[Paper Review] The effect of the interlayer ordering on the Fermi surface of Kagome superconductor CsV$_3$Sb$_5$ revealed by quantum oscillations

Christopher Broyles, David Graf+3 more|arXiv (Cornell University)|Sep 2, 2022

Quantum, superfluid, helium dynamics4 citations

TL;DR

This study uses high-field quantum oscillation measurements to demonstrate that the Fermi surface of the Kagome superconductor CsV₃Sb₅ is dramatically modified by interlayer ordering of Star-of-David (SD) and inverse-SD (ISD) structures. The observed number of quantum oscillation frequencies exceeds predictions from density functional theory (DFT) calculations based on isolated SD or ISD distortions, providing strong evidence that the 2×2×4 superlattice modulation along the c-axis fundamentally reshapes the Fermi surface.

ABSTRACT

The connection between unconventional superconductivity and charge density waves (CDW) has intrigued the condensed matter community and found much interest in the recently discovered superconducting Kagome family of AV$_3$Sb$_5$ (A = K, Cs, Rb). Xray diffraction and Raman spectroscopy measurements established that the CDW order in CsV$_3$Sb$_5$ comprises of a 2x2x4 structure with stacking of layers of star-of-David (SD) and inverse-star-of-David (ISD) pattern along the $c$-axis direction. Such interlayer ordering will induce a vast normalization of the electronic ground state; however, it has not been observed in Fermi surface measurements. Here we report quantum oscillations of CsV$_3$Sb$_5$ using tunnel diode oscillator frequency measurements. We observed a large number of frequencies, many of which were not reported. The number of frequencies can not be explained by DFT calculations when only SD or ISD distortion is considered. Instead, our results are consistent with calculations when interlayer ordering is taken into account, providing strong evidence that CDW phase of CsV$_3$Sb$_5$ has complicated structure distortion which in turn has dramatic effects on the Fermi surface properties.

Motivation & Objective

• To resolve the discrepancy between observed quantum oscillation frequencies and theoretical predictions in CsV₃Sb₅'s Fermi surface.
• To investigate the impact of interlayer stacking of SD and ISD structures on electronic structure and Fermi surface topology.
• To determine whether the complex Fermi surface observed in quantum oscillation experiments can be explained by a 2×2×4 superlattice modulation.
• To test whether interlayer ordering, previously inferred from XRD and Raman spectroscopy, leaves a detectable signature in quantum oscillation data.
• To clarify the role of CDW-induced structural distortions in modifying electronic properties in Kagome superconductors.

Proposed method

• Performed tunnel diode oscillator (TDO) frequency measurements on high-quality CsV₃Sb₅ single crystals under magnetic fields up to 41.5 T.
• Acquired quantum oscillation data at temperatures from 0.59 K to 30 K to probe the Fermi surface topology.
• Conducted fast Fourier transform (FFT) analysis on the TDO frequency data to extract quantum oscillation frequencies.
• Compared observed frequencies with DFT calculations based on isolated SD or ISD distortions and with predictions from a 2×2×4 superlattice model.
• Used noise subtraction and field-inversion analysis to improve accuracy of effective mass and frequency fitting.
• Evaluated the presence of higher harmonics and independent orbits by comparing frequency patterns across different field ranges.

Experimental results

Research questions

• RQ1 Can the large number of observed quantum oscillation frequencies in CsV₃Sb₅ be explained by DFT calculations assuming only SD or ISD distortions?
• RQ2 Does the interlayer stacking of SD and ISD layers—specifically a 2×2×4 superlattice—produce a Fermi surface consistent with experimental quantum oscillation data?
• RQ3 Are the newly observed frequencies in the 500–1000 T and 1200–1800 T ranges harmonics of lower-frequency orbits or independent Fermi surface pockets?
• RQ4 Why do certain frequencies persist in bulk samples despite being previously reported only in thin flakes, and what does this imply about their origin?
• RQ5 To what extent does interlayer ordering in the CDW phase significantly renormalize the electronic ground state and Fermi surface structure?

Key findings

• A total of 14 distinct quantum oscillation frequencies were observed in a single measurement, with several not previously reported.
• The number and pattern of observed frequencies cannot be explained by DFT calculations assuming only SD or ISD distortions, indicating a need for a more complex structural model.
• The observed frequencies show strong qualitative agreement with theoretical predictions based on a 2×2×4 superlattice structure, providing direct evidence for interlayer SD/ISD ordering.
• Six previously unreported frequencies in the 1200–1800 T range are not harmonics of lower-frequency orbits but correspond to independent Fermi surface pockets.
• The presence of similar high-frequency modes in bulk samples, despite their absence in earlier studies on thin flakes, suggests these features are intrinsic and not due to oxidation or hole doping.
• The results demonstrate that interlayer ordering in the CDW phase of CsV₃Sb₅ induces a substantial reconstruction of the Fermi surface, beyond what is predicted by single-layer distortions.