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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We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev's non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κxx due to phonons is much larger than the expected quantized thermal Hall conductance κ q xy = πT 12 k 2 B of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an effective Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length L , where is a thermalization length. We obtain ∼ T −5 for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κxy/κxx ∼ 10 −3 , in α-RuCl3. arXiv:1805.10532v2 [cond-mat.str-el]

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