## Abstract

Spin-triplet superconductors are condensates of electron pairs with spin 1 and an odd-parity wavefunction^{1}. An interesting manifestation of triplet pairing is the chiral *p*-wave state, which is topologically non-trivial and provides a natural platform for realizing Majorana edge modes^{2,3}. However, triplet pairing is rare in solid-state systems and has not been unambiguously identified in any bulk compound so far. Given that pairing is usually mediated by ferromagnetic spin fluctuations, uranium-based heavy-fermion systems containing *f*-electron elements, which can harbour both strong correlations and magnetism, are considered ideal candidates for realizing spin-triplet superconductivity^{4}. Here we present scanning tunnelling microscopy studies of the recently discovered heavy-fermion 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 in-gap 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 chiral-triplet 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 DE-SC0014335. 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 DE-FG02-99ER45747. 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.

## Author information

### Affiliations

### Contributions

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.

### Corresponding author

Correspondence to Vidya Madhavan.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

**Peer review information** *Nature* thanks Xi Chen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

**Publisher’s note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## 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 specific-heat and STS measurements presented in **c**. **c**, Specific heat of UTe_{2}, showing a pronounced single jump around 1.6 K. The specific-heat jump at *T*_{sc} is particularly large, indicating bulk superconductivity of heavy electrons. The specific-heat measurement and the temperature-dependent STS measurement shown in Fig. 1d were conducted on the same sample, indicating a well defined superconducting phase of UTe_{2}.
Source Data

### 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 next-nearest 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.
Source Data

### Extended Data Fig. 3 Large-energy LDOS of UTe_{2}.

**a**. d*I*/d*V* curve of UTe_{2} obtained at 0.3K from 500 mV to −500 mV. The curve follows a V-shape 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 d*I*/d*V*-curve 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 V-shaped background, which are subtracted from the spectra, as shown in Extended Data Fig. 5b, for further analysis. arb. u., arbitrary units.
Source Data

### Extended Data Fig. 4 Phenomenology of the superconducting gap of UTe_{2}.

**a**, Comparison of the superconducting-gap structure of UTe_{2} obtained with a tungsten tip (W-tip) 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 normal-state 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**, Magnetic-field-dependent d*I*/d*V* curves at 0.3 K. As discussed in the main text, the intrinsic superconducting gap is small. Therefore, tracking the superconducting-gap 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 1.86*T*_{sc}. Meanwhile, the derived upper critical field of ~10 T is consistent with transport measurements with the field perpendicular to the (0−11) plane.
Source Data

### 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 (d*I*/d*V*) obtained by subtracting a V-shaped background (dashed blue lines in Extended Data Fig. 3). **c**, Simulation of d*I*/d*V* 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, −*D*1 and *D*2 are the energy levels of the lower and upper conduction band edges, respectively, *v* is the hybridization amplitude, and *γ* is the self-energy. For simplicity, we take the same *E*_{0}, *q* from Extended Data Table 2. *D*1 ≈ 3 eV is obtained from angle-resolved photoemission spectroscopy. Then the remaining free parameters are *D*2, *v* and γ. Extended Data Table 2 presents the fitting parameters. Given the Kondo hybridization gap *Δ*_{K} = 2*v*^{2}/(*D*1 + *D*2), we also calculated the hybridization gap size in Extended Data Table 2, which is comparable to *Γ* in Extended Data Table 1.
Source Data

### 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 d*I*/d*V* 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 specific-heat data, and *G* quantifies the effect of the pair-breaking processes, which is related to the quasiparticle lifetime (*ω*, energy; *θ*, polar angle; *ϕ*, azimuthal angle). The most important parameter here is the superconducting-gap function *Δ*(*θ*, *ϕ*). Here, we tried both the *s*-wave gap *Δ*(*θ*, *ϕ*) = *Δ*_{0} and the proposed spin-triplet *p*_{x} + i*p*_{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 *p*-wave gap functions. The fit parameters are summarized in Extended Data Table 3. For both *s*- and *p*-wave 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 zero-bias LDOS are shown in the figure.
Source Data

### 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**, d*I*/d*V* 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 in-gap 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**, d*I*/d*V* spectra obtained on Te2 and Te1 sites. The two spectra obtained at Te2- and Te1-terminated 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 step-edge termination.
Source Data

### Extended Data Fig. 8 Schematic of momentum-selective 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 quasi-linear dispersive chiral in-gap 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 momentum-selective 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 heavy-fermion metal UTe_{2}.
*Nature* **579, **523–527 (2020). https://doi.org/10.1038/s41586-020-2122-2

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