[Paper Review] Chiral superconductivity in UTe2 probed by anisotropic low-energy excitations

K. Ishihara, M. Roppongi+6 more|arXiv (Cornell University)|May 28, 2021

Rare-earth and actinide compounds4 citations

TL;DR

This study identifies chiral spin-triplet superconductivity in UTe2 through anisotropic magnetic penetration depth measurements, revealing power-law temperature dependence with exponents near 2, indicating multiple point nodes. The data favor a chiral $B_{3u}+iA_u$ non-unitary state, confirming time-reversal symmetry breaking and supporting topological Majorana quasiparticles.

ABSTRACT

Chiral spin-triplet superconductivity is a topologically nontrivial pairing state with broken time-reversal symmetry, which can host Majorana quasiparticles. The recently discovered heavy-fermion superconductor UTe$_2$ exhibits peculiar properties of spin-triplet pairing, and the possible chiral state has been actively discussed. However, the symmetry and nodal structure of its order parameter in the bulk, which determine the Majorana surface states, remains controversial. Here we focus on the number and positions of superconducting gap nodes in the ground state of UTe$_2$. Our magnetic penetration depth measurements for three field orientations in the Meissner state reveal the power-law temperature dependence with exponents nearly equal to 2 or less than 2, which excludes single-component spin-triplet states. The anisotropy of low-energy quasiparticle excitations indicates multiple point nodes near the $k_y$- and $k_z$-axes, evidencing that the order parameter has multiple components in a chiral complex form. We find that most consistent is a chiral $B_{3u}+iA_u$ non-unitary state, which provides fundamentals of the topological properties in UTe$_2$.

Motivation & Objective

• To determine the superconducting order parameter symmetry and nodal structure in UTe2, a heavy-fermion superconductor near a ferromagnetic quantum critical point.
• To resolve the controversy over whether UTe2 hosts a chiral, time-reversal-symmetry-breaking superconducting state with topological properties.
• To identify the presence and positions of superconducting gap nodes using anisotropic low-energy quasiparticle excitations.
• To distinguish between single-component and multi-component order parameters based on temperature-dependent penetration depth anisotropy.
• To establish a link between nodal structure and the potential for topological Majorana quasiparticles in UTe2.

Proposed method

• Performed magnetic penetration depth measurements ($\Delta\lambda(T)$) in the Meissner state for three field orientations (a, b, c axes) to probe anisotropic quasiparticle excitations.
• Analyzed the power-law temperature dependence of $\Delta\lambda(T)$ to infer the nodal structure: $T^2$ dependence indicates nodes along the current direction, $T^4$ otherwise.
• Used tunnel-diode oscillator technique with weak ac magnetic fields along a, b, and c axes to measure frequency shifts proportional to $\Delta\lambda(T)$.
• Evaluated theoretical models of odd-parity superconducting states (e.g., $B_{3u}$, $A_u$, $B_{3u}+iA_u$) and compared predicted nodal positions and $T$-dependence with experimental data.
• Conducted numerical simulations varying order parameter component coefficients ($c_4$, $c_5$, $c_6$) to assess their impact on $n_b$ and $n_c$ in the $T$-dependence of $\Delta\lambda$.
• Accounted for Fermi surface geometry by comparing results on spherical vs. realistic 3D/quasi-2D Fermi surfaces, noting discrepancies in $n_a$ and $n_b$ values.

Experimental results

Research questions

• RQ1 Does UTe2 host a chiral superconducting state with time-reversal symmetry breaking?
• RQ2 What is the nodal structure of the superconducting gap in UTe2, and how does it vary with field orientation?
• RQ3 Which multi-component order parameter symmetry (e.g., $B_{3u}+iA_u$) best explains the observed anisotropic $T$-dependence of the penetration depth?
• RQ4 How do the relative magnitudes of different order parameter components influence the quasiparticle excitation anisotropy?
• RQ5 Can the observed $T^2$-like dependence in certain field directions confirm the presence of point nodes aligned with the current direction?

Key findings

• The magnetic penetration depth $\Delta\lambda(T)$ exhibits $T^2$-like dependence for all field orientations, indicating multiple point nodes rather than line nodes or full gaps.
• The anisotropy of $\Delta\lambda(T)$ across different field directions rules out single-component spin-triplet states, which would show $T^4$ dependence for currents perpendicular to nodal directions.
• The data are best explained by a chiral $B_{3u}+iA_u$ non-unitary state, which supports time-reversal symmetry breaking and topological superconductivity.
• The $c_4$ component of the $A_u$ order parameter is identified as a key factor in the sample-dependent variation of the $T$-dependence exponent, likely due to node splitting and interference effects.
• The $a$-axis quasiparticle excitations are significantly suppressed compared to $b$- and $c$-axis, consistent with the absence of nodes along the $a$-axis in the $B_{3u}+iA_u$ state.
• Theoretical modeling suggests that realistic Fermi surface geometry (3D at Z-point, quasi-2D sheets) leads to better agreement with experiment than spherical Fermi surface approximations, particularly for $n_a$ and $n_b$.