Field-angle-resolved heat transport in UTe$_2$: determination of nodal positions in the superconducting order parameter

One of the recurring hurdles in studying unconventional superconductivity is the challenge of efficiently and conclusively identifying the symmetry of the superconducting order parameter in a new material. Uranium ditelluride (UTe$_2$) exhibits an unprecedented number of superconducting phases as a function of pressure and magnetic field, each presumably characterized by a different symmetry of the superconducting gap function. None of these phases has had its symmetry conclusively identified so far. In this article, we report results of an extensive study of the thermal conductivity of UTe$_2$ in its low-field, low-temperature superconducting state as a function of the angle of an applied magnetic field rotated in the $b$-$c$ plane. We observe clear and substantial oscillations in the thermal conductivity as a function of field angle, which naturally suggests the existence of point nodes in the gap. Utilizing the experimentally determined Fermi surface, we are able to model this phenomenon for all the potential gap structures in UTe$2$ and positively identify the location of these nodes as being along the crystallographic $b$-axis, implying that the superconducting order parameter belongs to the $B{2u}$ irreducible representation of the crystal point group. The clarity of this result will accelerate the identification of other superconducting phases in UTe$_2$, and guide future studies through the use of high resolution field-angle-dependent measurements.

💡 Research Summary

This paper presents a definitive determination of the symmetry of the superconducting order parameter in the heavy-fermion candidate UTe2 under ambient pressure and low magnetic fields. The central challenge addressed is the longstanding controversy over the gap structure of UTe2, with conflicting evidence from various probes pointing towards different possible odd-parity irreducible representations (A_u, B1_u, B2_u, B3_u) of the D2h point group.

The authors employ a powerful bulk technique: high-resolution measurements of the thermal conductivity (κ) at ultra-low temperatures (down to 70 mK, ~0.03Tc) and in very low magnetic fields (~1% of Hc2). The experiment involves applying a heat current along the crystallographic a-axis and rotating an applied magnetic field within the perpendicular b-c plane. They observe clear and substantial two-fold oscillations in κ/T as a function of the field angle, with a minimum when the field is aligned along the b-axis and a maximum along the c-axis. This oscillatory pattern is much stronger than the weak angular variation of the upper critical field Hc2(θ) in this plane. Furthermore, κ/T increases quasi-linearly with field at all angles in this low-field regime, consistent with the Volovik effect where a magnetic field Doppler-shifts quasiparticle energies near gap nodes.

To interpret these observations beyond simplistic models, the authors perform detailed theoretical calculations. They utilize a realistic tight-binding model of the electronic structure of UTe2, constructed to be consistent with existing ARPES and quantum oscillation data. This model features two hybridized bands (U-derived and Te-derived) forming cylindrical Fermi surfaces with highly anisotropic Fermi velocities. Using this realistic Fermi surface, they calculate the field-angle-dependent electronic thermal conductivity κ_el for all possible single-component order parameters (the four irreps) as well as for two-component, time-reversal symmetry-breaking states. The calculations properly account for the Doppler shift mechanism and the complex angular distribution of the Fermi velocity.

The key result is that only the model with a B2u symmetry order parameter successfully reproduces the experimental data. The B2u state has symmetry-imposed point nodes along the b-axis, which leads to calculated κ_el(θ) oscillations with a minimum along b, matching the experiment perfectly. In contrast, a B3u state (nodes along a) predicts an opposite phase (minimum along c), while the fully gapped Au and B1u states predict only weak oscillations inconsistent with the strong modulation observed. Analysis of two-component states also showed that only those with spectral nodes near the b-axis were compatible with the data.

Therefore, the study concludes that the superconducting order parameter in UTe2 at zero pressure and low field belongs to the B2u irreducible representation, characterized by point nodes along the crystallographic b-direction. This work demonstrates the efficacy of field-angle-resolved thermal transport as a direct, bulk probe of gap structure anisotropy and provides a crucial benchmark for understanding the multiple superconducting phases in UTe2 under different tuning parameters like pressure and field.