Abstract
has recently been reported to be a rare case of a multiphase unconventional superconductor close to a quantum critical point (QCP). Here, we present a comprehensive study of its normal-state properties and of the phase (I) below which preempts superconductivity at . The second-order phase transition at presents signatures in specific heat and thermal expansion but none in magnetization and ac susceptibility, indicating a nonmagnetic origin of phase I. In addition, an upturn of the in-plane resistivity at points to a gap opening at the Fermi level in the basal plane. Thermal expansion indicates a strong-positive-pressure dependence of , , in contrast to the strong-negative-pressure coefficient observed for magnetic order in Ce-based Kondo lattices close to a QCP. Similarly, an in-plane magnetic field shifts to higher temperatures and transforms phase I into another nonmagnetic phase (II) through a first-order phase transition at about 9 T. Using renormalized band-structure calculations, we find that the Kondo effect () leads to substantial mixing of the excited crystalline-electric-field states into the ground state. This allows quadrupolar degrees of freedom in the resulting heavy bands at the Fermi level which are prone to nesting. The huge sensitivity of the quadrupole moment on hybridization together with nesting causes an unprecedented case of phase transition into a quadrupole-density-wave state at a temperature , which explains the nature of phases I and II.
- Received 13 August 2021
- Revised 2 November 2021
- Accepted 16 December 2021
DOI:https://doi.org/10.1103/PhysRevX.12.011023
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Free conduction electrons in a periodic environment, such as a crystalline metal, can organize themselves into ordered states with a spatial modulation of their charge or magnetic dipoles. Such ordered states are called charge-density waves and spin-density waves, respectively. Basic electrodynamics allows for patterns more complex than a point charge or a magnetic dipole, such as electric quadrupoles. However, free electrons do not carry quadrupoles and, accordingly, a quadrupole density wave formed by conduction electrons has not been reported yet. Here, we show that exactly such a quadrupole density wave probably occurs in the material .
We determine the thermodynamic and transport properties across the ordering temperature in this material. Several unusual findings point to a quadrupole density wave: the absence of an anomaly in magnetic probes, the increase of the transition temperature with magnetic field, and a transition temperature increase with pressure that we predict from our results. We show that a quadruple density wave can exist in metals in which atomiclike “local” electrons hybridize with conduction electrons. Under these conditions, the quadrupole of the local electrons is partially transferred to the conduction electrons. Our calculations show that is particularly prone to the formation of a quadrupole density wave.
Previous work has shown that this material enters an extraordinary superconducting state with two distinct superconducting phases. Our work raises the question of how the quadrupole density wave is related to this superconducting state.