Extended strange metal and superconductivity in partially filled moir'e Hubbard bands

The gist: This work reports the emergence of an extended strange metal (ESM) and a new superconducting dome in a partially filled Hubbard band away from half-band-filling in twisted bilayer WSe2, suggesting this state is an intrinsic state of matter driven by strong electronic correlations rather than quantum criticality or electron-phonon pairing.

Model and System Realization

The Hubbard model is used as a simple theoretical model attempting to capture the effects of electronic correlations in materials with flat bands on page 1. Moiré semiconductors provide an approximate realization of the Hubbard model with tunable doping density and electronic bandwidth (W ∝ t) on page 2. Twisted homobilayer WSe2 (tWSe2) further allows efficient control of W to the intermediate coupling regime through the twist angle (θ) on page 2. This enables the realization of a bandwidth-tuned Mott transition and superconductivity in its vicinity, mimicking high-temperature superconductors on page 2. The topmost moiré valence band of tWSe2 can be mapped to a single-band triangular lattice Hubbard model with a widely tunable coupling strength! proportional to the number of layers on page 3.

Experimental Control and Phase Diagram

The authors fabricated dual-gated Hall bar devices of tWSe2 with varying twist angles for electrical transport studies on page 2. These gates allow independent control of E and the doping density (n) measured in the lattice filling factor (ν ≡ %!) on page 2. The combined effects of θ and E provide a powerful control of the moiré Hubbard Hamiltonian on page 3. Figure 1d shows longitudinal resistivity ρ'' as a function of ν and E for different samples at T = 30mK and B = 0 T on page 2. The phase diagram can be divided into the layer-polarized and layer-hybridized regions on page 2. A Mott insulator with diverging ρ'' is observed at ν = 1 inside the layer-hybridized region on page 2.

Emergence of Superconducting States

The study reports the observation of a new superconducting dome near ν = 0.55 and E = 0mV/nm, labeled SC2 on page 2. This superconducting region (SC2) is observed over a narrow twist-angle range θ ≈ 3.4° − 3.7° on page 2. The optimal T) for SC2 is found to be ≈ 120mK at ν ≈ 0.55 on page 3. The superconducting domes are centered at fillings away from the van Hove singularity (vHS), which is centered at ν ≈ 0.78 on page 3.

Characteristics of the Extended Strange Metal (ESM)

The normal-state transport properties reveal an ESM characterized by a T-linear resistivity for T) ≲ T ≲ 2K over a wide doping density range on page 4. The resistivity curves can be described by ρ'' = ρ. + A × T/(1) on page 4. The extracted exponent is close to α = 1 for T) ≲ T ≲ 3K over the doping density range 0.5 ≲ ν ≲ 1 at B = 0T on page 4. The result shows that the normal state of the material is a clean strange metal over the examined doping density range on page 4.

Twist-Angle Dependence and Correlation with Superconductivity

The twist-angle evolution of the ESM is examined, showing an ESM with α ≲ 1 is observed for T) ≳ T) and 0.6 ≲ ν ≲ 1 in the θ ≈ 3.4° device on page 5. The presence of a Mott insulator at ν = 1 in the θ ≈ 3.4° but not the θ ≈ 3.5° device shows that a Mott transition happens near the critical angle θ: ≈ 3.4° − 3.5° on page 5. SC2 also appears near θ: and coexists with the ESM over the twist angle range θ ≈ 3.5° − 3.7° on page 5, disappearing when Fermi liquid transport emerges at larger twist angles on page 5.

Theoretical Implications

The observed ESM in the clean limit is unusual and calls for a new understanding of the electrical transport in a partially filled Hubbard band near the Mott transition on page 6. The ESM is compatible with a model involving Umklapp scattering between itinerant holes of a hole-doped Mott insulator and the spinon Fermi surface of a quantum spin liquid on page 6. This model predicts non-Fermi liquid transport (including α < 1) in the clean limit, obedience to Kohler’s rule, and conventional Hall response, all consistent with experimental observations on page 6. The ESM is not associated with an extended quantum criticality or marginal Fermi liquids emerging at a quantum critical point on page 1.

Conclusion

The results suggest that the superconducting domes are not induced simply by the large density of states effect at the vHS on page 3. The findings indicate that strong electronic correlations are the origin of these observed superconducting domes rather than a pure electron-phonon pairing mechanism on page 3. The ESM is different from those reported in twisted bilayer graphene in several ways, including negligible ρ. compared to both 78 and Δρ'' on page 6. The ESM is incompatible with any theoretical model for non-Fermi liquids or marginal Fermi liquids emerging at a quantum critical point on page 6.

Methods Summary

The determination of the power-law exponent α(T) involved taking a logarithmic derivative of the measured resistivity ρ'' ≈ ρ. + A × T/ on page 7. The construction of the twist angle dependent phase diagram involved combining ρ'' data from six devices and plotting a contour map on page 7. The analysis of magnetoresistivity showed an approximate obedience to Kohler’s rule and quadrature scaling due to the negligible ρ. on page 8. The study also examined the Zeeman splitting of the vHS and its effect on magneto-transport, noting that a small magnetic field is sufficient to induce a strong Zeeman splitting on page 8. The analysis of Hall resistivity showed a weak temperature dependence for ρ' in contrast to some strange metals on page 8. The final phase diagram construction utilized the temperature dependence data in Fig. 3 on page 7.

References

1 Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moiré bands on page 8

2 Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator on page 8

3 Mak, K. F. & Shan, J. Semiconductor moiré materials on page 8

4 Ghiotto, A. et al. Quantum criticality in twisted transition metal dichalcogenides on page 8

5 Xia, Y. et al. Bandwidth-tuned Mott transition and superconductivity in moiré WSe2 on page 8

6 Arovas, D. P., Berg, E., Kivelson, S. A. & Raghu, S. The Hubbard Model on page 8

7 Qin, M., Schäfer, T., Andergassen, S., Corboz, P. & Gull, E. The Hubbard Model: A Computational Perspective on page 8

8 Guo, Y. et al. Angle evolution of the superconducting phase diagram in twisted bilayer WSe2 on page 8

9 Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides on page 8

10 Löhneysen, H. v., Rosch, A., Vojta, M. & Wölfle, P. Fermi-liquid instabilities at magnetic quantum phase transitions on page 8

11 Phillips, P. W., Hussey, N. E. & Abbamonte, P. Stranger than metals on page 8

12 Varma, C. M. Colloquium: Linear in temperature resistivity and associated mysteries including high temperature superconductivity on page 8

13 Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation on page 8

14 Bloch, I., Dalibard, J. & Zwerger, W.

1. Improved material simulation for correlated electron systems by incorporating the Hubbard model as a physical realization of moiré semiconductors, allowing researchers to explore physics in regimes far away from the Mott insulator.

2. Enhanced understanding of transport in moiré systems by enabling the mapping of the topmost moiré valence band to a single-band triangular lattice Hubbard model with a widely tunable coupling strength, providing better predictive power for intermediate coupling regimes.

3. Development of predictive models for electronic phase diagrams by utilizing experimental control over twist angle and electric field to map out the electronic phase diagram versus ν and θ at E = 0mV/nm, allowing for the prediction of emergent states like the extended strange metal (ESM) and new superconducting dome.

4. Refinement of non-Fermi liquid theories by providing a benchmark against which existing models can be tested, as the paper suggests that the ESM here is incompatible with any theoretical model for non-Fermi liquids and contrasts its behavior with other strange metals.

5. Calibration of transport scaling analyses by providing empirical rules for analysis, such as the observation that the magnetoresistivity approximately follows a quadrature scaling, which can be used to assess the validity of scaling assumptions in future experiments.

Moiré semiconductors provide a physical realization of the Hubbard model. Bandwidth-tuned Mott transitions and complex phase diagrams mimicking those of high-temperature superconductors have been demonstrated near a weak Mott insulating state at half-band-filling. The platform also provides an opportunity to explore the physics of a partially filled Hubbard band at doping densities far away from the Mott insulator, a regime that has remained largely unexplored. Here we report the emergence of an extended strange metal (ESM), in both doping density and twist angle, in a partially filled Hubbard band of twisted bilayer WSe2. The ESM is in the clean limit, persists down to 100mK, and spans over multiple symmetry-breaking ground states; it also appears only at small twist angles, where electronic correlations are strong. These observations distinguish the state from the reported strange metals associated with quantum criticality and favor the viewpoint that it is an intrinsic state of matter. We also report the observation of a new superconducting dome being developed from the ESM but far away from both the Mott insulating state and the van Hove singularity of the material. Our work opens the door to exploring the new regime of partially filled Hubbard bands in the clean limit.