Point-node gap structure of the spin-triplet superconductor ${\mathrm{UTe}}_{2}$

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Point-node gap structure of the spin-triplet superconductor ${UTe}_{2}$

Tristin Metz, Seokjin Bae, Sheng Ran, I-Lin Liu, Yun Suk Eo, Wesley T. Fuhrman, Daniel F. Agterberg, Steven M. Anlage, Nicholas P. Butch, and Johnpierre Paglione

Phys. Rev. B 100, 220504(R) – Published 19 December 2019

Abstract

Low-temperature electrical and thermal transport, magnetic penetration depth, and heat capacity measurements were performed on single crystals of the actinide superconductor ${UTe}_{2}$ to determine the structure of the superconducting energy gap. Heat transport measurements performed with currents directed along both crystallographic $a$ and $b$ axes reveal a vanishingly small residual fermionic component of the thermal conductivity. The magnetic field dependence of the residual term follows a rapid, quasilinear increase consistent with the presence of nodal quasiparticles, rising toward the $a$ -axis upper critical field where the Wiedemann-Franz law is recovered. Together with a quadratic temperature dependence of the magnetic penetration depth up to $T / T_{c} = 0.3$ , these measurements provide evidence for an unconventional spin-triplet superconducting order parameter with point nodes. Millikelvin specific heat measurements performed on the same crystals used for thermal transport reveal an upturn below 300 mK that is well described by a divergent quantum-critical contribution to the density of states (DOS). Modeling this contribution with a $T^{- 1 / 3}$ power law allows restoration of the full entropy balance in the superconducting state and a resultant cubic power law for the electronic DOS below $T_{c}$ , consistent with the point-node gap structure determined by thermal conductivity and penetration depth measurements.

Received 2 August 2019
Revised 26 November 2019

DOI:https://doi.org/10.1103/PhysRevB.100.220504

Physics Subject Headings (PhySH)

Penetration depth Specific heat Spin-triplet pairing Superconducting gap Superconductivity Thermal conductivity

Single crystal materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tristin Metz¹, Seokjin Bae ¹, Sheng Ran^1,2, I-Lin Liu^1,2,3, Yun Suk Eo¹, Wesley T. Fuhrman¹, Daniel F. Agterberg⁴, Steven M. Anlage ^1,3, Nicholas P. Butch^1,2, and Johnpierre Paglione ^1,3,5,*

¹Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
²NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
³Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA
⁴Department of Physics, University of Wisconsin, Milwaukee, Wisconsin 53201, USA
⁵Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8

^*paglione@umd.edu

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Vol. 100, Iss. 22 — 1 December 2019

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Figure 1
Thermal conductivity of ${UTe}_{2}$ samples S1 and S2. (a) Measured thermal conductivity in comparison to the estimated (elastic) charge contribution $L_{0} / ρ$ (solid and dashed lines) determined using the Wiedemann-Franz law and in situ measured electrical resistivities of both samples. $L_{0} / ρ (T)$ is extrapolated below $T_{c}$ here assuming the resistivity follows the Fermi-liquid temperature dependence $ρ = ρ_{0} + A T^{2}$ . (b) and (c) present signatures of the superconducting transition in thermal conductivity measurements for (b) $j ∥ a$ and (c) $j ∥ b$ orientations. The observed increase in $κ / T$ below $T_{c}$ is thought to arise from a decrease in scattering due to the opening of the superconducting gap, and the suppression with increasing magnetic fields due to vortex scattering.
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Figure 2
Low-temperature thermal conductivity of ${UTe}_{2}$ single-crystal samples (a) S1 and (b) S2, measured with heat current applied along crystallographic $a$ and $b$ axes, respectively, and magnetic fields applied along the $a$ axis. The black $\times$ in (a) and (b) represent the converted normal-state charge conductivity $L_{0} / ρ$ measured in situ at 7 T and calculated using the Wiedemann-Franz law. (c) Magnetic field dependence of $T \to 0$ K extrapolated values $[κ_{0} / T \equiv κ (T \to 0) / T]$ taken from the data in (a) and (b). Error bars correspond to uncertainty in the extrapolation from fitting to a power law over different temperature windows. For comparison we include data for the elemental clean-limit fully gapped superconductor Nb [29] and clean-limit nodal superconductors ${UPt}_{3}$ [18] and ${KFe}_{2} {As}_{2}$ [21]. The inset shows a comparison of the detailed low field dependence of $Δ κ (H) / Δ κ_{N} \equiv [κ (H) - κ (0)] / [κ (7 T) - κ (0)]$ measured in the field-sweep mode at 100 mK, with the $T \to 0$ extrapolated values from the main panel. (d) Lorenz ratio $L / L_{0}$ calculated using the ratio of measured quantities $κ ρ / T$ at 7 T (a) from and (b) to the Lorenz number $L_{0}$ . Linear extrapolations to $T = 0$ show agreement with $L_{0}$ to within 8% and 5% for $j ∥ a$ and $j ∥ b$ , respectively. The inset shows the zero-field anisotropy ratio $\bar{κ} = κ_{b} / κ_{a}$ normalized to the anisotropy ratio in the normal state ${\bar{κ}}_{N} = \bar{κ} (7 T)$ .
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Figure 3
Effective penetration depth of ${UTe}_{2}$ samples S3 (red circles) and S4 (blue squares) plotted vs normalized temperature. The solid lines are power-law fits of the form $a T^{n} + b$ , with extracted exponents $n = 2.00$ for S3 and $n = 1.92$ for S4. The vertical bars indicate uncertainty for each data set determined by a 5% root-mean-square-error in resonant frequency and quality factor (see text). The inset presents the same data in terms of ${(T / T_{c})}^{2}$ to illustrate the quadratic temperature dependence, with linear dashed lines as guides.
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Figure 4
Analysis of the low-temperature heat capacity of ${UTe}_{2}$ single-crystal samples S1 and S2 (same crystals used for thermal transport measurements). (a) The total measured heat capacity (open circles) of sample S1 decomposed into a weak power-law divergence (dashed line), phonon term (dashed-dotted line), and electronic heat capacity (solid circles) obtained by subtracting the diverging and phonon terms (see text for details). (b) The obtained electronic heat capacities of samples S1 and S2 plotted vs $T^{2}$ . Solid lines are fits to the $T^{2}$ dependence in the superconducting state with $T_{c}$ determined by balancing entropy.
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Physical Review B

covering condensed matter and materials physics

Point-node gap structure of the spin-triplet superconductor ${UTe}_{2}$

Tristin Metz, Seokjin Bae, Sheng Ran, I-Lin Liu, Yun Suk Eo, Wesley T. Fuhrman, Daniel F. Agterberg, Steven M. Anlage, Nicholas P. Butch, and Johnpierre Paglione

Phys. Rev. B 100, 220504(R) – Published 19 December 2019

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Physical Review B

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Point-node gap structure of the spin-triplet superconductor UTe2

Tristin Metz, Seokjin Bae, Sheng Ran, I-Lin Liu, Yun Suk Eo, Wesley T. Fuhrman, Daniel F. Agterberg, Steven M. Anlage, Nicholas P. Butch, and Johnpierre Paglione

Phys. Rev. B 100, 220504(R) – Published 19 December 2019

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Point-node gap structure of the spin-triplet superconductor ${UTe}_{2}$