Spin-orbit coupling induced degeneracy in the anisotropic unconventional superconductor ${\mathrm{UTe}}_{2}$

Spin-orbit coupling induced degeneracy in the anisotropic unconventional superconductor ${UTe}_{2}$

Alexander B. Shick and Warren E. Pickett

Phys. Rev. B 100, 134502 – Published 4 October 2019

Abstract

The orthorhombic uranium dichalcogenide ${UTe}_{2}$ displays superconductivity below 1.7 K, with the anomalous feature of retaining 50% of normal state (ungapped) carriers, according to heat capacity data from two groups. Incoherent transport that crosses over from above 50 K toward a low-temperature, Kondo lattice Fermi liquid regime indicates strong magnetic fluctuations and the need to include correlation effects in theoretical modeling. We report density functional theory plus Hubbard $U$ ( $DFT + U$ ) results for ${UTe}_{2}$ to provide a platform for modeling its unusual behavior, focusing on ferromagnetic (FM, time-reversal breaking) long-range correlations along the $\hat{a}$ axis as established by magnetization measurements and confirmed by our calculations. States near the Fermi level are dominated by the $j = \frac{5}{2}$ configuration, with the $j_{z} = \pm \frac{1}{2}$ sectors being effectively degenerate and half-filled. Unlike the small-gap insulating nonmagnetic electronic spectrum, the FM Fermi surfaces are large (strongly metallic) and display low-dimensional features, reminiscent of the FM superconductor ${UGe}_{2}$ .

Received 21 June 2019
Revised 3 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.134502

Physics Subject Headings (PhySH)

Multiband superconductivity Spin-orbit coupling Spin-triplet pairing

Unconventional superconductors

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

Warren E. Pickett ^*

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

^*pickett@physics.ucdavis.edu

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Vol. 100, Iss. 13 — 1 October 2019

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Figure 1
Total and projected densities of states/eV (per unit cell) for nonmagnetic ${UTe}_{2}$ from the local spin density approximation plus Hubbard $U$ [LSDA $+$ $U$ (OP)] functional, showing the total (black) and projections for U $5 f$ (blue) and Te $5 p$ (magenta). The $I m m m {UTe}_{2}$ crystal structure is shown in the inset: blue spheres are U, and magenta spheres are Te. Note that the states near the Fermi level $E_{F} = 0$ are entirely U $5 f$ in character.
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Figure 2
The band structure from nonmagnetic $LSDA + U$ (OP) calculations, which is essentially unchanged from the LSDA bands (the high-symmetry $k$ points $Γ [0, 0, 0], X [π / a, 0, 0], U [π / a, 0, π / c], R [π / a, π / b, π / c], S [π / a, π / b, 0], Y [0, π / b, 0]$ [23] were used). Without magnetism there is a 13-meV gap. The colors simply distinguish the bands. The circle size, which indicates the amount of $f$ character of the eigenstates, is uniform in this region because the states are uniformly and almost totally U $5 f$ in character, consistent with Fig. 1.
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Figure 3
Comparison of the density of states for ferromagnetic alignment (metallic) with that of the gapped nonmagnetic state, on a fine energy scale. The 13-meV gap is thoroughly washed out when magnetic moments are allowed to emerge and align.
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Figure 4
Total (a) and $f$ -projected (b) densities of states for ferromagnetic ${UTe}_{2}$ from $LSDA + U$ (OP) functional, with the moment along the easy $\hat{a}$ axis. In panel (a) the majority spin $5 f$ states are plotted upward and the minority spin states are plotted downward, both in red. In panel (b) the $j_{z}$ -decomposed DOS for both $j = \frac{5}{2}$ , plotted in red, and $j = \frac{7}{2}$ , shown in blue, are displayed. Occupied states arise almost entirely from $j = \frac{5}{2}$ states with negative $j_{z}$ . Note the orderly progression in energy of both $\frac{5}{2}$ and $\frac{7}{2}$ manifolds.
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Figure 5
Fermi surface for FM order, from $LSDA + U$ (OP), centered at the $Γ$ point. The Fermi surface is large and multisheeted, with a nesting feature for FS-3 near (0, $\frac{π}{b}$ , 0). FS-1 is in the center; FS-2 parallels FS-3 along parts of its length. The low velocities, given by the colorbar, extend over at least an order of magnitude, up to nearly 2 eV/Å ( $\sim 2.5 \times 10^{7}$ cm/s).
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Figure 6
The $5 f$ fat-band structure of nonmagnetic ${UTe}_{2}$ from $LDA + U$ (OP) calculations. The circle size indicates the amount of $j = \frac{5}{2}$ and $m_{j}$ character in the bands, as indicated. The two contributions to the $j_{z} = - \frac{5}{2}$ character are quite different; the differences in the other two cases isare not so pronounced. Note that the full energy range is only 300 meV.
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Physical Review B

covering condensed matter and materials physics

Spin-orbit coupling induced degeneracy in the anisotropic unconventional superconductor ${UTe}_{2}$

Alexander B. Shick and Warren E. Pickett

Phys. Rev. B 100, 134502 – Published 4 October 2019

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Physical Review B

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Spin-orbit coupling induced degeneracy in the anisotropic unconventional superconductor UTe2

Alexander B. Shick and Warren E. Pickett

Phys. Rev. B 100, 134502 – Published 4 October 2019

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Spin-orbit coupling induced degeneracy in the anisotropic unconventional superconductor ${UTe}_{2}$