Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1–4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity. An unconventional chiral charge order is observed in a kagome superconductor by scanning tunnelling microscopy. This charge order has unusual magnetic tunability and intertwines with electronic topology.

Unconventional chiral charge order in kagome superconductor KV3Sb5.

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

Author(s): Wang, Z; Jiang, YX; Yin, JX; Li, Y; Wang, GY; Huang, HL; Shao, S; Liu, J; Zhu, P; Shumiya, N; Hossain, MS; Liu, H; Shi, Y; Duan, J; Li, X; Chang, G; Dai, P; Ye, Z; Xu, G; Wang, Y; Zheng, H; Jia, J; Hasan, MZ; Yao, Y | Abstract: Kagome superconductors with TC up to 7 K have been discovered for over 40 y. Recently, unconventional chiral charge order has been reported in kagome superconductor KV3Sb5, with an ordering temperature of one order of magnitude higher than the TC. However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV3Sb5, and the electronic nature of the chirality remains elusive. In this paper, we report the observation of electronic chiral charge order in CsV3Sb5 via scanning tunneling microscopy (STM). We observe a 2 × 2 charge modulation and a 1 × 4 superlattice in both topographic data and tunneling spectroscopy. 2 × 2 charge modulation is highly anticipated as a charge order by fundamental kagome lattice models at van Hove filling, and is shown to exhibit intrinsic chirality. We find that the 1 × 4 superlattices form various small domain walls, and can be a surface effect as supported by our first-principles calculations. Crucially, we find that the amplitude of the energy gap opened by the charge order exhibits real-space modulations, and features 2 × 2 wave vectors with chirality, highlighting the electronic nature of the chiral charge order. STM study at 0.4 K reveals a superconducting energy gap with a gap size 2Δ=0.85meV, which estimates a moderate superconductivity coupling strength with 2Δ/kBTC=3.9. When further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity.

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Electronic nature of chiral charge order in the kagome superconductor Cs V 3 Sb 5

The kagome lattice provides a fascinating playground to study geometrical frustration, topology and strong correlations. The newly discovered kagome metals AV3Sb5 (where A can refer to K, Rb or Cs) exhibit phenomena including topological band structure, symmetry-breaking charge-density waves and superconductivity. Nevertheless, the nature of the symmetry breaking in the charge-density wave phase is not yet clear, despite the fact that it is crucial in order to understand whether the superconductivity is unconventional. In this work, we perform scanning birefringence microscopy on all three members of this family and find that six-fold rotation symmetry is broken at the onset of the charge-density wave transition in all these compounds. We show that the three nematic domains are oriented at 120° to each other and propose that staggered charge-density wave orders with a relative π phase shift between layers is a possibility that can explain these observations. We also perform magneto-optical Kerr effect and circular dichroism measurements. The onset of both signals is at the transition temperature, indicating broken time-reversal symmetry and the existence of the long-sought loop currents in that phase. The interplay between superconductivity that might break time-reversal symmetry and charge order is a key issue in kagome materials. Now, optical measurements show that spatial and time-reversal symmetries are broken at the onset of charge order. 

/pdf/three-state-nematicity-and-magneto-optical-kerr-effect-in-10sa03ht.pdf

Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors

$A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) is a novel kagome superconductor coexisting with the charge density wave (CDW) order. Identifying the structure of the CDW order is crucial for understanding the exotic normal state and superconductivity in this system. Here, we report $^{51}$V nuclear magnetic resonance (NMR) and $^{121/123}$Sb nuclear quadrupole resonance (NQR) studies on kagome-metal CsV$_3$Sb$_5$. Below the CDW transition temperature $T_\textrm{CDW} \sim$ 98 K, an abrupt change of spectra was observed, indicating that the transition is of the first order. By further analysing the spectra, we find that the CDW order is commensurate. And most remarkably, the obtained experimental results suggest that the charge modulation of the CDW order is of star-of-David pattern and accompanied by an additional charge modulation in bulk below $T^* \sim$ 40 K. Our results revealing the unconventional CDW order provide new insights into $A$V$_3$Sb$_5$. 

https://www.nature.com/articles/s41535-022-00437-7.pdf

Possible star-of-David pattern charge density wave with additional modulation in the kagome superconductor CsV3Sb5

Kagome superconductors with TC up to 7K have been discovered over 40 years. Recently, unconventional chiral charge order has been reported in kagome superconductor KV3Sb5, with an ordering temperature of one order of magnitude higher than the TC. However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV3Sb5, and the electronic nature of the chirality remains elusive. In this letter, we report the observation of electronic chiral charge order in CsV3Sb5 via scanning tunneling microscopy (STM). We observe a 2x2 charge modulation and a 1x4 superlattice in both topographic data and tunneling spectroscopy. 2x2 charge modulation is highly anticipated as a charge order by fundamental kagome lattice models at van Hove filling, and is shown to exhibit intrinsic chirality. We find that the 1x4 superlattices forms various small domain walls, and can be a surface effect as supported by our first-principles calculations. Crucially, we find that the amplitude of the energy gap opened by the charge order exhibits real space modulations, and features 2x2 wave vectors with chirality. Our new results point to the electronic nature of the chiral charge order.

Electronic nature of chiral charge order in kagome superconductor CsV3Sb5

Deposition of Bi on InSb(111)B reveals a striking Sierpinski-triangle (ST)-like structure in Bi thin films. Such a fractal geometric topology is further shown to turn off the intrinsic electronic topology in a thin film. Relaxation of a huge misfit strain of about 30% to 40% between Bi adlayer and substrate is revealed to drive the ST-like island formation. A Frenkel-Kontrova model is developed to illustrate the enhanced strain relief in the ST islands offsetting the additional step energy cost. Besides a sufficiently large tensile strain, forming ST-like structures also requires larger adlayer-substrate and intra-adlayer elastic stiffnesses, and weaker intra-adlayer interatomic interactions.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1915&context=ameslab_manuscripts

Sierpiński Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Kagome superconductors with TC up to 7K have been discovered over 40 years. In this work, we report our crystal growth, transport, and scanning tunneling microscopy (STM) study of the kagome superconductor CsV3Sb5. We have grown large single crystals, which show transport behaviors including a charge order below 90K with an unusual Hall response, and superconductivity below 2.5K. A fundamental kagome lattice model often predicts a 2x2 charge order. STM study at 4.2K confirms the 2x2 charge order and reveals additional 1x4 superlattices. On defect-free areas, the 2x2 charge order displays intrinsic chirality that can be related to the unusual Hall response, while defects can induce extrinsic effects. The 1x4 superlattices form various small domains, and are likely of surface origin whose relationship with the underlying kagome lattice is unclear. STM study at 0.4K reveals a superconducting energy gap with a gap size 2{\Delta}=0.85meV, which estimates a moderate superconductivity coupling strength with 2{\Delta}/kBTC=3.9. When further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity. Finally, we discuss the tantalizing relevance of the chiral kagome charge order with Haldane model and Varma model for orbital currents.

Anomalous transport and chiral charge order in kagome superconductor CsV3Sb5

Moire superlattice has recently been found in topological insulators, which can lead to periodic modulation on the electronic structure. In this work, we report the low-temperature scanning tunneling microscopy study of Sb2Te3 films grown on graphitized 4H-SiC. We find that substrate temperature can strongly influence the rotation angles between Sb2Te3 film and graphene substrate. Three kinds of moire patterns are observed at the first quintuple layer Sb2Te3 film under different substrate temperatures. One shows complicated patterns with a rotation angle of nearly 0° relative to the substrate, another just exhibits simple 1 × 1 structure with a rotation angle of 30°. Other rotation angle like 8.2° is observed at higher substrate temperature as well, which is relatively rare. Comparison of the dI/dV curves from Sb2Te3 films with different moire patterns indicates that the superstructure can offer degrees of freedom in tailoring electronic structure. This work may stimulate the further study on the moire modulation to the electronic properties of topological insulators.

Haili Huang

Papers

Electronic nature of chiral charge order in kagome superconductor CsV3Sb5

Sierpiński Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Anomalous transport and chiral charge order in kagome superconductor CsV3Sb5

Moiré-pattern-modulated electronic structures in Sb2Te3/graphene heterostructure