Abstract
Spintriplet superconductors are condensates of electron pairs with spin 1 and an oddparity wavefunction^{1}. An interesting manifestation of triplet pairing is the chiral pwave state, which is topologically nontrivial and provides a natural platform for realizing Majorana edge modes^{2,3}. However, triplet pairing is rare in solidstate systems and has not been unambiguously identified in any bulk compound so far. Given that pairing is usually mediated by ferromagnetic spin fluctuations, uraniumbased heavyfermion systems containing felectron elements, which can harbour both strong correlations and magnetism, are considered ideal candidates for realizing spintriplet superconductivity^{4}. Here we present scanning tunnelling microscopy studies of the recently discovered heavyfermion superconductor UTe_{2}, which has a superconducting transition temperature of 1.6 kelvin^{5}. We find signatures of coexisting Kondo effect and superconductivity that show competing spatial modulations within one unit cell. Scanning tunnelling spectroscopy at step edges reveals signatures of chiral ingap states, which have been predicted to exist at the boundaries of topological superconductors. Combined with existing data that indicate triplet pairing in UTe_{2}, the presence of chiral states suggests that UTe_{2} is a strong candidate for chiraltriplet topological superconductivity.
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Acknowledgements
The authors thank T. L. Hughes, Y. Tanaka, N. Mason, D. Van Harlingen, P. Abbamonte, C. Kallin, Y. Yanase, O. Erten, R. Flint, Y. Wang, J. C. Davis, L. Hu and R. Huang for discussions. The work at UIUC was supported by a grant from the US Department of Energy, Office of Science, Basic Energy Sciences, under award number DESC0014335. V.M. acknowledges partial support from Gordon and Betty More Foundation’s EPiQS Initiative through grant GBMF4860. Z.W. is supported by the US Department of Energy, Basic Energy Sciences through grant number DEFG0299ER45747. The work at UMD was supported by NIST. M.S. was supported by a grant from the Swiss National Science Foundation through Division II, number 184739.
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V.M., N.P.B. and L.J. conceived the experiments. L.J., Z.W. and J.O.R. obtained the STM data and characterized the samples. L.J., S.H., M.S., Z.W. and V.M. performed the data analysis and wrote the paper. S.R. and N.P.B. provided the characterized single crystals.
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Extended data figures and tables
Extended Data Fig. 1 High quality of UTe_{2} single crystal.
a, Optical micrograph of a UTe_{2} single crystal after being cut along the a axis. The exposed (0−11) surface is flat and shiny with several step edges along the a axis. b, Laue diffraction pattern of one UTe_{2} single crystal, with selected (hkl) surfaces marked. The same crystal was used for the specificheat and STS measurements presented in c. c, Specific heat of UTe_{2}, showing a pronounced single jump around 1.6 K. The specificheat jump at T_{sc} is particularly large, indicating bulk superconductivity of heavy electrons. The specificheat measurement and the temperaturedependent STS measurement shown in Fig. 1d were conducted on the same sample, indicating a well defined superconducting phase of UTe_{2}.
Extended Data Fig. 2 Crystal structure and cleaved plane of UTe_{2}.
a, Crystal structure of UTe_{2}. The lattice parameters are a = 4.161 Å, b = 6.122 Å and c = 13.955 Å. b, The primitive cell of UTe_{2} with the nearest bond distances between U and Te1, Te2 are denoted in the figure. c, (100) view of the crystal showing the cleaved plane, which is between the primitive cells and breaks the nextnearest U–Te1 bond (3.201 Å). d, Top view of the cleaved (0−11) plane. e, Typical STM topography image of a sample with multiple random distributed step edges. f, Height profile along the orange dashed line in the centre of c. The height of the step edge is ~5.5 Å. g, A 8 × 8 nm^{2} topography image showing chains of Te1 and Te2 along the a axis. h, Height profile measured along the red dashed line in g. The periodicity of the height profile fits very well with the lattice parameters in d. The step heights and the atomic spacings are consistent with the identification of the cleaved surface as the (0−11) plane.
Extended Data Fig. 3 Largeenergy LDOS of UTe_{2}.
a. dI/dV curve of UTe_{2} obtained at 0.3K from 500 mV to −500 mV. The curve follows a Vshape at higher energies and drops close to zero around zero bias. The almost zero DOS at E_{F} suggests that this material is close to being a Kondo insulator. b, A fit of the spatially averaged dI/dVcurve to the Fano model: \(\frac{{\rm{d}}I}{{\rm{d}}V}(V)\propto \frac{{[(V{E}_{0})/\varGamma +{q}_{{\rm{K}}}]}^{2}}{1+{[(V{E}_{0})/\varGamma ]}^{2}}\). Red and black curves are the raw data and the fitted curve, respectively. The fitting parameters are q_{K} = 0.57(2), E_{0} = 0.70(8) meV and Γ = 3.60(6) meV, and the uncertainties were derived from the standard errors of our fitting. Blue dashed lines are simple extrapolations (linear for V_{b} > 0 and quadratic for V_{b} < 0) of the Vshaped background, which are subtracted from the spectra, as shown in Extended Data Fig. 5b, for further analysis. arb. u., arbitrary units.
Extended Data Fig. 4 Phenomenology of the superconducting gap of UTe_{2}.
a, Comparison of the superconductinggap structure of UTe_{2} obtained with a tungsten tip (Wtip) and a UTe_{2} tip (a W tip with a UTe2 flake at the apex) with data on superconducting MoTe_{1.85}S_{0.15}. The spectra were all obtained using the same STM system at ~0.3 K without an external magnetic field. MoTe_{1.85}S_{0.15} has T_{sc} ≈ 2.2 K and a gap of Δ ≈ 0.3 meV, slightly larger than UTe_{2}. In UTe_{2}, the LDOS at zero bias drops by only 5–10% compared with its normalstate DOS, whereas it drops by ~80% in MoTe_{1.85}S_{0.15}. Even in the data measured by the UTe_{2} tip, which show a larger gap than MoTe_{1.85}S_{0.15}, the LDOS drop is smaller. Given that all the data were collected with similar tunnelling parameters and by the same STM system, the large residual LDOS in UTe_{2} is unlikely to be a simple thermal broadening effect or to be due to some external artefact. b, Magneticfielddependent dI/dV curves at 0.3 K. As discussed in the main text, the intrinsic superconducting gap is small. Therefore, tracking the superconductinggap structure in a high magnetic field is challenging. Instead, we present the data obtained with a superconducting tip. The figure shows that the superconducting gap is continuously suppressed up to 10 T. Because T_{sc} is around 1.6 K, this result suggests a large upper critical field of UTe_{2}, exceeding the Pauli limit of 1.86T_{sc}. Meanwhile, the derived upper critical field of ~10 T is consistent with transport measurements with the field perpendicular to the (0−11) plane.
Extended Data Fig. 5 Analyses of the Kondo lattice peak.
a, Fits to the Kondo resonance feature obtained as a function of position from Te1 (site A) to Te2 (site E) (see main text). Curves are fitted to the Fano line shape. The fitting parameters are summarized in Extended Data Table 1. The Kondo temperature T_{K} can be derived from Γ = k_{B}T_{K} (k_{B}, Boltzmann constant). As shown in the table, T_{K} varies from ~19.6 K to 26 K. b, The LDOS (dI/dV) obtained by subtracting a Vshaped background (dashed blue lines in Extended Data Fig. 3). c, Simulation of dI/dV by a Kondo lattice model with a quantum cotunnelling effect. The model used here was proposed by Maltseva et al.^{2}, \(\frac{{\rm{d}}I}{{\rm{d}}V}(V)={\rm{IM}}\left[{\left(1+\frac{vq}{V{\rm{i}}\gamma {E}_{0}}\right)}^{2}\,\log \left(\frac{V{\rm{i}}\gamma +D1\frac{{v}^{2}}{V{\rm{i}}\gamma {E}_{0}}}{V{\rm{i}}\gamma D2\frac{{v}^{2}}{V{\rm{i}}\gamma {E}_{0}}}\right)+\frac{(D1+D2){q}^{2}}{V{\rm{i}}\gamma {E}_{0}}\right]\), where the definitions of E_{0}, q are the same as those in the Fano model, −D1 and D2 are the energy levels of the lower and upper conduction band edges, respectively, v is the hybridization amplitude, and γ is the selfenergy. For simplicity, we take the same E_{0}, q from Extended Data Table 2. D1 ≈ 3 eV is obtained from angleresolved photoemission spectroscopy. Then the remaining free parameters are D2, v and γ. Extended Data Table 2 presents the fitting parameters. Given the Kondo hybridization gap Δ_{K} = 2v^{2}/(D1 + D2), we also calculated the hybridization gap size in Extended Data Table 2, which is comparable to Γ in Extended Data Table 1.
Extended Data Fig. 6 Analyses of the superconducting gap.
a, Fits to a series of superconducting gaps obtained at the positions shown in the inset as we move from Te1 (site A) to Te2 (site E). The dI/dV curves are fitted with the Dynes function including the thermal broadening effect^{40,41}: \(\frac{{\rm{d}}I}{{\rm{d}}V}(V)={N}_{0}\int {\rm{Re}}\left[\frac{V+\omega +{\rm{i}}G}{\sqrt{{(V+\omega +{\rm{i}}G)}^{2}{{\Delta }}^{2}(\theta ,\varphi )}}\right]\left(\frac{\partial f}{\partial \omega }\right){\rm{d}}\omega +{N}_{{\rm{u}}}\), where f is the Fermi–Dirac distribution function at 0.3 K, N_{0} is proportional to the LDOS in the normal state, N_{u} is related to the residual LDOS dominated by unpaired electrons, which is set at 0.5 based on the specificheat data, and G quantifies the effect of the pairbreaking processes, which is related to the quasiparticle lifetime (ω, energy; θ, polar angle; ϕ, azimuthal angle). The most important parameter here is the superconductinggap function Δ(θ, ϕ). Here, we tried both the swave gap Δ(θ, ϕ) = Δ_{0} and the proposed spintriplet p_{x} + ip_{y} gap \({\Delta }({\theta },\varphi )={{\Delta }}_{0}{\hat{k}}_{x}+{\rm{i}}{\hat{k}}_{y}\). As N_{u} is approximately 50% of N_{0}, the derived gap sizes Δ_{0} at each site are similar for the s and pwave gap functions. The fit parameters are summarized in Extended Data Table 3. For both s and pwave gap functions, Δ_{0} increases about 2.7 times from site A to site E, while G shows much smaller changes. b, Spatial variation of the superconducting gap from one Te2 chain to the next Te2 chain. Oscillations of the coherence peak and the zerobias LDOS are shown in the figure.
Extended Data Fig. 7 Robustness of the Kondo effect and ‘chirality’ of the tunnelling current around the step edge.
a, Topography image with a [0−1−1] step edge. b, dI/dV curves along the black arrow in a, obtained at nine points equally distributed within 2 nm. The results shown in b reveal a weak modulation of the Kondo effect, consistent with Extended Data Fig. 5. Importantly, no clear change of the energy level of the Kondo lattice peak is observed around the step edge when the asymmetric edge states appear. Therefore, the ingap states coexist with the Kondo effect in UTe_{2}. c, Topography image showing that a step edge can terminate at either Te1 or Te2 chains. d, dI/dV spectra obtained on Te2 and Te1 sites. The two spectra obtained at Te2 and Te1terminated step edges shown in c are similar, with the peak always appearing at negative bias, indicating that the ‘chirality’ of the tunnelling current is robust against local stepedge termination.
Extended Data Fig. 8 Schematic of momentumselective tunnelling on a step edge.
a, Schematic illustration of a sample showing the orientations of the a axis (which coincides with the chiral axis, \(\hat{c}\)) and the momentum K (spontaneous current direction). b, For a chiral superconductor, a quasilinear dispersive chiral ingap state (dark blue line) is expected to reside on the surface layers. c, On the step edge, the momentum distributions of incident tunnelling electrons are skewed. In this case, a momentumselective tunnelling effect is realized close to the step edge, enabling us to tunnel into states with either +k (blue dotted oval) or −k (red dotted oval).
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Jiao, L., Howard, S., Ran, S. et al. Chiral superconductivity in heavyfermion metal UTe_{2}. Nature 579, 523–527 (2020). https://doi.org/10.1038/s4158602021222
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DOI: https://doi.org/10.1038/s4158602021222
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