Pair Kondo effect: A mechanism for time-reversal symmetry breaking superconductivity in ${\mathrm{UTe}}_{2}$

Pair Kondo effect: A mechanism for time-reversal symmetry breaking superconductivity in ${UTe}_{2}$

Tamaghna Hazra and Pavel A. Volkov

Phys. Rev. B 109, 184501 – Published 2 May 2024

Abstract

An important open puzzle in the superconductivity of ${UTe}_{2}$ is the emergence of broken time reversal superconductivity from a nonmagnetic normal state. Breaking time reversal symmetry in a single second-order superconducting transition requires the existence of two degenerate superconducting order parameters, which is not natural for orthorhombic ${UTe}_{2}$ . Moreover, experiments under pressure [D. Braithwaite et al., Commun. Phys. 2, 147 (2019)] suggest that superconductivity sets in at a single transition temperature in a finite parameter window, in contrast to the splitting between the symmetry-breaking temperatures expected for accidental degenerate orders. Motivated by these observations, we propose a mechanism for the emergence of broken time reversal superconductivity without accidental or symmetry-enforced order-parameter degeneracies in systems close to a magnetic phase transition. We demonstrate using Landau theory that a cubic coupling between proximate magnetic order and magnetic moments of Cooper pairs (pair Kondo coupling) can drive time reversal symmetry-breaking superconductivity that onsets in a single, weakly first-order transition over an extended region of the phase diagram. We discuss the experimental signatures of such transition in thermodynamic and resonant ultrasound measurements. A microscopic origin of pair Kondo coupling is identified as screening of magnetic moments by chiral Cooper pairs, built out of two nondegenerate order parameters, an extension of Kondo screening to unconventional pairs.

Received 22 November 2023
Revised 28 March 2024
Accepted 2 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.184501

Physics Subject Headings (PhySH)

Superconductivity

Heavy-fermion systems Unconventional superconductors

Ultrasound techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tamaghna Hazra ^1,2,3,* and Pavel A. Volkov ^4,5,1

¹Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
²Institut für Quanten Materialien und Technologien, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
³Institut für Theorie der Kondensierten Materie, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany
⁴Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA
⁵Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

^*tamaghna.hazra@kit.edu

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Vol. 109, Iss. 18 — 1 May 2024

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Figure 1
Schematic demonstration of pair Kondo coupling for triplet pairs: An $S = 1, S_{y} = 0$ triplet pair scatters off a local moment into an $S = 1, S_{z} = 0$ state, rotating the $d$ vector about the $x$ axis along which the moment is aligned. The process is equivalent to an antiferromagnetic superexchange of the pair spin with the $S_{x}$ component of the moment.
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Figure 2
(a) Theoretical phase diagram as a function of temperature and tuning parameter $r$ . Solid black (blue) line is a first- (second-) order phase boundary. SC2 is a $T$ -invariant triplet superconductor with $Δ_{1} \neq 0, Δ_{2} = M = 0$ . SC1 is a broken $T$ superconductor with $Δ_{1}, Δ_{2}, M \neq 0$ . Dashed lines indicate the underlying critical temperatures in absence of coupling between magnetic and superconducting orders: $T_{c 1} / J = 1 + 0.001 r, T_{m} / J = 1 - 0.002 r, a_{2} / J = 0.005 (1 + 0.04 r), b_{1} = b_{2} = b_{M} = 2 J, b_{1 M} = b_{2 M} = b_{12} = 0, α_{1} (1 + 0.001 r) = α_{m} (1 - 0.002 r) = 1$ . Color scale is defined by the RGB values $red = 255 (1 - Δ_{1} / Max)$ , $green = 255 (1 - Δ_{2} / Max)$ , $blue = 255 (1 - M / Max)$ with $Max = 0.15 J$ . (b) Experimental phase diagram from AC calorimetry (from Refs. [39, 40]) as a function of pressure and temperature, where the second transition at low pressure (dashed) is not observed. The observed phase boundaries at low-pressure (boxed) are qualitatively captured by the free energy in (2). (c) Theoretical phase diagram for a different parametrization of the free energy in (14) with $T_{c 1} / J = 1 + 0.001 r, T_{c 2} / J = 0.995 (1 - 0.0004 r), T_{m} / J = 1 - 0.0014 r, b_{1} = b_{2} = b_{M} = 2 J = 2 J, b_{1 M} = b_{2 M} = b_{12} = 0, α_{1} (1 + 0.001 r) = 0.995 (1 - 0.0004 r) α_{2} = α_{m} (1 - 0.0014 r) = 1$ .
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Figure 3
Free-energy profile, Eq. (2), as a function of order-parameter magnitudes for temperature $T$ above [(a), (c), (e)] and below [(b), (d), (f)] the onset of superconductivity. We normalize all quantities by setting $T_{c 1} = T_{m} \equiv 1$ ; the other parameters are $b_{1} = b_{2} = b_{M} = 2, b_{1 M} = b_{2 M} = b_{12} = 0, α_{1} = α_{m} = 1$ . (a), (b) For $J = 1, a_{2} = 0.005$ , a first-order transition occurs between $T = 1.018$ and 1.019: in the ordered state (a), the local minimum at $Δ_{1} = M = 0$ (red arrow) coexists with the global minimum at $Δ_{1} = M = 0.08$ . (c), (d) For $J = 1, a_{2} = 0.067$ , a second-order transition occurs at $T = 1$ . In the ordered state (c), there is no minimum at $Δ_{1} = M = 0$ . For $T > 1$ (d), the only true local minimum is at $Δ_{1} = M = Δ_{2} = 0$ . The apparent minima as a function of $Δ_{1} = M$ are unstable to decreasing $Δ_{2}$ , which smoothly connects them to the $Δ_{1} = M = Δ_{2} = 0$ , forming two “valleys.” (e), (f) For $J = 0, a_{2} = 0.005$ , a second-order transition occurs at $T = 1$ and neither additional local minima nor valleys are present for $T > 1$ .
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Figure 4
(a) Entropy (blue) and (b) specific heat across the first-order transition for $α_{1} = α_{m} = T_{c 1} = T_{m} = J, b_{1} = b_{2} = b_{M} = 2 J, b_{1 M} = b_{2 M} = b_{12} = 0, a_{2} = 0.005 J$ (cf. experimentally measured specific heat in Ref. [38]). As $J \to J_{c}$ , $Δ S \to 0$ , and $cot θ \to \infty$ , becoming nearly vertical. In addition, the red dashed curve schematically indicates what would be expected if the first-order transition is slightly broadened by disorder. Note that this is very hard to distinguish from the entropy in a second-order transition.
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Physical Review B

covering condensed matter and materials physics

Pair Kondo effect: A mechanism for time-reversal symmetry breaking superconductivity in ${UTe}_{2}$

Tamaghna Hazra and Pavel A. Volkov

Phys. Rev. B 109, 184501 – Published 2 May 2024

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Physical Review B

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Pair Kondo effect: A mechanism for time-reversal symmetry breaking superconductivity in UTe2

Tamaghna Hazra and Pavel A. Volkov

Phys. Rev. B 109, 184501 – Published 2 May 2024

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Pair Kondo effect: A mechanism for time-reversal symmetry breaking superconductivity in ${UTe}_{2}$