Abstract
When the ground state of a localized ion is a non-Kramers doublet, such localized ions may carry multipolar moments. For example, ions in a cubic environment would possess quadrupolar and octupolar, but no magnetic dipole, moments. When such multipolar moments are placed in a metallic host, unusual interactions between these local moments and conduction electrons arise, in contrast to the familiar magnetic dipole interactions in the classic Kondo problem. In this work, we consider the interaction between a single quadrupolar-octupolar local moment and conduction electrons with -orbital symmetry as a concrete model for the multipolar Kondo problem. We show that this model can be written most naturally in the spin-orbital entangled basis of conduction electrons. Using this basis, the perturbative renormalization-group (RG) fixed points are readily identified. There are two kinds of fixed points, one for the two-channel Kondo and the other for a novel fixed point. We investigate the nature of the novel fixed point nonperturbatively using non-Abelian bosonization, current algebra, and conformal field theory approaches. It is shown that the novel fixed point leads to a, previously unidentified, non-Fermi liquid state with entangled spin and orbital degrees of freedom, which shows resistivity and diverging specific heat coefficient , with . Our results open up the possibility of myriads of non-Fermi liquid states, depending on the choices of multipolar moments and conduction electron orbitals, which would be relevant for many rare-earth metallic systems.
- Received 26 May 2020
- Revised 31 July 2020
- Accepted 15 September 2020
DOI:https://doi.org/10.1103/PhysRevX.10.041021
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.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In exotic metals known as non-Fermi liquids (NFLs), strong correlation effects between the electrons lead to thermodynamic and electrical behavior that is quite different from conventional metals, where interactions among electrons can be modeled relatively simply. Developing a robust understanding of these anomalous metals is an outstanding challenge to the community, a difficulty compounded by a relative lack of concrete theoretical examples of NFLs. Here, we expand the number of examples by providing and establishing the existence of a novel NFL state.
Our work is based on a classic scenario known as the Kondo problem, where mobile conduction electrons interact with a single localized ionic impurity. In particular, we analyze a case we call the multipolar Kondo problem, where the conduction electrons interact with multipolar moments of the ion. Through mathematical analysis, we find that this interaction leads to temperature-dependent changes in the resistivity and specific heat that are hallmarks of an NFL state. We also discover that this novel NFL is characterized by conduction spin and orbital entanglement.
Our findings are broadly applicable to rare-earth metallic systems with localized multipolar moments, and provide a concrete, solvable model that offers the possibility of a myriad of NFL behaviors, arising from the diversity of multipolar moments and conduction electron-orbital degrees of freedom.
