Charge density wave order in kagome metal AV$_3$Sb$_5$ (A= Cs, Rb, K)

Abstract

We employ polarization-resolved electronic Raman spectroscopy and density functional theory to study the primary and secondary order parameters, as well as their interplay, in the charge density wave (CDW) state of the kagome metal AV3Sb5. Previous x-ray diffraction data at 15 K established that the CDW order in CsV3Sb5 comprises of a 2 × 2 × 4 structure: one layer of inverse-starof-David and three consecutive layers of star-of-David pattern. We analyze the lattice distortions based the 2 × 2 × 4 structure at 15 K, and find that U1 lattice distortion is the primary-like (leading) order parameter while M + 1 and L − 2 distortions are secondary-like order parameters for Vanadium displacements. This conclusion is confirmed by the calculation of bare susceptibility χ 0 (q) that shows a broad peak at around qz = 0.25 along the hexagonal Brillouin zone face central line (Uline). We also identify several phonon modes emerging in the CDW state, which are lattice vibration modes related to V and Sb atoms as well as alkali atoms. The detailed temperature evolution of these modes' frequencies, half-width-at-half-maximums, and integrated intensities support a phase diagram with two successive structural phase transitions in CsV3Sb5: the first one with a primarylike order parameter appearing at TS = 94 K and the second isostructural one appearing at around T * = 70 K. Furthermore, the T -dependence of the integrated intensity for these modes show two types of behavior below TS: the low-energy modes show a plateau-like behavior below T * while the high-energy modes monotonically increase below TS. These two behaviors are captured by Landau free energy model incorporating the interplay between the primary-like and the secondarylike order parameters via trilinear coupling. Especially, the sign of the trilinear term that couples order parameters with different wave-vectors determines whether the primary-like and secondarylike order parameters cooperate or compete with each other, thus determining the shape of the T -dependence of the intensities of Bragg peak in x-ray data and the amplitude modes in Raman data below TS. These results provide an accurate basis for studying the interplay between multiple CDW order parameters in kagome metal systems. I. INTRODUCTIONKagome lattice is a model system to study the electronic and magnetic properties [1,2]. The corner shared triangle network of the kagome lattice enables three sublattice interference, which give rise to a variety of exotic physics, for example, flat bands, van Hove singularities, Dirac-dispersions in its electronic structure, frustrated magnetism, to name a few. Various electronic orders such as charge/spin density wave order, charge bond order, chiral flux order, nematic order, and superconductivity are under rigorous investigations [3][4][5][6][7][8][9][10][11][12][13][14][15][16].Recently, a three-dimensional charge density wave (CDW) order, which coexists with superconductivity (SC) at low temperatures, was discovered in AV 3 Sb 5 (A= Cs, Rb, K) kagome metals [Fig. 1 ...

Charge order breaks time-reversal symmetry in CsV$_3$Sb$_5$

“…a 2×2×4 configuration) are also unstable, expanding the landscape of possible CDW configurations even further. 58 It is important to note, however, that these non-spinpolarized first-principles calculations that do not take spin-orbit coupling into account refer only to the real component of the complex CDW order parameter. As such, they do not capture the role of orbital currents.…”

Electronic properties of correlated kagomé metals AV3Sb5 (A = K, Rb, and Cs): A perspective

“…62 Thickness-dependent Raman spectroscopy measurements on CsV 3 Sb 5 63 demonstrate enhanced changes in phonon properties as the thickness decreases, which highlights large electron-phonon coupling. More recently, studies from temperature-dependent x-ray diffraction, 64,65 polarization-resolved electronic Raman spectroscopy, 66 and ARPES 67 reveal the existence of a 2 Â 2 Â 4 superstructure in CsV 3 Sb 5 at higher temperatures in contrast to the 2 Â 2 Â 2 superstructure at lower temperatures. Although the temperature values do not agree between these studies, the evidence of this superstructure reveals a change in the stacking of the V 3 Sb 5 layers along the c axis, which may explain the two successive phase transitions above 60 K and different temperature scales in the magneto-transport data.…”

Charge density wave order and fluctuations above T$_{CDW}$ and below superconducting T$_c$ in the kagome metal CsV$_{3}$Sb$_{5}$

“…The observation of this feature in the OP (H c) susceptibility measurement alone would seem to be consistent with this argument. Nonetheless, a recent polarization-resolved electronic Raman spectroscopy study as well as x-ray results combined with the group theoretical analysis suggest that the uniaxial charge modulation below 60 K may not be a bulk effect [15].…”

“…Focusing on the case of CsV 3 Sb 5 , several recent studies have investigated its electronic ordering instability, a CDW that is associated with a magnetic susceptibility anomaly at T CDW = 94 K [14][15][16][17]. Somewhat surprisingly the CDW order in CsV 3 Sb 5 is three-dimensional [3,5,8,[18][19][20][21], which means that there are electron correlations not only in the kagome plane (ab-plane), but also between the kagome layers, along the c-axis.…”