Pseudo point nodal superconducting gap in spin-triplet UTe₂

Abstract

UTe₂ is an unconventional heavy-fermion superconductor discussed as a candidate for spin-triplet pairing. However, conflicting reports on gap structure, particularly regarding point nodes, have hindered understanding of the order parameter symmetry. Here, we report b-axis thermal conductivity κ_b/T measurements on high-quality UTe₂ single crystals down to  ~ 50 mK that definitively resolve the gap anisotropy. κ_b/T shows negligible residual conductivity as T → 0, while magnetic fields induce only weak enhancement of the residual term. Remarkably, a threshold-like field scale is observed at low fields for H∥a, characterized by a kink signaling a change in quasiparticle transport normal to the field. Above this threshold, strong anisotropy develops for transport along and normal to the field. These results strongly suggest that UTe₂ hosts a fully gapped state with pseudo point nodes, where the gap minima approach but never reach zero, placing strong constraints on the order parameter and exotic pairing mechanism.

The authors report thermal conductivity measurements on UTe2 down to 50 mK. From the data, they argue that UTe2 exhibits a fully-gapped state with a pseudo point-nodal structure, where gap minima along the b axis approach but never reach zero.

Introduction

Spin-triplet superconducting states have garnered significant attention due to their unconventional pairing mechanism and potential to host topologically protected Majorana zero modes, which offer a promising platform for fault-tolerant topological quantum computation¹. While liquid ³He exemplifies spin-triplet superfluidity, identifying solid-state analogs remains a central challenge in condensed matter physics. Recently, the heavy fermion superconductor UTe₂ has emerged as an exceptionally promising candidate for realizing spin-triplet superconductivity². This uranium-based compound exhibits a number of anomalous superconducting properties that together provide compelling evidence for unconventional pairing. Most notably, UTe₂ displays extraordinarily large upper critical fields H_c2 that substantially exceed the Pauli paramagnetic limit^2,3. The superconducting phase diagram under both magnetic field and pressure reveals additional complexity through the existence of multiple distinct superconducting phases^4–8, indicating highly unusual pairing states.

Critically, the unconventional superconducting state in UTe₂ emerges from a paramagnetic normal state at ambient pressure, distinguishing it from uranium-based compounds such as UGe₂⁹, URhGe¹⁰, and UCoGe¹¹, where superconductivity coexists with ferromagnetic order. Moreover, the Fermi surface structure of UTe₂ appears to be simpler than that of many other heavy fermion superconductors, with fewer sheets and less complex topology^3,12–14. These characteristics establish UTe₂ as an ideal model system for investigating spin-triplet superconductivity.

The comprehensive characterization of the superconducting gap structure in UTe₂ represents a critical prerequisite for understanding the Cooper pair formation mechanism and determining its topological nature. However, despite extensive experimental investigations, the precise gap structure of UTe₂ remains unresolved. The challenge is further amplified by pronounced surface-bulk electronic structure disparities, most notably manifested through the emergence of a surface charge density wave (CDW) instability that does not occur in the bulk^15–17. The surface-bulk dichotomy presents systematic challenges for interpreting surface-sensitive spectroscopic techniques, including scanning tunneling microscopy (STM)¹⁸ and tunnel junction measurements^19,20. In addition, magnetic penetration depth measurements^21–23 may be influenced by the sample edge²³ or anomalous surface normal state²². We also note that, since low-energy quasiparticle excitations in UTe₂ are particularly sensitive to disorder, ultraclean crystals are required, whereas lower quality samples obscure intrinsic gap features.

Thermodynamic measurements under uniaxial strain²⁴ and ultrasound measurements²⁵, combined with polar Kerr effect spectroscopy²⁶ and muon spin relaxation measurements²⁷, have provided evidence against bulk chiral superconductivity. Accordingly, four single-component irreducible representations within the D_2h point group characterize potential spin-triplet pairing states: A_u (fully gapped, Fig. 1a, b), B_1u (point nodes along the crystallographic c-axis), B_2u (point nodes along the b-axis, Fig. 1c), and B_3u (point nodes along the a-axis).

Fig. 1. Superconducting gap structure and Doppler shift.

a–c Superconducting gap structure Δ (yellow) on a 2D cylindrical Fermi surface (yellow-green) for A_u (a and b) and B_2u (c) symmetries. a Full gap opens uniformly. b At pseudo point nodes, the gap amplitude approaches zero but remains finite. The accompanying figure (right) shows the quasiparticle dispersion in the vicinity of the gap minimum. c The B_2u state hosts point nodes (dark green) along the b-axis (k_y direction). The Dirac cone emerges where the gap amplitude vanishes at a point node. d, e Schematic representation of Doppler shift effects under magnetic field H applied parallel and perpendicular to point nodes, respectively. The supercurrent velocity v_s circulating around vortex cores is oriented perpendicular to H. d For H∥ nodes, Doppler-shifted quasiparticle excitations are suppressed due to v_F ⋅ p_s = 0 at the node. e For H⊥ nodes, the Doppler shift energy v_F ⋅ p_s exceeds the superconducting gap magnitude Δ close to the nodal directions, thereby activating low-energy quasiparticle excitations in the near-nodal directions (red-shaded region). When thermal current j_Q is applied parallel to the nodal directions (j_Q∥ nodes), thermal conductivity exhibits selective sensitivity to nodal excitations, while it becomes insensitive when j_Q⊥ nodes.

A definitive determination of the superconducting order parameter requires directionally-resolved, bulk-sensitive experimental probes capable of directly accessing nodal quasiparticle excitations at ultra-low temperatures²⁸. In contrast to specific heat, thermal conductivity preferentially samples itinerant quasiparticles with the Fermi velocity v_F parallel to the thermal current j_Q. Since in anisotropic superconductors at low energies, such quasiparticles are confined to the regions where the gap is minimal, the directional dependence of thermal transport reflects the underlying nodal structure. Notably, thermal conductivity remains immune to extrinsic Schottky contributions, permitting measurements at sufficiently low temperatures to unambiguously differentiate nodal and gapped states. Most significantly, as the magnetic field also serves as a directional probe that excites quasiparticles through the Doppler shift of the quasiparticle spectra, the combination of magnetic field orientation with thermal conductivity measurements constitutes a powerful probe for superconducting gap determination, enabling precise mapping of nodal directions (Fig. 1d, e).

Thermal conductivity studies in UTe₂ have established the absence of point nodes along the a direction through the a-axis thermal conductivity (κ_a) measurements (j_Q∥a)^29,30. In contrast, the conclusions regarding point nodes along the b axis remain controversial. This discrepancy arises because κ_a measurements probe mostly the quasiparticles with the Fermi velocity along the a-axis, and are much less sensitive to the excitations in the vicinity of the potential b-axis nodes (Fig. 1e). While b-axis thermal conductivity (κ_b) measurements (j_Q∥b) would directly probe the b-axis nodal structure, such experiments were previously precluded by insufficient sample sizes along the b direction, preventing definitive determination of the complete nodal topology.

Results and discussion

Here, we measured the thermal conductivity κ_b along the b-axis using molten-salt-grown ultraclean single crystals³¹ (lower inset of Fig. 2a). The upper inset of Fig. 2a shows the resistivity along the b-axis, ρ_b, plotted as a function of T² for samples #A and #B. The resistivity follows standard Fermi-liquid behavior, described by ${\rho }_b\left(T\right)={\rho }_b^0+A{T}^2$. This behavior is consistently observed under magnetic field H∥a down to very low temperatures (Supplementary 1). We estimated residual resistivities of ${\rho }_b^0\approx 1.72$μΩcm for sample #A and  ≈ 2.12 μΩcm for sample #B in zero field. These values correspond to residual resistivity ratios of $RRR\equiv {\rho }_b\left(300\text{K}\right)/{\rho }_b^0\approx 410$ and  ≈ 350 for samples #A and #B, respectively.

Fig. 2. Thermal conductivity in zero magnetic field.

a The main panel shows the b-axis thermal conductivity divided by temperature, κ_b/T, in zero field for sample #A (RRR ≈ 410) and #B (RRR ≈ 350). Both samples exhibit a sharp discontinuity at T_c (arrow). The lower inset illustrates the experimental configuration for thermal conductivity measurements with thermal current j_Q applied along the crystallographic b-axis. The upper inset shows electrical resistivity along the b-axis in zero field plotted as a function of T² for #A and #B. ρ_b(T) is well fit by ${\rho }_b\left(T\right)={\rho }_b^0+A{T}^2$ (orange and cyan dashed lines, respectively). b κ_b/T in zero field for #A and #B at very low temperatures. The upper inset shows κ_b/T vs. T². The gray dashed line indicates the residual thermal conductivity expected for a superconductor with line nodes in the gap structure. The lower inset provides an expanded view of the low-temperature regime. c Calculated temperature dependence of normalized κ/T for point nodes (${\mathrm{\Delta }}_{\min }=0$) and pseudo point nodes (${\mathrm{\Delta }}_{\min }=0.1{\mathrm{\Delta }}_0$), with heat current parallel to the nodal direction.

We first examine the zero-field thermal conductivity. The main panel of Fig. 2a depicts the temperature dependence of κ_b. At the superconducting transition temperature T_c = 2.1 K, κ_b/T exhibits a pronounced discontinuity, followed by a pronounced maximum at around 1.2 K. The enhancement below T_c for #B (with lower RRR) is slightly suppressed compared to #A. This enhancement arises from the dramatic increase in quasiparticle mean free path, which results from the suppression of electron–electron inelastic scattering following superconducting gap opening. The temperature dependence of κ_b/T at very low temperatures for both samples #A and #B is shown in Fig. 2b. Similar to κ_a/T^29,30, κ_b/T decreases monotonically upon cooling. As shown in the inset of Fig. 2b, κ_b/T exhibits a nearly T² dependence. The thermal conductivity in the superconducting state comprises quasiparticle and phonon contributions. Our results indicate a substantial quasiparticle contribution to κ_b/T at low temperatures. This contrasts with κ_a/T, where the weak impurity dependence below ~ 0.2 K was attributed to dominant phonon transport²⁹. In the present case, the impurity independence of κ_b/T persists only below approximately 0.1 K, suggesting a more significant quasiparticle contribution to heat transport along the b-axis. This anisotropy between κ_a/T and κ_b/T is consistent with a scenario in which low-energy quasiparticles contribute more effectively along the b-axis.

For superconductors with line nodes, the low temperature residual thermal conductivity has a universal, impurity-independent value, which for UTe₂ is estimated to be κ₀₀/T ≈ 0.054 W/K²m (gray dashed line in the inset of Fig. 2b)²⁹. The extrapolation of κ_b/T to zero temperature (red and blue dotted lines in the main panel of Fig. 2b) yields a vanishing intercept within experimental accuracy, indicating negligibly small residual thermal conductivity, with an upper bound estimate of ${\kappa }_b^0/T=0.0017$ W/K²m for both #A and #B. Thus ${\kappa }_b^0/T$ is significantly smaller than κ₀₀/T, similar to κ_a/T^29,30. These results exclude line-nodal gap structures compatible with D_2h symmetry under weak spin-orbit coupling, constraining the pairing to either a full gap or point nodes as expected in the strong spin-orbit coupling regime.

The temperature dependence of κ_b/T in zero field provides important constraints on the presence or absence of point nodes along the b-axis³⁰. For the heat current along the point nodes, the residual term in the thermal conductivity is finite only if the impurity scattering rate, Γ, exceeds a threshold value, and vanishes otherwise³². The threshold value is finite for any scattering phase shift, δ, away from the unitary limit ($c=\cot \delta =0$). Therefore, the near absence of the residual linear term observed here is strongly suggestive of a clean sample (Γ ≪ Δ₀) with a finite c, although it may also be consistent with a sample of extreme purity in the unitary limit. For clean samples with a finite c and the heat current along a point node, the temperature dependence of κ/T is typically non-monotonic, exhibiting a characteristic peak at low temperature^32,33. This peak disappears if a small gap opens in the nodal region.

Figure 2 c shows the calculated κ/T (normalized as $\kappa {\mathrm{\Delta }}_0/N_0{v}_F^{2}T$, where N₀ is the normal-state density of states, v_F is the Fermi velocity, and the gap maximum is taken to be Δ₀ = 2k_BT_c) as a function of T/T_c for true point nodes (${\mathrm{\Delta }}_{\min }=0$) and pseudo point nodes (${\mathrm{\Delta }}_{\min }=0.1{\mathrm{\Delta }}_0$), with j_Q applied parallel to the nodal direction. Here, we use representative values Γ/Δ₀ = 0.002 and c = 0.15. Technical details of the calculations and additional data demonstrating that this is a generic behavior are given in Supplementary Note 4 and Supplementary Note 5. Our samples exhibit negligibly small residual thermal conductivity. In the presence of point nodes along the b-axis, a low-temperature peak in κ_b/T would be expected. However, although our measurements extend down to 50 mK, the thermal conductivity at the lowest temperatures is likely dominated by phonon contributions, and therefore the temperature dependence alone does not allow a definitive conclusion regarding the presence or absence of point nodes. These zero-field results are consistent with a finite minimum gap, but they do not by themselves completely rule out a true point node scenario within a restricted parameter regime. More definitive evidence for a finite minimal gap is provided by the field-dependence measurements discussed below.

Thermal conductivity measurements with applied magnetic fields along three crystallographic orientations provide a more stringent and direct test for the absence of point nodes and the presence of a small gap. Magnetic fields induce circulating supercurrents around vortices characterized by the superfluid momentum p_s(r) in the plane normal to the field. The resulting Doppler shift in quasiparticle energy, E_k → E_k − v_F ⋅ p_s(r) (Fig. 1d, e), selectively activates delocalized quasiparticles with the Fermi velocity aligned with p_s. Quasiparticle thermal transport in the low-field regime of nodal superconductors is dominated by these quasiparticles, whose density of states exhibits characteristic field dependence determined by nodal topology: $N_{\mathrm{del}}\left(\epsilon \right)\propto \sqrt{H}$ for line nodes and $N_{\mathrm{del}}\left(\epsilon \right)\propto H\mid lnH\mid$ for point nodes^34–36. Consequently, the thermal conductivity typically also varies as a power law of the field. Conversely, in full-gap type-II superconductors, quasiparticles remain localized within vortex cores. Although the density of states scales linearly with the number of vortices and hence the field, the thermal conductivity remains suppressed.

Critically, thermal conductivity in the field sensitively probes nodal quasiparticles when v_F has components parallel to both p_s(r) and j_Q, but is not affected by quasiparticles with v_F⊥p_s(r) or v_F⊥j_Q (Fig. 1e). In the presence of point nodes along the b direction, applying H perpendicular to the b axis (H∥a or H∥c) would activate Doppler-shifted quasiparticles near the nodes due to a finite p_s ⋅ v_F component for quasiparticles with v_F∥j_Q∥b, leading to enhanced thermal conductivity. Conversely, for H∥b, the supercurrent circulates in the ac-plane, resulting in p_s ⋅ v_F = 0 for heat-carrying quasiparticles along the b direction; thus, κ_b would be only weakly sensitive to such nodes (Fig. 1d). This directional sensitivity enables spatial mapping of gap nodes on the Fermi surface. Importantly, even in full-gap superconductors with significant gap anisotropy, quasiparticles are excited at finite fields when the Doppler shift exceeds the minimum gap. Therefore, low-temperature and low-field measurements taken together yield definitive information about the gap structure.

Figures 3a–c show the temperature dependence of κ_b/T, normalized by the normal state value ${\left({\kappa }_b/T\right)}_{\mathrm{N}}$, for three field orientations down to  ~ 50 mK and for magnetic fields up to 6 T. The crossing of κ_b/T at H = 0 with that at finite fields can arise from multiple effects, including inelastic scattering processes at finite temperatures and a reduction of the phonon-contribution by due to increased electron-phonon scattering. Below 0.3 K, the thermal conductivity is mainly carried by quasiparticles rather than phonons. To clarify this point, the comparison between H∥a and H∥c is particularly instructive, as the magnetic field is perpendicular to the heat current in both cases, while anisotropic field responses are present for all field directions. In this geometry, phonon thermal conductivity would be expected to depend primarily on the quasiparticle density rather than directly on the field orientation. Although the anisotropic quasiparticle populations may modify phonon scattering, the magnitude of the observed anisotropy is difficult to reconcile with a phonon-dominated mechanism alone. Regardless of these detailed mechanisms at finite temperatures, these effects do not affect the zero-temperature limit, and κ⁰/T provides a measure of the quasiparticle contribution.

Fig. 3. Low temperature thermal conductivity under magnetic fields along each crystallographic axis.

a–c Temperature dependence of low-temperature thermal conductivity along the b-axis under magnetic fields applied parallel to the a-axis (a), b-axis (b), and c-axis (c), respectively. The dashed lines represent polynomial fitting results.

Figure 4a shows ${\kappa }_b^0/T$ normalized by the normal-state value ${\left({\kappa }_b^0/T\right)}_N$ under applied magnetic fields along three crystallographic directions, where ${\kappa }_b^0/T\equiv {lim}_{T\to 0}{\kappa }_b\left(T\right)/T$ is obtained by polynomial extrapolation to T → 0. The magnetic fields are normalized by their respective upper critical fields to account for the strong H_c2 anisotropy: ${\mu }_0{H}_{c2}^a=11.7$ T, ${\mu }_0{H}_{c2}^b=23$ T, and ${\mu }_0{H}_{c2}^c=16.5$ T³⁷. The thermal conductivity exhibits pronounced anisotropic field dependence at higher fields, with κ_b/T showing the weakest growth with field H∥b despite the expected normal-state contributions from vortex cores in the j_Q∥H configuration. This indicates that vortex-core conduction is essentially negligible. One possible explanation for this is that the discreteness of Caroli–de Gennes–Matricon vortex core states reduces the contribution of the cores to the heat transport. Using Δ₀ ~ 2T_c ~ 4 K and ϵ_F ~ 120 K¹² as the characteristic superconducting gap energy scale and the Fermi energy respectively, we estimate the core level spacing to be ${\mathrm{\Delta }}_0^2/{ϵ}_{\mathrm{F}}~0.13$ K, in agreement with ref. ³⁸. The phase diagram of UTe₂ for H∥b is complex at high fields, with re-entrant superconductivity and other phases. However, in the range where the measurements are done, the field in the vortex core is still far below H_c2, and therefore, the emergence of additional order parameters, while possible, does not seem likely.

Fig. 4. Field-enhanced thermal conductivity in the T → 0 limit.

a–c The zero-temperature limit of the b-axis thermal conductivity divided by temperature ${\kappa }_0^b/T$, normalized by the normal state value ${\left({\kappa }_0^b/T\right)}_N$, plotted as a function of magnetic field applied parallel to the a, b, and c axes. The magnetic fields are normalized by the corresponding upper critical field $H_{c2}^{a,b,c}$. a $\left({\kappa }_b^0/T\right)/{\left({\kappa }_b^0/T\right)}_N$ as a function of $H/H_{c2}^{a,b,c}$ for H∥a, b and c. b $\left({\kappa }_b^0/T\right)/{\left({\kappa }_b^0/T\right)}_N$ as a function of $H/H_{c2}^{a,b}$ for H∥a and b. For H∥a, a kink is observed at $H^{*}/H_{c2}^a\approx 0.015$ (arrow), below which $\left({\kappa }_b^0/T\right)/{\left({\kappa }_b^0/T\right)}_N$ exhibits nearly isotropic behavior, whereas pronounced anisotropy develops above this characteristic threshold field. c The red circles show the thermal conductivity difference $\mathrm{\Delta }{\left({\tilde{\kappa }}_b^0/T\right)}^{\mathrm{DS}}={\left[\mathrm{\Delta }\left({\kappa }_b^0/T\right)/{\left({\kappa }_b^0/T\right)}_N\right]}_{\mathbf{H}\parallel a}-{\left[\mathrm{\Delta }\left({\kappa }_b^0/T\right)/{\left({\kappa }_b^0/T\right)}_N\right]}_{\mathbf{H}\parallel b}$ for #B, which represents the difference between field configurations with and without the Doppler shift contribution. For comparison, pink open circles represent the corresponding difference calculated by subtracting the #B (H∥b) data from the #A (H∥a) data. Both datasets exhibit good agreement. The dashed line is a guide to the eye. d Magnetic field dependence of the residual thermal conductivity term for the true point nodes (${\mathrm{\Delta }}_{\min }=0$) and pseudo-nodes (${\mathrm{\Delta }}_{\min }=0.1{\mathrm{\Delta }}_0$) in a model of a Fermi surface with a square cross-section in the a-b plane and nodes/minima along the b axis, as described in Supplementary Note 4. Inset: Schematic of Doppler shift effects in a model circular unit cell of the vortex lattice (radius R). Below the threshold energy $E_H^{\star }={\mathrm{\Delta }}_{\min }$ the Doppler shift at distances $R>r>R^{\star }~R{E}_H/{\mathrm{\Delta }}_{\min }$ is insufficient to generate unpaired quasiparticles (blue ring). For the heat current normal to the field, this yields an effective thermally insulating barrier, preventing net heat conduction, see text for details.

The low-field results provide strong evidence for pseudo-point nodes, characterized by gap minima that remain finite rather than reaching zero. The in-plane field response of ${\kappa }_b^0/T$ shown in Fig. 4b offers critical insights into the detailed structure of the superconducting gap. Notably, for H∥a in both samples #A and #B, a reproducible kink-like feature is observed at $H_a^{*}/H_{c2}^a~0.015$ (arrow), suggesting threshold behavior and indicating a change in quasiparticle transport. We note that the kink persists irrespective of the fitting function (polynomial or T²-linear) and remains visible within the uncertainty arising from the fitting range (Supplementary 3). Importantly, the kink is already visible in the raw data for H∥a, whereas no such feature is observed for H∥b. This kink is more clearly visualized in Fig. 4c, which shows the difference between H∥b (H∥j_Q) and H∥a (H⊥j_Q) configurations. The H∥b data are used as a first-approximation background to subtract the weak smooth field dependence, thereby highlighting the additional contribution associated with the onset of node-like excitations (see Supplementary Note 3).

These results strongly suggest that quasiparticle excitations undergo a qualitative change at this threshold field. Below $H_a^{*}$, ${\kappa }_b^0/T$ exhibits only weak anisotropy between field orientations. Above $H_a^{*}$, the in-plane response becomes strongly anisotropic, with H⊥j_Q yielding substantially larger values than H∥j_Q. The perpendicular field geometry more efficiently generates Doppler-shifted quasiparticles with velocities aligned along the thermal gradient. Consequently, the absence of significant anisotropy below $H_a^{*}$ indicates that such Doppler-shifted quasiparticles contribute very little to thermal transport across the vortex lattice. This is consistent with a finite minimal gap.

Consider the geometry for fields normal to the heat current, as illustrated in Fig. 4d. In the approximation where the vortex unit cell is a circle of radius $R~{\xi }_0\sqrt{H_{c2}/H}$ (ξ₀ is the coherence length), the characteristic Doppler shift energy scale $E_H=a{\mathrm{\Delta }}_0\sqrt{H/H_{c2}}$, where a ~ 1, is the minimal Doppler shift at the edge of the unit cell. The Doppler shift itself varies as E_H(R/r) with the distance r to the vortex core inside the unit cell. In the calculations below, we took a = 0.72, which is the value accepted in ref. ³⁰, but the qualitative picture does not depend on the exact value of a. To generate the unpaired quasiparticles in the absence of impurities, the Doppler shift needs to exceed the gap amplitude. Therefore in the presence of the minimal gap, such quasiparticles are generated everywhere in real space above the threshold field, $E_H^{*}={\mathrm{\Delta }}_{\min }$, or $H^{*}/H_{c2}=a^{-2}{\left({\mathrm{\Delta }}_{\min }/{\mathrm{\Delta }}_0\right)}^2$. Below this field, the unpaired quasiparticles only appear inside the circle of a radius $R^{*}=R\left(E_H/{\mathrm{\Delta }}_{\min }\right)<R$, while at R^* < r < R the system is fully gapped (see Fig. 4d).

Heat current normal to the vortices samples regions with all the Doppler shifts, and therefore the thermally insulating fully gapped region prevents heat conduction below H^*, yielding a sharp onset once this field is exceeded. This is shown in the main panel of Fig. 4d, where we calculated the thermal conductivity following ref. ³⁹, which took the “series” resistor connection to model transport normal to the vortices. The threshold field is clearly seen at H/H_c2 ~ 0.015 for the pseudo-nodal model with ${\mathrm{\Delta }}_{\min }=0.1{\mathrm{\Delta }}_0$, whereas it is absent for true nodes. The very rapid rise of the thermal conductivity at low fields for ${\mathrm{\Delta }}_{\min }=0$ is due to the square shape of the Fermi surface assumed in the model, see Supplementary Note 4 for details. Therefore, in this model, the experimental results are consistent with ${\mathrm{\Delta }}_{\min }=0.1{\mathrm{\Delta }}_0$ (Supplementary Fig. 7), although the exact magnitude of the minimal gap depends on the choice of parameter a. In our model, as in ref. ³⁹, the quasiparticles sample all available Doppler shift values along their path. We expect that beyond the semiclassical approach, there will be finite, albeit small, heat transport across the classically forbidden regions, while the kink at the threshold field should remain.

The experimentally measured κ/T exhibits a slight increase with applied field even below the threshold, which is not captured within semiclassical theory. The discrepancy reflects limitations of the Doppler shift picture for transport. In the Doppler shift method, one computes the local value of the transport coefficient. However, if the range over which the corresponding correlation function decays encompasses regions of different superfluid velocities, the results are only qualitatively correct even at low fields. In particular, if the mean free path is comparable to or greater than the width of the “forbidden” region in the schematic of Fig. 4d, the quasiparticles can traverse that region, and the heat current will be finite, albeit reduced.

Quantum oscillation studies, first reported by D. Aoki et al.⁴⁰, provide a bulk probe of the electronic structure and reveal two cylindrical Fermi surfaces. A subsequent study reported additional slow oscillations, suggesting the possible existence of a small three-dimensional (3D) Fermi surface pocket⁴¹. However, later high-resolution oscillation studies found no evidence for 3D Fermi surface sections¹² and demonstrated that the slow oscillations originate from quantum interference effects between quasi-2D sheets^42,43. Taken together, the available quantum oscillation data support the view that UTe₂ possesses distinct cylindrical electron and hole Fermi surface sheets that are topologically separated in momentum space, with no connectivity at the Brillouin zone boundaries^{12,40,42–44}. Based on these findings, we adopt a quasi-2D Fermi surface topology. In this topology, the gap function is nodeless along the c-axis due to the absence of Fermi surface sections extending along the c-axis direction, and the thermal conductivity under elevated fields reveals intrinsic gap anisotropy in 2D Fermi sheets.

Based on the observed fully gapped superconducting behavior in the ab-plane, the order parameter is expected to belong to either the A_u or B_1u irreducible representation. In the B_1u state, the gap function exhibits point nodes along the c axis; however, these remain experimentally inaccessible owing to the absence of Fermi-surface sections along this direction. Within the quasi-2D electronic structure, theoretical calculations suggest that UTe₂ likely realizes a topological crystalline superconducting state protected by time-reversal and crystal symmetries⁴⁵. Both pairing states support Majorana edge modes at the same open boundaries perpendicular to the a or b axes. The distinction lies in their dispersion: a flat band for the B_1u state and a linearly dispersing mode for the A_u state. These theoretical predictions could be tested by orientation-resolved STM, although surface CDW effects may obscure intrinsic topological superconducting signatures.

We next compare our conclusions to the reported results from bulk probes of the gap function, such as nuclear magnetic resonance (NMR) and specific heat measurements. The observed suppression of NMR Knight shifts along all crystallographic axes appears consistent with A_u symmetry⁴⁶; however, this holds only when the d-vector contains linear momentum terms proportional to k_i (where i = a, b, c). By contrast, d-vectors incorporating higher-order momentum components, such as cubic terms k_ak_bk_c, produce finite contributions along all crystallographic directions, resulting in Knight shift suppression along all axes irrespective of the underlying gap symmetry. Consequently, the observed Knight shift suppression cannot unambiguously distinguish between A_u, B_1u, B_2u, and B_3u representations, nor can it conclusively identify the fully gapped superconducting order.

Specific-heat measurements on UTe₂ exhibit power-law behavior, C_el ∝ Tⁿ with n ≈ 3 in zero field, attributed to quasiparticle excitations from point nodes^47,48. The anisotropic field dependence of C_el has been interpreted as evidence for point nodes oriented along the b-axis⁴⁸. However, the proposed b-axis pseudo point node scenario consistently explains both behaviors (Supplementary Fig. 8). The gap minima revealed by thermal conductivity measurements remain inaccessible to specific-heat measurements due to Schottky anomalies below T ~ 0.3 K, which are strongly enhanced under applied magnetic fields. As shown in Supplementary Fig. 8, the T-dependence of the specific heat exhibits C/T ∝ T² dependence above 0.3 K for pseudo point nodes with ${\mathrm{\Delta }}_{\min }/{\mathrm{\Delta }}_0\approx 0.1$. Magnetic field dependence of the specific heat is also unlikely to identify a small residual gap. While for the point nodes the expected field behavior is $C/T\propto -\left(H/H_{c2}\right)lnH/H_{c2}$, for a small gap it becomes $C/T\propto -\left(H/H_{c2}\right)ln\left[H/H_{c2}+{\left({\mathrm{\Delta }}_{\min }/a{\mathrm{\Delta }}_0\right)}^2\right]$, and hence the substantial difference is only observed for H ≪ H^⋆, where such measurements are not possible.

Finally, the emergence of a strongly anisotropic superconducting gap exhibiting pseudo point nodes in UTe₂ is highly unusual and represents a remarkable example of unconventional superconductivity. While multiorbital band structure effects can generate momentum-dependent gap variations, the pronounced gap minimum along the b-axis, characterized by a small but finite anisotropy ratio ${\mathrm{\Delta }}_{\min }/{\mathrm{\Delta }}_0~0.1$, is not naturally expected from Fermi-surface geometry alone in UTe₂. Although an accidental origin cannot be entirely excluded, achieving such a deep yet finite minimum without symmetry protection would generally require a delicate balance of microscopic parameters, such as a strong directional variation of the electronic structure, a momentum-dependent pairing interaction that suppresses the gap, or a combination of both. Given the relatively smooth electron and hole Fermi surfaces of UTe₂¹², the pseudo-point nodes are more naturally interpreted as reflecting strong anisotropy in the underlying pairing interaction. From this perspective, the observed gap structure places important constraints on the microscopic origin of superconductivity in UTe₂.

The presence of pseudo-point nodes in UTe₂ imposes important constraints on the superconducting gap function and its formation mechanism. To completely lift the point nodes, it is natural to consider weakly unitary mixing states where two order parameter components, such as B_2u+ αA_u, possess real relative phases. Alternatively, pseudo-point nodes can be interpreted as nodal structures that are quasi-protected by crystal symmetry but partially lifted by weak symmetry-breaking perturbations, possibly arising from spin-orbit coupling or weak interorbital hybridization. This results in the formation of a highly anisotropic superconducting gap with pronounced minima along specific crystallographic directions in momentum space. Further theoretical analysis and experimental verification are required to identify the dominant mechanism underlying pseudo-point node formation in UTe₂.

Methods

High-quality single-crystal samples of UTe₂ were grown by the molten-salt method. Both crystals were cut to dimensions suitable for thermal-conductivity measurements, typically with length  ~ 360 μm (∥b), width  ~ 370 μm (∥a), and thickness  ~ 110 μm (∥c). Thermal conductivity was measured using the standard steady-state method with one heater and two thermometers, applying a temperature gradient along the b axis. The typical thermal gradient was less than 3% of the bath temperature. To ensure good electrical and thermal contacts, four platinum wires were attached by spot welding. Electrical resistivity was measured in situ within the same set-up used for thermal-conductivity measurements. The Wiedemann-Franz law was employed as an internal consistency check for our thermal conductivity measurements in magnetic fields (Supplementary 2).

Author contributions

S.H. and Y.M. conceived the study. M.M.B., E.D.B., and P.F.S.R. synthesized the samples. S.H., K.I., and R.M. performed thermal conductivity and resistivity measurements. S.H. analyzed the data, and I.V. performed theoretical calculations. All authors discussed the results. S.H., Y.M., and I.V. prepared the manuscript with input from all authors.

Peer review

Peer review information

Nature Communications thanks anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Funding

Work at the Los Alamos National Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering, project “Quantum Fluctuations in Narrow-band Systems”. S.H. acknowledges the Director’s Postdoctoral Fellowship through the Laboratory Directed Research and Development Program at Los Alamos National Laboratory.

Data availability

The data supporting the findings of this study are available within the paper, its Supplementary Information and the Source Data file. Source data are provided in this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-75566-9.