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The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1–18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene. A study reveals a temperature-dependent cascade of different symmetry-broken electronic states in the kagome superconductor CsV3Sb5, and highlights intriguing parallels between vanadium-based kagome metals and materials exhibiting similar electronic phases.

Cascade of correlated electron states in the kagome superconductor CsV3Sb5.

The search for oxide materials with physical properties similar to the cuprate high Tc superconductors, but based on alternative transition metals such as nickel, has grown and evolved over time. The recent discovery of superconductivity in doped infinite-layer nickelates RNiO2 (R = rare-earth element) further strengthens these efforts.With a crystal structure similar to the infinite-layer cuprates - transition metal oxide layers separated by a rare-earth spacer layer - formal valence counting suggests that these materials have monovalent Ni1+ cations with the same 3d electron count as Cu2+ in the cuprates. Here, we use x-ray spectroscopy in concert with density functional theory to show that the electronic structure of RNiO2 (R = La, Nd), while similar to the cuprates, includes significant distinctions. Unlike cuprates with insulating spacer layers between the CuO2 planes, the rare-earth spacer layer in the infinite-layer nickelate supports a weakly-interacting three-dimensional 5d metallic state. This three-dimensional metallic state hybridizes with a quasi-two-dimensional, strongly correlated state with 3dx2-y2 symmetry in the NiO2 layers. Thus, the infinite-layer nickelate can be regarded as a sibling of the rare earth intermetallics, well-known for heavy Fermion behavior, where the NiO2 correlated layers play an analogous role to the 4f states in rare-earth heavy Fermion compounds. This unique Kondo- or Anderson-lattice-like "oxide-intermetallic" replaces the Mott insulator as the reference state from which superconductivity emerges upon doping.

Electronic structure of the parent compound of superconducting infinite-layer nickelates

Charge-density-wave-driven electronic nematicity in a kagome superconductor

The kagome lattice1, which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders2-8 and, most rarely, to unconventional superconductivity6,9. Recently, charge sensitive probes have indicated that the kagome superconductors AV3Sb5 (A = K, Rb, Cs)9-11 exhibit unconventional chiral charge order12-19, which is analogous to the long-sought-after quantum order in the Haldane model20 or Varma model21. However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV3Sb5. We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV3Sb5 and that the [Formula: see text] ratio (where Tc is the superconducting transition temperature and λab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice. 

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Time-reversal symmetry-breaking charge order in a kagome superconductor

In transition metal compounds, due to the interplay of charge, spin, lattice and orbital degrees of freedom, many intertwined orders exist with close energies. One of the commonly observed states is the so-called nematic electron state, which breaks the in-plane rotational symmetry. This nematic state appears in cuprates, iron-based superconductor, etc. Nematicity may coexist, affect, cooperate or compete with other orders. Here we show the anisotropic in-plane electronic state and superconductivity in a recently discovered kagome metal CsV$_3$Sb$_5$ by measuring $c$-axis resistivity with the in-plane rotation of magnetic field. We observe a twofold symmetry of superconductivity in the superconducting state and a unique in-plane nematic electronic state in normal state when rotating the in-plane magnetic field. Interestingly these two orders are orthogonal to each other in terms of the field direction of the minimum resistivity. Our results shed new light in understanding non-trivial physical properties of CsV$_3$Sb$_5$.

Twofold symmetry of $c$-axis resistivity in topological kagome superconductor CsV$_3$Sb$_5$ with in-plane rotating magnetic field

In transition metal compounds, due to the interplay of charge, spin, lattice and orbital degrees of freedom, many intertwined orders exist with close energies. One of the commonly observed states is the so-called nematic electron state, which breaks the in-plane rotational symmetry. This nematic state appears in cuprates, iron-based superconductor, etc. Nematicity may coexist, affect, cooperate or compete with other orders. Here we show the anisotropic in-plane electronic state and superconductivity in a recently discovered kagome metal CsV3Sb5 by measuring c-axis resistivity with the in-plane rotation of magnetic field. We observe a twofold symmetry of superconductivity in the superconducting state and a unique in-plane nematic electronic state in normal state when rotating the in-plane magnetic field. Interestingly these two orders are orthogonal to each other in terms of the field direction of the minimum resistivity. Our results shed new light in understanding non-trivial physical properties of CsV3Sb5.

Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field.

The newly found superconductivity in infinite-layer nickelate superconducting films has attracted much attention, because their crystalline and electronic structures are similar to high-$T_c$ cuprate superconductors. The upper critical field can provide much information on superconductivity, but detailed experimental data are still lacking in these films. Here we present temperature and angle dependence of resistivity measured under different magnetic fields ($H$) in Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$ thin films. The onset superconducting transition occurs at about 16.2 K at 0 T. Temperature dependent upper critical fields determined by using a criterion very close to the onset transition show a clear negative curvature near the critical transition temperature, which is explained as the consequence of the paramagnetically limited effect on superconductivity. The temperature dependent anisotropy of the upper critical field is obtained from resistivity data, which yields a value decreasing from 3 to 1.2 with lowering temperature. This can be explained by a variable contribution from the orbital limit effect on upper critical field. The angle dependent resistivity at a fixed temperature and different magnetic fields cannot be scaled to one curve, which deviates from the prediction of the anisotropic Ginzburg-Landau theory. However, at low temperatures, the increased resistivity by magnetic field can be scaled by the parameter $H^\beta |\cos\theta|$ ($1<\beta<6$) with $\theta$ the angle enclosed between $c$-axis and the applied magnetic field. As the first detailed study on the upper critical field of the nickelate thin films, our results clearly indicate a small anisotropy and paramagnetically limited effect of superconductivity in nickelate superconductors.

Physical properties revealed by transport measurements on superconducting Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$ thin films

The optical properties of Sn-doped ${\mathrm{Bi}}_{1.1}{\mathrm{Sb}}_{0.9}{\mathrm{Te}}_{2}\mathrm{S}$, the most bulk-insulating topological insulator thus far, have been examined at different temperatures over a broad frequency range. No Drude response is detected in the low-frequency range down to $30\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, corroborating the excellent bulk-insulating property of this material. Intriguingly, we observe a sharp peak at about $2200\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ in the optical conductivity at 5 K. Further quantitative analyses of the line shape and temperature dependence of this sharp peak, in combination with first-principles calculations, suggest that it corresponds to a van Hove singularity arising from Mexican-hat-shaped inverted bands. Such a van Hove singularity is a pivotal ingredient of various strongly correlated phases.

Ying Xiang

Papers

Twofold symmetry of $c$-axis resistivity in topological kagome superconductor CsV$_3$Sb$_5$ with in-plane rotating magnetic field

Twofold symmetry of c-axis resistivity in topological kagome superconductor CsV3Sb5 with in-plane rotating magnetic field.

Physical properties revealed by transport measurements on superconducting Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$ thin films

Van Hove singularity arising from Mexican-hat-shaped inverted bands in the topological insulator Sn-doped Bi 1.1 Sb 0.9 Te 2 S

Physical Properties Revealed by Transport Measurements for Superconducting Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$ Thin Films