Novel $$H_{\textrm{c2}}$$ Suppression Mechanism in a Spin-Triplet Superconductor: Application to $$\hbox {UTe}_2$$

Abstract A novel $$H_{\textrm{c2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mtext>c2</mml:mtext> </mml:msub> </mml:math> suppression mechanism is theoretically proposed in a spin-triplet superconductor (SC) with equal spin pairs. We show that the upper critical field $$H_{\textrm{c2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mtext>c2</mml:mtext> </mml:msub> </mml:math> can be reduced from the orbital depairing limit $$H^{\textrm{orb}}_{\textrm{c2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mtext>c2</mml:mtext> <mml:mtext>orb</mml:mtext> </mml:msubsup> </mml:math> to arbitrarily small value, keeping the second-order phase transition nature. This mechanism is sharply different from the known Pauli–Clogston limit for a spin-singlet SC where the reduction is limited to $$\sim$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∼</mml:mo> </mml:math> 0.3 $$H^{\textrm{orb}}_{\textrm{c2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mtext>c2</mml:mtext> <mml:mtext>orb</mml:mtext> </mml:msubsup> </mml:math> with the first-order transition when the Maki parameter goes infinity. This novel $$H_{\textrm{c2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mtext>c2</mml:mtext> </mml:msub> </mml:math> suppression mechanism is applied to $$\hbox {UTe}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>UTe</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , which is a prime candidate for a spin-triplet SC, to successfully analyze the $$H_{\textrm{c2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mtext>c2</mml:mtext> </mml:msub> </mml:math> data for various crystalline orientations both under ambient and applied pressure, and to identify the pairing symmetry. It is concluded that the non-unitary spin-triplet state with equal spin pairs is realized in $$\hbox {UTe}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>UTe</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , namely $$({\hat{b}}+i{\hat{c}})k_a$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>^</mml:mo> </mml:mover> <mml:mo>+</mml:mo> <mml:mi>i</mml:mi> <mml:mover> <mml:mi>c</mml:mi> <mml:mo>^</mml:mo> </mml:mover> <mml:mo>)</mml:mo> </mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> </mml:math> in $$^3\hbox {B}_{\textrm{3u}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>3</mml:mn> </mml:mmultiscripts> <mml:msub> <mml:mtext>B</mml:mtext> <mml:mtext>3u</mml:mtext> </mml:msub> </mml:mrow> </mml:math> which is classified under finite spin–orbit coupling scheme.