${\mathrm{UTe}}_{2}$: A nearly insulating half-filled $j=\frac{5}{2} 5{f}^{3}$ heavy-fermion metal

${UTe}_{2}$ : A nearly insulating half-filled $j = \frac{5}{2} 5 f^{3}$ heavy-fermion metal

Alexander B. Shick, Shin-ichi Fujimori, and Warren E. Pickett

Phys. Rev. B 103, 125136 – Published 16 March 2021

Abstract

Correlated band theory implemented as a combination of density functional theory with exact diagonalization [ $DFT + U$ (ED)] of the Anderson impurity term with Coulomb repulsion $U$ in the open 14-orbital $5 f$ shell is applied to ${UTe}_{2}$ . The small gap for $U = 0$ , evidence of the half-filled $j = \frac{5}{2}$ subshell of $5 f^{3}$ uranium, is converted for $U = 3 eV$ to a flat-band semimetal with small heavy-carrier Fermi surfaces that will make properties sensitive to pressure, magnetic field, and off-stoichiometry, as observed experimentally. Two means of identification from the Green's function give a mass enhancement of the order of 12 for already heavy (flat) bands, consistent with the common heavy-fermion characterization of ${UTe}_{2}$ . The predicted Kondo temperature around 100 K matches the experimental values from resistivity. The electric field gradients for the two Te sites are calculated by $DFT + U$ (ED) to differ by a factor of 7, indicating a strong site distinction, while the anisotropy factor $η = 0.18$ is similar for all three sites. The calculated uranium moment ${〈M^{2}〉}^{1 / 2}$ of $3.5 μ_{B}$ is roughly consistent with the published experimental Curie-Weiss values of 2.8 and $3.3 μ_{B}$ (which are field-direction dependent), and the calculated separate spin and orbital moments are remarkably similar to Hund's rule values for an $f^{3}$ ion. The $U = 3 eV$ spectral density is compared with angle-integrated and angle-resolved photoemission spectra, with agreement that there is strong $5 f$ character at, and for several hundred meV below, the Fermi energy. Our results support the picture that the underlying ground state of ${UTe}_{2}$ is that of a half-filled $j = \frac{5}{2}$ subshell with two half-filled $m_{j} = \pm \frac{1}{2}$ orbitals forming a narrow gap by hybridization and then driven to a conducting state by configuration mixing (spin-charge fluctuations). ${UTe}_{2}$ displays similarities to ${UPt}_{3}$ with its $5 f$ -dominated Fermi surfaces rather than a strongly localized Kondo lattice system.

Received 27 September 2020
Accepted 22 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.125136

Physics Subject Headings (PhySH)

Electrical conductivity Electronic structure Fermi surface First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Alexander B. Shick^*

Institute of Physics, Czech Academy of Science, Na Slovance 2, CZ-18221 Prague, Czech Republic

Shin-ichi Fujimori

Materials Sciences Research Center, Japan Atomic Energy Agency, Sayo, Hyogo 679-5148, Japan

Warren E. Pickett ^†

Department of Physics, University of California, Davis, California 95616, USA

^*shick@fzu.cz
^†pickett@physics.ucdavis.edu

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Vol. 103, Iss. 12 — 15 March 2021

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Figure 1
(a) Projected densities of states/eV (per unit cell) for nonmagnetic ${UTe}_{2}$ from the $DFT + U$ (OP) functional ( $U = J = 0.5 eV$ ), showing the projections for $U 5 f$ (blue) and Te $5 p$ (magenta). Inset: the orthorhombic $I m m m {UTe}_{2}$ crystal structure. (b) The $j = \frac{5}{2}$ and $\frac{7}{2}$ projected hybridization functions $Δ (z) = \frac{1}{π n_{f}} Im Tr [G_{0}^{- 1} (z)]$ (eV) obtained from LDA calculations [12]. (c) Total densities of states/eV (per unit cell), for nonmagnetic ${UTe}_{2}$ from the $DFT + U$ (ED) functional. Note that $U = 6 eV$ opens a gap.
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Figure 2
Band structures near the Fermi level $E_{F} = 0$ for unpolarized ${UTe}_{2}$ from (a) the $DFT + U$ (OP) functional, and from the $DFT + U$ (ED) functional for (b) $U = 3 eV$ and (c) $U = 6 eV$ . Note that in (b) for $U = 3 eV$ , a band crossing at $E_{F}$ lies very near the point $X$ . The special $k$ points lie along Cartesian directions: $Γ [0, 0, 0], X [π / a, 0, 0], U [π / a, 0, π / c], R [π / a, π / b, π / c], S [π / a, π / b, 0]$ , and $Y [0, π / b, 0]$ .
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Figure 3
Upper panel: The Fermi surfaces of ${UTe}_{2}$ from $DFT + U$ (ED), for Coulomb $U = 3 eV$ . The colors provide the relative Fermi velocities. The high-symmetry $k$ points are $Γ$ [0,0,0], $X [π / a, 0, 0], U [π / a, 0, π / c], R [π / a, π / b, π / c], S [π / a, π / b, 0]$ , and $Y [0, π / b, 0]$ . Lower panels: the $5 f$ flat-band structure of ${UTe}_{2}$ , with the circle size indicating the amount of $m_{l}, m_{s}, m_{j} = m_{l} + m_{s}$ character in the bands, as labeled.
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Figure 4
Measured angle-integrated photoemission spectrum (green) plotted with the resolution-broadened (120-meV Gaussian) and Fermi-Dirac cutoff (20 K) $DFT + U$ (ED) DOS. The agreement of the onsets below $E_{F}$ reflects flat and heavy bands that become the basis of the heavy-fermion superconductor state. The broadening of the experimental spectrum down to approximately $- 4$ eV is the expected effect of dynamical fluctuations in the uranium $5 f$ shell. The Te DOSs are enhanced by a factor of 5 to reveal possible Te influence on structure in the range of $- 4$ to $- 1$ eV, which is mostly due to single-particle excitations from the $5 f$ shell.
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Figure 5
Upper right panel: Brillouin zone structure of ${UTe}_{2}$ . (a)–(c) ARPES spectra (left) together with the band structure (right) for the designated directions and with energies aligned. The size of the calculated points provides the relative amount of $5 f$ character of the wave function. (a) and (c) provide new data, while (b) is a replot of earlier data [11] of one of the authors to provide clear comparison with our theoretical results. The $k$ -point notations of the orthorhombic pseudozone $Γ [0, 0, 0], X [π / a, 0, 0], U [π / a, 0, π / c], Z [0, 0, π / c], Y [0, π / b, 0]$ , and $Γ^{'} [0, 2 π / b, 0]$ are used in the text.
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Figure 6
Flowchart indicating the main steps in the charge and occupation matrix self-consistent procedure for our $DFT + U$ (ED) implementation. See the description in Appendix pp1. AIM, Anderson impurity model.
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Physical Review B

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${UTe}_{2}$ : A nearly insulating half-filled $j = \frac{5}{2} 5 f^{3}$ heavy-fermion metal

Alexander B. Shick, Shin-ichi Fujimori, and Warren E. Pickett

Phys. Rev. B 103, 125136 – Published 16 March 2021

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UTe2: A nearly insulating half-filled j=52 5f3 heavy-fermion metal

Alexander B. Shick, Shin-ichi Fujimori, and Warren E. Pickett

Phys. Rev. B 103, 125136 – Published 16 March 2021

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${UTe}_{2}$ : A nearly insulating half-filled $j = \frac{5}{2} 5 f^{3}$ heavy-fermion metal