Kagome superconductors AV 3 Sb 5 (A = K, Rb, Cs) provide a fertile playground for studying various intriguing phenomena such as non-trivial band topology, superconductivity, giant anomalous Hall e ﬀ ect, and charge density wave (CDW). Remarkably, the recent discovery of C 2 symmetric nematic phase prior to the superconducting state in AV 3 Sb 5 has drawn enormous attention, as the unusual superconductivity might inherit the symmetry of the nematic phase. Although many e ﬀ orts have been devoted to resolve the charge orders using real-space microscopy and transport measurements, the direct evidence on the rotation symmetry

Observation of electronic nematicity driven by three-dimensional charge density wave in kagome lattice KV 3 Sb 5

The recently discovered layered kagome metals of composition AV_{3}Sb_{5} (A=K, Rb, Cs) exhibit a complex interplay among superconductivity, charge density wave order, topologically nontrivial electronic band structure and geometrical frustration. Here, we probe the electronic band structure underlying these exotic correlated electronic states in CsV_{3}Sb_{5} with quantum oscillation measurements in pulsed fields up to 86 T. The high-field data reveal a sequence of magnetic breakdown orbits that allows the construction of a model for the folded Fermi surface of CsV_{3}Sb_{5}. The dominant features are large triangular Fermi surface sheets that cover almost half the folded Brillouin zone. These sheets have not yet been detected in angle resolved photoemission spectroscopy and display pronounced nesting. The Berry phases of the electron orbits have been deduced from Landau level fan diagrams near the quantum limit without the need for extrapolations, thereby unambiguously establishing the nontrivial topological character of several electron bands in this kagome lattice superconductor.

Magnetic Breakdown and Topology in the Kagome Superconductor CsV_{3}Sb_{5} under High Magnetic Field.

Kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) exhibit a characteristic superconducting ground state coexisting with a charge density wave (CDW), whereas the mechanisms of the superconductivity and CDW have yet to be clarified. Here we report a systematic angle-resolved photoemission spectroscopy (ARPES) study of Cs(V_{1-x}Nb_{x})_{3}Sb_{5} as a function of Nb content x, where isovalent Nb substitution causes an enhancement of superconducting transition temperature (T_{c}) and the reduction of CDW temperature (T_{CDW}). We found that the Nb substitution shifts the Sb-derived electron band at the Γ point downward and simultaneously moves the V-derived band around the M point upward to lift up the saddle point (SP) away from the Fermi level, leading to the reduction of the CDW-gap magnitude and T_{CDW}. This indicates a primary role of the SP density of states to stabilize the CDW. The present result also suggests that the enhancement of superconductivity by Nb substitution is caused by the cooperation between the expansion of the Sb-derived electron pocket and the recovery of the V-derived density of states at the Fermi level. 

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Fermiology and Origin of 
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 Enhancement in a Kagome Superconductor 
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The precise microscopic nature of charge-density-wave ordering in the 2D kagome superconductor RbV${}_{3}$Sb${}_{5}$ has been clearly identified by employing a unique approach that combines density-functional theory and nuclear magnetic resonance techniques. 

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Microscopic nature of the charge-density wave in the kagome superconductor 
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The recently discovered vanadium-based kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs) offer the possibility to study the interplay between competing electronic orderings, such as charge density order and superconductivity. We focus on the former and provide a comprehensive set of $^{51}$V, $^{87}$Rb, and $^{121}$Sb magnetic resonance measurements on an RbV$_3$Sb$_5$ single crystal. Elucidating the symmetries and properties of the CDW phase is essential to understanding the unconventional electronic orderings occurring in this material. We establish the structure of the $2\times 2 \times 2$ superlattice that describes the system below the charge density wave transition by combining both experimental and computational methods, with a methodology that can be readily applied to the remaining compounds of the same family. Our results give compelling evidence that the CDW structure occurring below 103 K for RbV$_3$Sb$_5$ is the so-called Inverse Start of David pattern $\pi$-shifted along the c axis (also known as staggered tri-hexagonal).

Microscopic nature of the charge-density wave in kagome superconductor RbV$_3$Sb$_5$

Kagome lattices offer a fertile ground to explore exotic quantum phenomena associated with electron correlation and band topology. The recent discovery of superconductivity coexisting with charge-density wave (CDW) in the kagome metals KV3Sb5, RbV3Sb5, and CsV3Sb5 suggests an intriguing entanglement of electronic order and superconductivity. However, the microscopic origin of CDW, a key to understanding the superconducting mechanism and its possible topological nature, remains elusive. Here, we report angle-resolved photoemission spectroscopy of KV3Sb5 and demonstrate a substantial reconstruction of Fermi surface in the CDW state that accompanies the formation of small three-dimensional pockets. The CDW gap exhibits a periodicity of undistorted Brillouin zone along the out-of-plane wave vector, signifying a dominant role of the in-plane inter-saddle-point scattering to the mechanism of CDW. The characteristics of experimental band dispersion can be captured by first-principles calculations with the inverse star-of-David structural distortion. The present result indicates a direct link between the low-energy excitations and CDW, and puts constraints on the microscopic theory of superconductivity in alkali-metal kagome lattices. 

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Three-dimensional energy gap and origin of charge-density wave in kagome superconductor KV3Sb5

Gas cluster ion beam (GCIB) sputtering has a high potential for obtaining clean and flat surfaces on materials without causing structural or compositional damage. We have developed an Ar cluster GCIB system for surface preparation in angle-resolved photoemission spectroscopy (ARPES). The constructed GCIB system is compatible with ultrahigh vacuum and achieves a beam current of 10 µA. We examined the usefulness of our GCIB system for high surface-sensitive ARPES measurements by applying it to several representative materials, e.g., Sb, GaAs, and Te. The results show that the constructed GCIB system is very useful for preparing a clean flat surface on crystals, widening opportunities for precise ARPES measurements for materials whose crystal surfaces or orientations are hardly obtained by a simple cleaving method.

Development of Ar gas cluster ion beam system for surface preparation in angle-resolved photoemission spectroscopy.

We have performed micro-/nanofocused angle-resolved photoemission spectroscopy (ARPES) on cleaved single-crystal surfaces of bismuth to clarify the spatially resolved electronic states. While the dominant area of the cleaved surface was found to display the well-known Rashba-spin-split surface state with the (111)-surface origin, the steplike region with a typical width of $\ensuremath{\sim}10\text{--}20$ $\textmu{}\mathrm{m}$ shows distinctly different band structure and fermiology originating from the hard-to-cleave (100) surface. This unexpected mixture of the (100)-derived electronic states in a tiny area of the cleaved (111) surface is attributed to the crystal planes separated by a twin boundary, as supported by laser microscopy and electron backscatter diffraction measurements. The present study paves a pathway toward investigating electronic states associated with inhomogeneities and coexisting phases of hard-to-cleave crystal planes and complex materials by spatially resolved ARPES, making this technique a powerful method to investigate the interplay between local electronic states and crystal structures when combined with structural characterization techniques. 

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Ayumi Moriya

Papers

Three-dimensional energy gap and origin of charge-density wave in kagome superconductor KV3Sb5

Development of Ar gas cluster ion beam system for surface preparation in angle-resolved photoemission spectroscopy.

Visualizing crystal twin boundaries of bismuth by high-spatial-resolution ARPES

Fermiology of a topological line-nodal compound CaSb2 and its implication to superconductivity: Angle-resolved photoemission study