Fermi surface instabilities in electronic Raman scattering of the metallic kagome lattice CsV3Sb5

Understanding the link between a charge density wave (CDW) instability and superconductivity is a central theme of the 2D metallic kagome compounds A V 3 Sb 5 ( A =K, Rb, and Cs). Using polarization-resolved electronic Raman spec- troscopy, we shed light on Fermi surface ﬂuctuations and electronic instabili- ties. We observe a quasielastic peak (QEP) whose spectral weight is progres- sively enhanced towards the superconducting transition. The QEP temperature- dependence reveals a steep increase in coherent in-plane charge correlations within the charge-density phase. In contrast, out-of-plane charge ﬂuctuations 32 remain strongly incoherent across the investigated temperature range. In-plane phonon anomalies appear at T ∗ ∼ 50 K in addition to right below T CDW ∼ 95 K, 34 while showing no apparent evidence of reduced symmetry at low temperatures. In conjunction with the consecutive phonon anomalies within the CDW state, 36 our electronic Raman data unveil additional electronic instabilities that persist down to the superconducting phase, thereby oﬀering a superconducting mecha- nism.

Understanding the link between a charge density wave (CDW) instability 25 and superconductivity is a central theme of the 2D metallic kagome compounds 26 AV 3 Sb 5 (A=K, Rb, and Cs). Using polarization-resolved electronic Raman spec-27 troscopy, we shed light on Fermi surface fluctuations and electronic instabili-28 ties. We observe a quasielastic peak (QEP) whose spectral weight is progres-29 sively enhanced towards the superconducting transition. The QEP temperature-30 dependence reveals a steep increase in coherent in-plane charge correlations 31 within the charge-density phase. In contrast, out-of-plane charge fluctuations 32 remain strongly incoherent across the investigated temperature range. In-plane 33 phonon anomalies appear at T * ∼ 50 K in addition to right below T CDW ∼ 95 K, 34 while showing no apparent evidence of reduced symmetry at low temperatures. 35 In conjunction with the consecutive phonon anomalies within the CDW state,  The sought-after many-body states in kagome materials include topological superconduc-43 tivity, unconventional charge density wave (CDW), fractional quantum Hall, and Majorana 44 fermions 1-9 . 45 The recently discovered kagome metals AV 3 Sb 5 (A=K, Rb, and Cs; P 6/mmm space 46 group) have opened a new avenue toward establishing the relationship between CDW, 47 anomalous Hall effect (AHE), and superconductivity (SC) 10 . In this V-based kagome family, 48 an alkali metal layer and a V 3 Sb 5 layer are alternately stacked, forming quasi-2D kagome 49 layers of the V ions. CsV 3 Sb 5 features Z 2 band topology and a two-stage symmetry break- b Raman spectra measured in three distinct symmetry channels A 1g +E 2g , E 2g , and E 1g at two temperatures T = 300 K and 5 K. The symbols mark symmetry-allowed optical phonons and a broad electronic background (green pentagon).
transition and the latter QEP pertains to a long-wavelength dynamical electronic response.

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The in-plane QEP forms a maximum at 2.5 meV, while the out-of-plane QEP is centered 86 around zero energy. The difference of the QEP maximum between the in-plane and out-of-87 plane channels signifies anisotropic electronic scattering processes.

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Besides, we observe two Raman-active A 1g and E 2g phonons at 17.9 meV and 14.7 meV, 89 respectively, for in-plane scattering geometries. In the out-of-plane configuration, a single 90 E 1g mode appears at 19.2 meV, in accordance with the Raman tensors (see Methods). We 91 further note that a weak remnant of the A 1g phonon can be seen in the E 1g channel (the 92 triangle in brackets). Since a fresh cut along the c axis was performed at a random in-plane 93 orientation, a finite leakage from the A 1g channel might be inevitable. This is contrasted by 94 no leakage of the E 1g phonon in our in-plane measurements. b Raman conductivity χ ′′ (ω)/ω measured between 5 K and 300 K in an in-plane scattering channel. as the temperature is lowered through T CDW . Overall, the divergent or steady increase of 112 χ ′′ (ω, T ) below T CDW , depending on the scattering channels, alludes to a secondary electronic 113 instability of the pre-existing CDW ordered state and anisotropic scattering mechanism. Raman susceptibility χ dyn at zero frequency using the Kramers-Kronig relation 39 : χ dyn (T ) allows us to access dynamic electronic fluctuations for a given symmetry channel, (left panel Fig. 3d) and at T = 80 K (right panel Fig. 3d). Within our signal-noise ratio, This leads to a total of three Raman-active modes A 1g + E 1g + E 2g , with their corresponding 236 Raman tensors The temperature dependence of the phonon energies has been approximated by a cubic 239 anharmonic, second-order model 44 : where ω 0 is the bare phonon energy at T = 0, and A is a fitting constant.

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In metals electronic Raman scattering probes the long wavelength dynamical charge re-   in the in-plane polarization over a range of 0 • − 180 • at T = 5 K (i.e., close to T c ), at T = 80 373 K (i.e., below T CDW ), and at T = 300 K (T ≫ T CDW ). As seen from these three plots, 374 we cannot resolve rotational symmetry breaking for phonons, charge-density-wave modes, 375 as well as for electronic Raman scattering. Our angular variation data demonstrate that 376 s-wave-like symmetry is largely retained for the electronic phases, while alluding to a subtle