconductors $Fe_{1+y}Te_{1-x}Se_x$. We show that our model exhibits both commensurate antiferromagnetic and incommensurate magnetic order along the crystal a-axis. The transition from the commensurate to the incommensurate phase is induced when the concentration of excess $Fe$ atoms is larger than a critical value. Experimentally measurable spin-wave features are calculated, and the mean-field phase diagram of the model is obtained. Our model also suggests the existence of a large quantum critical region due to strong spin frustration upon increasing $Se$ concentration.