A strongly inhomogeneous superfluid in an iron-based superconductor


Although the possibility of spatial variations in the superfluid of unconventional, strongly correlated superconductors has been suggested1,2,3,4,5,6,7, it is not known whether such inhomogeneities—if they exist—are driven by disorder, strong scattering or other factors. Here we use atomic-resolution Josephson scanning tunnelling microscopy to reveal a strongly inhomogeneous superfluid in the iron-based superconductor FeTe0.55Se0.45. By simultaneously measuring the topographic and electronic properties of the superconductor, we find that this inhomogeneity in the superfluid is not caused by structural disorder or strong inter-pocket scattering and is not correlated with variations in the energy required to break electron pairs. Instead, we see a clear spatial correlation between the superfluid density and the quasiparticle strength (the height of the coherence peak) on a local scale. This result places iron-based superconductors on equal footing with copper oxide superconductors, where a similar relation has been observed on the macroscopic scale. Our results establish the existence of strongly inhomogeneous superfluids in unconventional superconductors, excluding chemical disorder and inter-band scattering as the causes of the inhomogeneity, and shed light on the relation between quasiparticle character and superfluid density. When repeated at different temperatures, our technique could further help to elucidate what local and global mechanisms limit the critical temperature in unconventional superconductors.

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Fig. 1: Principles of Josephson STM.
Fig. 2: Josephson tunnelling spectra on FeTe0.55Se0.45.
Fig. 3: Visualizing the superfluid in FeTe0.55Se0.45.
Fig. 4: Correlation between (ICRN)2 and coherence peak height.

Data and code availability

The data and code used in this work are available from the corresponding author upon reasonable request.


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We acknowledge J. C. Davis, S. D. Edkins, M. H. Fischer, K. J. Franke, H. Grabert, M. H. Hamidian, K. Heeck, M. Leeuwenhoek, D. K. Morr, M. T. Randeria, G. Verdoes and J. Zaanen for discussions. This work was supported by the European Research Council (ERC StG SpinMelt) and by the Netherlands Organization for Scientific Research (NWO/OCW), as part of the Frontiers of Nanoscience programme, as well as through a Vidi grant (680-47-536). G.D.G. is supported by the Office of Basic Energy Sciences, Materials Sciences and Engineering Division, US Department of Energy (DOE) under contract number de-sc0012704.

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Nature thanks Peter Wahl and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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D. Cho, K.M.B. and D. Chatzopoulos performed experiments and data analysis. G.D.G. grew and characterized the samples. M.P.A. supervised the project and wrote the paper with input from all authors.

Corresponding author

Correspondence to M. P. Allan.

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Extended data figures and tables

Extended Data Fig. 1 Schematic of a Josephson tunnelling junction.

The Josephson junction consists of a Pb-coated platinum–iridium (Pt-Ir) tip and an atomically flat FeTe0.55Se0.45 surface, separated by a thin vacuum barrier. Inset, the Fe lattice is encapsulated by the chalcogen atoms selenium (Se) and tellurium (Te).

Extended Data Fig. 2 Various models used to describe Josephson tunnelling and their IV characteristic curves.

a, Tilted-washboard potential Uϕ) for Ibias < IC. b, IV curve calculated using the RCSJ model for Z(ω) = 0 and T = 0 K. The voltage drop is zero (dissipationless supercurrent) until Ibias > IC. c, Thermal phase fluctuations (illustrated by yellow dashed arrows) in the tilted-washboard potential. d, IV and corresponding differential conductance dI/dV, calculated using the IZ model for Z(ω) = R and the phase-diffusive regime (ET > EJ). For the simulation we used RN = 1 kΩ and T = 2 K. e, Energy diagram of sequential inelastic Cooper pair tunnelling. f, IV and differential conductance dI/dV, calculated using P(E) theory for a Z(ω) corresponding to the tip-induced antenna mode of energy  = 200 μeV and the Coulomb blockade regime (ET < EC). The IV and dI/dV curves in d and f correspond to a voltage of VB inside the gap.

Extended Data Fig. 3 Tunnelling spectra of Pt–Ir/Pb and Pb/Pb junctions.

a, Differential tunnelling spectra of a Pt–Ir/Pb junction with (blue dots) and without (red dots) electronic filtering using home-built lumped-element low-pass filters in series with commercial 1.9-MHz low-pass filters and grounding for all non-essential lines (Vset = +5 mV, Iset = 0.10 nA). We use a modified Dynes formula to fit our spectra, and the results give effective temperatures of 2.38 K (green line) and 2.20 K (yellow line). The other parameters are the same in both cases (ΔCP = 1.30 meV and γ = 50 μeV). b, Normalized conductance spectrum (blue curve) of a Pb/Pb junction, acquired with a junction resistance of 5 MΩ (Vset = +5 mV, Iset = 1.0 nA). The fit (red dashed curve) is consistent with the quasiparticle spectrum of a symmetric Josephson junction with a pair-breaking gap of 1.3 meV at 2.2 K.

Extended Data Fig. 4 Josephson tunnelling spectroscopy in a Pb/FeTe0.55Se0.45 junction.

a, b, RN-dependent IV curves (see key in e). cd, Corresponding RN-dependent dI/dV curves, multiplied by RN. The datasets are offset for clarity. For decreasing RN, the zero-bias peak and the small modulations (with a period of 0.1 meV) induced by Cooper pair tunnelling become more pronounced. e, Linear relation (black dashed line) between the critical Josephson current IC and the normal-state conductance, GN. Each point is the average of 20 points extracted from 20 IV curves, as described in the main text. For each GN, we also extract the standard deviation of Imax and obtain the error bars shown in the figure by performing error propagation via the IZ formula. The red dashed line corresponds to the AB formula for a asymmetry Josephson junction in which two superconductor electrodes have the same s-wave symmetry with different pair-breaking gaps (ΔCP,t = 1.30 meV and ΔCP,s = 1.68 meV). f, Fitting (black curve) of a normalized conductance spectrum (red circles) using the IZ model. All dI/dV spectra are acquired with Vset = −10 mV and a lock-in modulation of Vmod = 20 μV peak to peak.

Extended Data Fig. 5 Superfluid density maps with inhomogeneous normal-state resistance.

a, b, Maps of the critical Josephson current IC. c, d, Spatial variations of the normal-state resistance, RN. e, f, Maps of (ICRN)2 associated with the superfluid density. The images in the left (right) column were acquired with a setup bias of −10 mV (+10 mV) and a setup current of 10 nA. To map the intrinsic superfluid density, it is necessary to normalize the measured IC by multiplying with RN. Topographs were acquired simultaneously with these measurements and used to align the different maps.

Extended Data Fig. 6 Determination of normal-state junction resistance, RN.

a, RN-dependent differential conductance curves, dI/dV (see key in c). For the normal-state conductance GN, we use average values of dI/dV over the full energy range. The GN values are indicated with the dashed lines and labels. b, RN-dependent IV curves acquired simultaneously with dI/dV. c, The IV curves multiplied with RN. All of the curves coincide. All spectra were acquired with Vset = −10 mV and a lock-in modulation of Vmod = 100 μV peak to peak.

Extended Data Fig. 7 Quasiparticle interference induced by inter-pocket scattering in FeTe0.55Se0.45.

a, Top-view of the atomic structure of FeTe0.55Se0.45. The blue and red spheres denote the chalcogen and the transition metal atoms, respectively. b, Fermi surface of FeTe0.55Se0.45. Two hole pockets are at the Γ point and one electron pocket at the M point, marked by black circles and ellipses. The red (blue) dashed lines correspond to the reciprocal lattice of Fe (chalcogen) layer. Because the unit cell includes two Fe atoms, the Brillouin zone of Fe (red square) atoms is two times larger than that of the full crystal structure (blue square). The alternate vertical positions of the chalcogen atoms above and below the Fe layer lead to a folded band (grey ellipse centred at the M point) composed of out-of-plane d orbitals59. Here we highlight the inter-pocket scattering wavevectors with black, yellow and red solid arrows. c, Sketch of scattering wavevectors in the reciprocal lattice. The colour coding is identical to that in b. d, Stripy patterns in a dI/dV map at +3.9 meV induced by inter-pocket scattering (Vset = −10 mV, Iset = 20 nA and Vmod = 200 μV peak to peak). e, FFT spectrum of quasiparticle interference patterns. The circles correspond to the inter-pocket scattering wavevectors in b with the same colour coding.

Extended Data Fig. 8 Determination of quasiparticle interference strength.

a, dI/dV map at VB = +3.6 meV (shown in Fig. 3d). b, Band-pass-filtered FFT (not symmetrized) spectrum. c, Inverse FFT map of the filtered spectrum in b. d, Amplitude map of inter-pocket scattering pattern. The amplitude is determined by smoothing the filtered image in c. The red contours correspond to the mean amplitude of the map.

Extended Data Fig. 9 Correlation plots between superfluid density and various parameters.

a–d, Correlation between superfluid density and pair-breaking gap (a); strength of quasiparticle interference (b); topographic height (c) and quasiparticle strength minus the normal-state conductance (d; see inset), which gives similar results to those obtained without subtracting the normal conductance, as in the main text.

Extended Data Fig. 10 Suppression of superfluid density at the atomic scale.

a, b, Topograph (a) and superfluid density map (b). To highlight the atomic-scale variation of the superfluid density, we show the magnified map centred at the atomic defect (marked by a red and white arrow). Same data as in Fig. 3a, b.

Extended Data Table 1 Variables and symbols used in the paper

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Cho, D., Bastiaans, K.M., Chatzopoulos, D. et al. A strongly inhomogeneous superfluid in an iron-based superconductor. Nature 571, 541–545 (2019). https://doi.org/10.1038/s41586-019-1408-8

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