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Recently, layered kagome metals AV3Sb5 (A = K, Rb, and Cs) have emerged as a fertile platform for exploring frustrated geometry, correlations, and topology. Here, using first-principles and mean-field calculations, we demonstrate that AV3Sb5 can crystallize in a mono-layered form, revealing a range of properties that render the system unique. Most importantly, the two-dimensional monolayer preserves intrinsically different symmetries from the three-dimensional layered bulk, enforced by stoichiometry. Consequently, the van Hove singularities, logarithmic divergences of the electronic density of states, are enriched, leading to a variety of competing instabilities such as doublets of charge density waves and s- and d-wave superconductivity. We show that the competition between orders can be fine-tuned in the monolayer via electron-filling of the van Hove singularities. Thus, our results suggest the monolayer kagome metal AV3Sb5 as a promising platform for designer quantum phases.

Funder: Cambridge Research Computing Service funded by EPSRC [EP/P020259/1], Recently, layered kagome metals AV3Sb5 (A = K, Rb, and Cs) have emerged as a fertile platform for exploring frustrated geometry, correlations, and topology. Here, using first-principles and mean-field calculations, we demonstrate that AV3Sb5 can crystallize in a mono-layered form, revealing a range of properties that render the system unique. Most importantly, the two-dimensional monolayer preserves intrinsically different symmetries from the three-dimensional layered bulk, enforced by stoichiometry. Consequently, the van Hove singularities, logarithmic divergences of the electronic density of states, are enriched, leading to a variety of competing instabilities such as doublets of charge density waves and s- and d-wave superconductivity. We show that the competition between orders can be fine-tuned in the monolayer via electron-filling of the van Hove singularities. Thus, our results suggest the monolayer kagome metal AV3Sb5 as a promising platform for designer quantum phases.

The Hofstadter energy spectrum of twisted bilayer graphene is found to have recursive higher-order topological properties. We demonstrate that higher-order topological insulator (HOTI) phases, characterized by localized corner states, occur as replicas of the original HOTIs to fulfill the self-similarity of the Hofstadter spectrum. We show the existence of the exact flux translational symmetry of twisted bilayer graphene at all commensurate angles. Based on this result, we carefully identify that the original HOTI phase at zero flux is re-entrant at a half-flux periodicity, where the effective twofold rotation is preserved. In addition, numerous replicas of the original HOTIs are found for fluxes without protecting symmetries. Similar to the original HOTIs, replica HOTIs feature both localized corner states and edge-localized real-space topological markers. The replica HOTIs originate from the different interaction scales, namely, intralayer and interlayer couplings, in twisted bilayer graphene. The topological aspect of Hofstadter butterflies revealed in our results highlights symmetry-protected topology in quantum fractals., 6 pages, 4 figures + Supplemental Material

We study topological phase transitions in tetragonal NaZnSb$_{1-x}$Bi$_x$, driven by the chemical composition $x$. Notably, we examine mirror Chern numbers that change without symmetry indicators. First-principles calculations are performed to show that NaZnSb$_{1-x}$Bi$_x$ experiences consecutive topological phase transitions, diagnosed by the strong $\mathbb Z_{2}$ topological index $\nu_{0}$ and two mirror Chern numbers $\mu_{x}$ and $\mu_{xy}$. As the chemical composition $x$ increases, the topological invariants ($\mu_{x}\mu_{xy}\nu_{0}$) change from $(000)$, $(020)$, $(220)$, to $(111)$ at $x$ = 0.15, 0.20, and 0.53, respectively. A simplified low-energy effective model is developed to examine the mirror Chern number changes, highlighting the central role of spectator Dirac fermions in avoiding symmetry indicators. Our findings suggest that NaZnSb$_{1-x}$Bi$_{x}$ can be an exciting testbed for the exploration of the interplay between the topology and symmetry.

Recently, Lee \textit{et. al.} [Nano Lett. \textbf{21}, 4305 (2021)] newly synthesized monochalcogenide GeSe in a polar phase, referred to as $γ$-phase. Motivated by this work, we study shift current of $γ$-GeSe and its tunability via an in-plane uniaxial strain. Using first-principles calculations, we uncover the electronic structure of the strained $γ$-GeSe systems. We then calculate frequency-dependent shift current conductivities at various strains. The tunability is demonstrated to enhance the shift current up to $\sim$ 20 $μ$A/V$^2$. Moreover, the direction of shift current can be inverted by a light strain. Markedly, an anomalous behavior is found in the zero-frequency limit, which can be an indicative of band inversion and a potential topological phase transition driven by the strain. Our results suggest that shift current can be a tangible prove of bulk electronic states of $γ$-GeSe.

We propose a new type of instanton interference effect in two-dimensional higher-order topological insulators. The intercorner tunneling consists of the instanton and the anti-instanton pairs that travel through the boundary of the higher-order topological insulator. The Berry phase difference between the instanton pairs causes the interference of the tunneling. This topological effect leads to the gate-tunable oscillation of the energy splitting between the corner states, where the oscillatory nodes signal the perfect suppression of the tunneling. We suggest this phenomenon as a unique feature of the topological corner states that differentiate from trivial bound states. In the view of experimental realization, we exemplify twisted bilayer graphene, as a promising candidate of a two-dimensional higher-order topological insulator. The oscillation can be readily observed through the transport experiment that we propose. Thus, our work provides a feasible route to identify higher-order topological materials., 4+9 pages, 4 figures