The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology, which continues to bear surprises. In this work, using spectroscopic imaging scanning tunneling microscopy, we discover a cascade of different symmetry-broken electronic states as a function of temperature in a new kagome superconductor, CsV3Sb5. At a temperature far above the superconducting transition Tc ~ 2.5 K, we reveal 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-shape spectral gap opening at the Fermi level and an additional breaking of the six-fold rotation symmetry, which persists through the superconducting transition. This rotation 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 V kagome bands. Our experiments reveal a complex landscape of electronic states that can co-exist on a kagome lattice, and provide intriguing parallels to high-Tc superconductors and twisted bilayer graphene.Quantum solids composed of atoms arranged on a lattice of corner-sharing triangles (kagome lattice) are a fascinating playground for the exploration of novel correlated and topological electronic phenomena [1][2][3][4] . Due to their intrinsic geometric frustration, kagome systems are predicted to host to a slew of exotic electronic states [5][6][7][8][9][10][11][12][13][14][15][16][17][18] , such as bond and charge ordering 7,8,10,[16][17][18] , spin liquid phases 5,15 and chiral superconductivity 9,10,17 . The majority of the experimental efforts thus far have focused on transition-metal kagome magnets, for example Co3Sn2S2 [19][20][21][22][23] FeSn 24,25 and Fe3Sn2 26,27 , in which different forms of magnetism dominate the low-temperature electronic ground state. Electronic correlations in the absence of magnetic ordering could in principle favor the emergence of new symmetry-broken electronic states, but this has been difficult to explore in many of the existing kagome materials due to a tendency towards magnetic ordering.

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The asymmetric responses of the system between the external force of right and left directions are called "nonreciprocal". There are many examples of nonreciprocal responses such as the rectification by p-n junction. However, the quantum mechanical wave does not distinguish between the right and left directions as long as the time-reversal symmetry is intact, and it is a highly nontrivial issue how the nonreciprocal nature originates in quantum systems. Here we demonstrate by the quantum ratchet model, i.e., a quantum particle in an asymmetric periodic potential, that the dissipation characterized by a dimensionless coupling constant α plays an essential role for nonlinear nonreciprocal response. The temperature (T ) dependence of the second order nonlinear mobility µ2 is found to be µ2 ∼ T 6/α−4 for α < 1, and µ2 ∼ T 2(α−1) for α > 1, respectively, where αc = 1 is the critical point of the localization-delocalization transition, i.e., Schmid transition. On the other hand, µ2 shows the behavior µ2 ∼ T −11/4 in the high temperature limit. Therefore, µ2 shows the nonmonotonous temperature dependence corresponding to the classical-quantum crossover. The generic scaling form of the velocity v as a function of the external field F and temperature T is also discussed. These findings are relevant to the heavy atoms in metals, resistive superconductors with vortices and Josephson junction system, and will pave a way to control the nonreciprocal responses.

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