Quasi-Two-Dimensional Fermi Surfaces and Unitary Spin-Triplet Pairing in the Heavy Fermion Superconductor ${\mathrm{UTe}}_2$

We report first-principles and strongly correlated calculations of the newly discovered heavy fermion superconductor ${\mathrm{UTe}}_2$. Our analyses reveal three key aspects of its magnetic, electronic, and superconducting properties that include (i) a two-leg ladder-type structure with strong magnetic frustrations, which might explain the absence of long-range orders and the observed magnetic and transport anisotropy, (ii) quasi-two-dimensional Fermi surfaces composed of two separate electron and hole cylinders with similar nesting properties as in ${\mathrm{UGe}}_2$, which may potentially promote magnetic fluctuations and help to enhance the spin-triplet pairing, and (iii) a unitary spin-triplet pairing state of strong spin-orbit coupling at zero field, with point nodes presumably on the heavier hole Fermi surface along the $k_x$ direction, in contrast to the previous belief of nonunitary pairing. Our proposed scenario is in excellent agreement with latest thermal conductivity measurement and provides a basis for understanding the peculiar magnetic and superconducting properties of ${\mathrm{UTe}}_2$.

Figure 1

(a) Illustration of the crystal structure of ${\mathrm{UTe}}_2$, showing the two-leg U ladders surrounded by face-shared Te prisms. (b) Four chosen magnetic configurations in a $2\times 1\times 1$ supercell for calculations of the exchange couplings $J_i$ between U ions up to the 3rd nearest neighbors. (c) The calculated magnetic moment of the U ion and the energy differences (per supercell) relative to the lowest energy state as a function of $U$. (d) The derived values of $J_i$ with varying $U$, showing a dominant ferromagnetic (FM) rung coupling $J_1$ and much smaller antiferromagnetic (AFM) couplings $J_2$ on the leg and $J_3$ between ladders at large $U$. The inset illustrates how magnetic frustrations are induced between ladders by their relative shift of half lattice constant $0.5a$ along the $a$ axis.

Figure 2

Comparison of the calculated band structures and density of states with $\mathrm{DFT}+U$ for (a),(b) $U=0$ and (c),(d) $U=7\mathrm{eV}$. The colors represent the contributions from different U or Te orbitals. We see a small semiconducting gap of about 10 meV for $U=0$ and flat metallic bands crossing the Fermi level for $U=7\mathrm{eV}$. In both cases, the total density of states near the Fermi energy is dominated by the $J=5/2$ manifold of the U-$5f$ orbitals. The $J=7/2$ manifold is pushed to higher energies by about 1.0–1.5 eV. The inset shows the high symmetry points in the first Brillouin zone.

Figure 3

(a) The calculated density of states of U $5f$ electrons with self-consistent $\mathrm{DFT}+\mathrm{DMFT}$, showing a sharp quasiparticle peak at 10 K that is suppressed at 200 K. (b) Temperature evolution of the peak height and the imaginary part of the self-energy at the Fermi energy. The temperature derivative of the latter is compared with the measured resistivity [46], showing similar tendency below the coherence temperature of about 50K. (c) and (d) Comparison of the spectral functions at 200 and 10 K. Extremely flat heavy electron and hole bands are seen to emerge in a narrow window around the Fermi energy at low temperature. The background colors reflect the intensity of the total spectral function.

Figure 4

(a) The calculated Fermi surfaces with two separate quasi-2D electron and (heavier) hole cylinders. (b) The predicted quantum oscillation frequencies with field rotating from the $c$ axis to $a$ or $b$ axes for dHvA measurements. (c) Real part of the dynamical susceptibility at zero frequency limit, showing nesting properties along the $k_x$ direction near half of the reciprocal lattice unit (r.l.u.). All data were based on $\mathrm{DFT}+U$ calculations as in Fig. 2 but with $8000\mathbf{k}$ points in order to get a high-quality plot. The color bars represent the value of the Fermi velocity in (a) and the magnitude (arbitrary unit) of the susceptibility in (c). (d) Illustration of the nodal properties of the candidate strong-SOC pairing states, showing point nodes for $B_{2u}$ and $B_{3u}$ representations on the calculated electron and hole Fermi surfaces, respectively. The gap magnitude is zero on the dashed lines given by $k_x=k_y=0$ for $B_{1u}$, $k_x=k_z=0$ for $B_{2u}$, and $k_y=k_z=0$ for $B_{3u}$.