A DFT + DMFT study of the two-channel quadrupolar Kondo effect in PrV₂Al₂₀

Praseodymium-based cubic 1-2-20 materials like PrV₂Al₂₀ exhibit a strong coupling between Pr 4f states and conduction electrons. They experimentally show traces of a two-channel quadrupolar Kondo effect in competition with quadrupolar ordering and superconductivity [1]. Valence fluctuations on the Pr atom occur between the magnetic quadrupole 4f² Γ₃ doublet and the excited 4f¹ configuration with a dipole Kramers-doublet Γ₇. This specific setup leads to an exotic two-channel quadrupolar Kondo effect, where the channel degree of freedom carries a dipole moment and the Kondo degree of freedom a quadrupolar moment. A quadrupolar analog to the famous Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction principally allows for quadrupolar ordering in competition with the Kondo singlet formation.

We develop a dynamical mean-field theory (DMFT) with a non-crossing approximation (NCA) local impurity solver, that is able to faithfully capture the exotic two-channel Kondo physics in this class of materials, including a momentum-dependent hybridization. This method is then combined with a density functional theory (DFT) calculation, allowing us to quantitatively compare the results to experimental data down to the Kondo regime. Within this approximation, we calculate several temperature dependent quantities: density of states, band structure and magnetic susceptibility.

[1] For review, see: T. Onimaru and H. Kusunose, J. Phys. Soc. Jpn. 85, 082002 (2016)