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Honeycomb or triangular lattices were extensively studied and thought to be proper platforms for realizing quantum anomalous Hall effect (QAHE), where magnetism is usually caused by d orbitals of transition metals. Here we propose that square lattice can host three magnetic topological states, including the fully spin polarized nodal loop semimetal, QAHE and topologically trivial ferromagnetic semiconductor, in terms of the symmetry and k$cdot$p model analyses that are materials-independent. A phase diagram is presented. We further show that the above three magnetic topological states can be indeed implemented in two-dimensional (2D) materials ScLiCl5, LiScZ5 (Z=Cl, Br), and ScLiBr5, respectively. The ferromagnetism in these 2D materials is microscopically revealed from p electrons of halogen atoms. This present study opens a door to explore the exotic topological states as well as quantum magnetism from p-orbital electrons by means of the materials-independent approach.
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We investigate the quantum fluctuation effects in the vicinity of the critical point of a $p$-orbital bosonic system in a square optical lattice using Wilsonian renormalization group, where the $p$-orbital bosons condense at nonzero momenta and display rich phases including both time-reversal symmetry invariant and broken BEC states. The one-loop renormalization group analysis generates corrections to the mean-field phase boundaries. We also show the quantum fluctuations in the $p$-orbital system tend to induce the ordered phase but not destroy it via the the Coleman-Weinberg mechanism, which is qualitative different from the ordinary quantum fluctuation corrections to the mean-field phase boundaries in $s$-orbital systems. Finally we discuss the observation of these phenomena in the realistic experiment.
We report a polarized Raman scattering study of non-symmorphic topological insulator KHgSb with hourglass-like electronic dispersion. Supported by theoretical calculations, we show that the lattice of the previously assigned space group $P6_3/mmc$ (No. 194) is unstable in KHgSb. While we observe one of two calculated Raman active E$_{2g}$ phonons of space group $P6_3/mmc$ at room temperature, an additional A$_{1g}$ peak appears at 99.5 ~cm$^{-1}$ upon cooling below $T^*$ = 150 K, which suggests a lattice distortion. Several weak peaks associated with two-phonon excitations emerge with this lattice instability. We also show that the sample is very sensitive to high temperature and high laser power, conditions under which it quickly decomposes, leading to the formation of Sb. Our first-principles calculations indicate that space group $P6_3mc$ (No. 186), corresponding to a vertical displacement of the Sb atoms with respect to the Hg atoms that breaks the inversion symmetry, is lower in energy than the presumed $P6_3/mmc$ structure and preserves the glide plane symmetry necessary to the formation of hourglass fermions.
We study the topological phase in dipolar-coupled two-dimensional breathing square lattice of magnetic vortices. By evaluating the quantized Chern number and $mathbb{Z}_{4}$ Berry phase, we obtain the phase diagram and identify that the second-order topological corner states appear only when the ratio of alternating bond lengths goes beyond a critical value. Interestingly, we uncover three corner states at different frequencies ranging from sub GHz to tens of GHz by solving the generalized Thieles equation, which has no counterpart in condensed matter system. We show that the emerging corner states are topologically protected by a generalized chiral symmetry of the quadripartite lattice, leading to particular robustness against disorder and defects. Full micromagnetic simulations confirm theoretical predictions with a great agreement. A vortex-based imaging device is designed as a demonstration of the real-world application of the second-order magnetic topological insulator. Our findings provide a route for realizing symmetry-protected multi-band corner states that are promising to achieve spintronic higher-order topological devices.
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