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Evidence for unconventional superconductivity in twisted trilayer graphene

Abstract

Magic-angle twisted trilayer graphene (MATTG) has emerged as a moiré material that exhibits strong electronic correlations and unconventional superconductivity1,2. However, local spectroscopic studies of this system are still lacking. Here we perform high-resolution scanning tunnelling microscopy and spectroscopy of MATTG that reveal extensive regions of atomic reconstruction favouring mirror-symmetric stacking. In these regions, we observe symmetry-breaking electronic transitions and doping-dependent band-structure deformations similar to those in magic-angle bilayers, as expected theoretically given the commonality of flat bands3,4. Most notably in a density window spanning two to three holes per moiré unit cell, the spectroscopic signatures of superconductivity are manifest as pronounced dips in the tunnelling conductance at the Fermi level accompanied by coherence peaks that become gradually suppressed at elevated temperatures and magnetic fields. The observed evolution of the conductance with doping is consistent with a gate-tunable transition from a gapped superconductor to a nodal superconductor, which is theoretically compatible with a sharp transition from a Bardeen–Cooper–Schrieffer superconductor to a Bose–Einstein-condensation superconductor with a nodal order parameter. Within this doping window, we also detect peak–dip–hump structures that suggest that superconductivity is driven by strong coupling to bosonic modes of MATTG. Our results will enable further understanding of superconductivity and correlated states in graphene-based moiré structures beyond twisted bilayers5.

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Fig. 1: Topography and spectroscopy of MATTG at zero magnetic field.
Fig. 2: LDOS Landau fan diagram and doping-dependent band deformations in MATTG.
Fig. 3: Spectroscopic gap in the −3 < v < −2 range and signatures of unconventional superconductivity.
Fig. 4: Peak–dip–hump structure in MATTG.

Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request.

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Acknowledgements

We acknowledge discussions with F. von Oppen, G. Refael, Y. Peng and A. Yazdani. This work was primarily supported by the Office of Naval Research (grant number N142112635); the National Science Foundation (grant number DMR-1753306); and the Army Research Office under grant award W911NF17-1-0323. Nanofabrication efforts were in part supported by Department of Energy DOE-QIS programme (DE-SC0019166) and National Science Foundation (grant number DMR-2005129). S.N.-P. acknowledges support from the Sloan Foundation. J.A. and S.N.-P. also acknowledge support from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through grant GBMF1250; C.L. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant GBMF8682. A.T. and J.A. are grateful for the support of the Walter Burke Institute for Theoretical Physics at Caltech. H.K. and Y.C. acknowledge support from the Kwanjeong fellowship.

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Contributions

H.K. and Y.C. fabricated samples with the help of Y.Z. and R.P., and performed STM measurements. H.K., Y.C. and S.N.-P. analysed the data. C.L. and A.T. provided the theoretical analysis supervised by J.A. S.N.-P. supervised the project. H.K., Y.C., C.L., A.T., J.A. and S.N.-P. wrote the manuscript with input from the other authors.

Corresponding author

Correspondence to Stevan Nadj-Perge.

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Extended data figures and tables

Extended Data Fig. 1 Spectroscopy of twisted bilayer and twisted trilayer graphene.

a, Point spectra of twisted bilayer graphene (TBG) on an AA site at a twist angle θ = 1.44°, from a bilayer region found in the same sample. b, Point spectra of twisted trilayer graphene (TTG) on an AAA site at a twist angle θ = 1.45°. Unlike TBG at the similar angle, signatures of correlations, such as enhancement of VHS separations at charge neutrality and cascade of flavour symmetry breaking, are observed. c, Linecuts taken from a, b around v = −4 (white dashed lines). While the dI/dV LDOS between the flat bands and the remote band is zero for TBG, the value is finite for TTG due to the existence of the additional Dirac cones.

Extended Data Fig. 2 Comparison between spectra on ABA and AAA sites at finite fields.

a, b, Point spectroscopy as a function of VGate on ABA stacked (a, the same as panel Fig. 2d) and on AAA stacked (b) region (B = 3 T, θ = 1.46°). In comparison, flat bands appear to be more prominent on the AAA site (b), while LLs from Dirac-like dispersion and dispersive bands appear more pronounced at ABA site. This is a direct consequence of LDOS from the flat bands being localized on the AAA sites. The LDOS from Dirac-like bands is spatially uniformly distributed.

Extended Data Fig. 3 Distinguishing dispersive band LLs and Dirac band LLs.

a, b, Point spectroscopy as a function of VGate on ABA stacked (a) and AAA stacked (b) region (B = 8 T, θ = 1.46°). Zeroth LL from Dirac dispersion is clearly distinguished from other LLs as it crosses the flat band. Other LLs from Dirac dispersion is distinguished from the dispersive band from being parallel to the zeroth LL as a function of doping. Additional LL is observed at this high magnetic field at VGate > 12 V which is more pronounced at AAA stacked region and can be attributed to second Dirac cone due to finite displacement field present at these VGate.

Extended Data Fig. 4 Spectroscopy near v = −2.

Linecuts taken from Fig. 3a for VGate ranging from −6.3 V to −7.4 V in 100 mV steps. Starting from top, the observed gap is highly asymmetric and gradually evolves to the more symmetric spectrum on the bottom. Vertical dashed line shows the position of VBias = 0 mV. We interpret that asymmetric gap (brown lines) corresponds to correlated insulator regime, while the symmetric gap (black lines) indicates superconducting regime.

Extended Data Fig. 5 Spectral features around CNP and their comparison to the superconducting (SC) gap at v   ≈    −2.1.

a, Zoom-in 2D gate spectroscopy of Fig. 1f in the main text. Green triangles mark the position of LDOS suppression around VBias = 0 mV at multiple VGate. b, Linecuts of (a) at VGate = 1.4 V to 0 V as indicated by numbers (in volts) indicated in the legend. Green triangles mark the position of same LDOS suppression in (a). Line traces are offset for clarity. Red dashed line is linecut at VGate = −7.6 V from same 2D gate spectroscopy in Fig. 1f of the main text showing the spectrum of SC gap.

Extended Data Fig. 6 Andreev reflection signal from point contact spectroscopy of MATTG.

a, Point contact conductance (dI/dV) spectroscopy as a function of VGate at twist angle θ = 1.42° at T = 400 mK. The black box highlights the filling factor range −3 < v < −2.2 where clear signatures of the we Andreev reflection are observed. b, Linecut of point contact dI/dV as a function of VGate. Grey region marks the filling factor range where Andreev reflection signal is observed. c, PCS dI/dV spectra for 4 different perpendicular magnetic field at twist angle θ = 1.44°. Lines are offset for clarity. d, PCS dI/dV conductance as a function of temperature and VBias. e, Linecuts from d for T = 0.4 − 1.1 K and the additional trace at T = 1.7 K showing the suppression of the Andreev reflection. These temperatures are slightly smaller (by a factor of 1.5−2) compared to the temperature scales where coherence peaks get completely suppressed.

Extended Data Fig. 7 Additional datasets showing magnetic field and temperature dependence of spectroscopic gap in the −3 < v < −2 range.

a–d, Point spectroscopy as a function of VGate at twist angle of θ = 1.51° at magnetic field B = 0 T (a), B = 300 mT (b), B = 600 mT (c), B = 1 T (d). e, Line traces showing magnetic field dependence for VGate = −7.8 V (U-shaped regime). Colour coding corresponds to magnetic field B = 0, 0.1, 0.2, 0.3, 0.4, 0.4, 0.8, 1 T. Plots are offset for clarity. f, g, Gate spectroscopy measured at B = 2 T (f) and B = 4 T (g), for θ = 1.54° featuring gapped spectrum persisting \(B\gtrsim 4\,{\rm{T}}\) (data taken at different point compared to ae). hk, Gate spectroscopy taken at different temperatures T = 400 mK (h), T = 2 K (i), T = 4 K (j), T = 7 K (k). i, Point spectroscopy measured as a function of VBias and temperature at the same point as (hk) for VGate = −7.8 V.

Extended Data Fig. 8 Spectroscopic gap in the +2 < v < +3 range.

a, Tunnelling conductance spectroscopy at twist angle of θ = 1.57° on AAA stacked region at T = 2 K showing well-developed gapped region on the electron-side. b, Spectroscopy measured at the same region at T = 400 mK. c, Spectroscopy as a function of temperature at the same point as (a, b) for VGate = 10 V. d, Spectroscopy focusing on hole doping taken with the same micro-tip. While the spectrum for hole doping (d) shows clear coherence peaks and dip–hump structures these features are absent for the gap on the electron-side. We speculate that for electron doping, the coherence peaks are suppressed even at our base temperature (T = 400 mK), which would suggest that the observed gap corresponds to pseudogap phase. However, further investigation is needed to confirm this scenario and rule out other possible origins.

Extended Data Fig. 9 Normalization of tunnelling conductance and fitting.

a, Tunnelling conductance measured on Pb (110) surface at T = 400 mK showing superconducting gap. Blue dashed line is Dynes formula fit with two gaps with following parameters, Δ1 = 1.42 meV, Δ2 = 1.26 meV, Γ = 10 μeV, T = 400 mK used to obtain the base temperature. b, Same data as Fig. 3a showing larger VBias range. Black dashed lines mark gate voltages VGate = −7.5, −7.89, −8.4 V with the corresponding line traces shown in subsequent panels. c, Line cut in the U-shaped regime (VGate = −7.5 V). Red dotted line is polynomial fitting curve obtained as described in Supplementary Information 4. d, Normalized data obtained by dividing the raw data (black line in c) by polynomial fit (red line in c). Blue line is Dynes formula fit with isotropic gap. e, Same data as d with Dynes formula fits using different types of the pairing gap symmetry: s + id pairing gap with Δs = 0.88 meV, Δd = 1.10 meV, Γ = 135 eV (brown); d + id pairing gap with Δd1 = 0.85 meV, Δd2 = 1.35 meV, Γ = 135 eV (cyan). f, In the V-shaped regime (VGate = −7.89 V). g, Normalized data from f and Dynes formula fit using an isotropic gap (blue). h, Normalized data from f with Dynes formula fits using a nodal gap with Δ = 1.44 meV (green). i, Another linecut in the V-shaped regime (VGate = −8.4 V). j, Normalized data from i and Dynes formula fit using an isotropic gap (blue, purple). k, Normalized data from i and Dynes formula fits green line is nodal gap with Δ = 1.26 meV.

Extended Data Fig. 10 Comparing Nodal and s-wave pairing symmetry fit in the V-shaped region.

a, b, Normalized dI/dV spectrum and its nodal (a) and s-wave (b) fit at VGate = −8.4 V. Fit parameters Δ and Γ are obtained by performing least square method within −2Δc to 2Δc VBias range where Δc is 1.04 meV defined by half of the separation between coherence peaks. Nodal fit from 1Δc to 1Δc shows almost The inset is a zoom-in around VBias = 0 mV where the deviation between the two is largest. c, d, Nodal (c) and s-wave (d) fit for same data in (a, b) with fixed Δ so that the position of the coherence peak from the fit curve matches to the position of the coherence peak in the data. Fit parameter Γ is obtained by fitting within −2Δc to 2Δc. S-wave fit shows even larger deviation from the data in this case. e, f, Nodal (e) and s-wave(f) fit for the same data in (a, b) where fit parameters Δ and Γ are obtained within reduced VBias range −0.5Δc c to 0.5Δc. All χ2/df values are calculated within the VBias range where least square method is performed.

Extended Data Fig. 11 Dynes formula fit to nodal and s-wave gap in the U-shaped region.

a, b, Normalized dI/dV spectrum and its nodal fit (a) and s-wave fit (b) at VGate = −7.4 V. Fit parameters Δ and Γ are obtained by performing least square optimization in −2Δc to 2Δc range of VBias, where Δc = 1.2 meV. c, Same data as (a, b) with fit parameters obtained from reduced VBias range −0.5Δc to 0.5Δc. This gives better fit around VBias = 0 meV. χ2 values are calculated within the VBias range where least square optimization is performed.

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Kim, H., Choi, Y., Lewandowski, C. et al. Evidence for unconventional superconductivity in twisted trilayer graphene. Nature 606, 494–500 (2022). https://doi.org/10.1038/s41586-022-04715-z

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