Angle evolution of the superconducting phase diagram in twisted bilayer WSe2

TL;DR

The paper addresses how superconductivity in twisted bilayer WSe$_2$ evolves with twist angle and whether a common origin underlies the disparate phase diagrams observed at different angles. It combines systematic transport measurements across angles from $5^\u00b0$ down to $3.8^\u00b0$ with a three-orbital Wannier model and FRG/Hartree-Fock analyses to map magnetic and superconducting instabilities. The key finding is that superconductivity remains closely tied to antiferromagnetic ordering across angles, without requiring proximity to a Van Hove singularity or a half-band insulator, and $T_c$ decreases smoothly as the angle is reduced, indicating a crossover from weak to intermediate coupling. The work connects previously separate phase diagrams, demonstrates spin-fluctuation–mediated pairing across the studied regime, and establishes twisted TMDCs as a tunable platform to explore correlated phases as the interaction strength to bandwidth ratio is varied, with implications for understanding unconventional superconductivity in moiré systems.

Abstract

Recent observations of superconductivity in twisted bilayer WSe$_2$ have extended the family of moiré superconductors beyond twisted graphene. In WSe$_2$ two different twist angles were studied, 3.65° and 5.0°, and two seemingly distinct superconducting phase diagrams were reported, raising the question of whether the superconducting phases in the two devices share a similar origin. Here we address the question by experimentally mapping the evolution of the phase diagram across devices with twist angles spanning the range defined by the initial reports, and comparing the results to twist angle-dependent theory. We find that the superconducting state evolves smoothly with twist angle and at all twist angles is proximal to a Fermi surface reconstruction with, presumably, antiferromagnetic ordering, but is neither necessarily tied to the Van Hove singularity, nor to the half band insulator. Our results connect the previously distinct phase diagrams at 3.65° and 5°, and offer new insight into the origin of the superconductivity in this system and its evolution as the correlation strength increases. More broadly, the smooth phase diagram evolution, repeatability between different devices, and dynamic gate tunability within each device, establish twisted transition metal dichalcogenides as a unique platform for the study of correlated phases as the ratio of interaction strength to bandwidth is varied.

Figures (4)

• Figure 1: Twist angle evolution of the phase diagrama Illustration of the tWSe$_{2}$ device structure with dual gates. b Moiré superlattice formed by two layers of WSe2 monolayers rotated relatively to each other. c Illustration of band structures at zero and finite displacement field in tWSe$_{2}$. d Density and displacement field dependence of resistance measured in tWSe$_{2}$ with twist angle at 5.0$^\circ$, 4.8$^\circ$, 4.2$^\circ$, 3.8$^\circ$. e High resolution maps of regions around the superconducting pocket. All measurements were taken at dilution fridge base temperature.
• Figure 2: Superconducting propertiesa, Resistance versus temperature at different twist angles, measured at the density and displacement field corresponding to the highest critical temperature. 5.0$^\circ$: -8.93$\times$ 10$^{12}$ cm$^{-2}$, 0.50 V/nm; 4.8$^\circ$: -7.60$\times$ 10$^{12}$ cm$^{-2}$, 0.37 V/nm; 4.2$^\circ$: -5.53$\times$ 10$^{12}$ cm$^{-2}$, -0.12 V/nm; 3.8$^\circ$: -4.75$\times$ 10$^{12}$ cm$^{-2}$, 0.06 V/nm. Inset shows $I-V$ measurement as a function of temperature in 4.8$^\circ$ sample. The dashed line marks $V \propto I^3$. b, Highest critical temperature $T_c$ (defined as the $80$% point on the resistance curve) of the superconductors observed in tWSe$_{2}$ with different twist angles and BKT temperature $T_{BKT}$ (defined as the temperature at which $V\propto I^3$) measured at the density of highest $T_c$. Solid symbols are extracted from panel a. Open symbols represents data from Ref. xiaSuperconductivityTwistedBilayer2025xiaSimulatingHightemperatureSuperconductivity2025. c, Critical current density $J$ extracted from the coherence peaks of the $dV/dI$ vs $I_{dc}$ measurement. Inset shows differential resistance $dV/dI$ as a function of d.c. current bias $I_{d.c.}$ measured in different devices. d, $T_c/T_F$ and $T_c/T_D$, where $T_F$ is the Fermi temperature (defined as the energy difference of the chemical potential from the valence band maximum) and $T_D$ is the temperature associated to the Drude weight, both obtained from the calculated band structure. The dashed marks where the ratio is 1%, above which the superconductors have strong coupling. Inset shows where the superconductors fall on the Uemura plot.
• Figure 3: Insulating gaps at half fillinga Temperature dependence of resistivity at half filling density varying displacement field on 3.8$^\circ$ tWSe$_{2}$. Inset shows the line cut on the 1.5 K phase diagram where the measurement is taken at. b The resistivity plotted versus temperature showing an insulating behavior at intermediate displacement field range. Inset shows the same plot on linear scale. c,d The same measurements on 4.8$^\circ$ tWSe$_{2}$. e, Resistivity $\rho$ as a function of temperature at half filling. f, Arrhenius plot at the half filling insulating state in low twist angle devices. Logarithm of conductivity $\sigma$ versus 1/$T$ at the displacement field where the gap size is maximum. The linear region is fit to $\sigma \sim e^{{-\Delta}/{2k_BT}}$. g, Gap size $\Delta$ of the insulating state at half filling extracted from e. The value is set to be zero for 4.8$^\circ$ and 5.0$^\circ$ devices since no fully opened gaps are observed. The solid dots and curves show the calculated gap size from Hartree Fock using different dielectric constant value $\varepsilon$.
• Figure 4: The superconductor and the IVC-AFM ordering.a-d Illustration of the phase diagram at positive displacement field, representing the relationship between the superconductors and the neighboring resistive ordering states. e-h Functional renormalization group (FRG) calculations of the phase diagram as a function of displacement field and filling factor simulated for the same twist angles compared to the experimental data. The critical RG scale $\Lambda_{\mathrm{c}}$ indicates the onset temperature of SC (blue) and magnetic ordering (orange-red) in the phase diagram and is encoded in the opacity of the respective colormaps. The maximal critical temperature $T_\mathrm{c}^{\text{max}}$ of the SC pocket is marked by the cross. Different magnetic orderings (orange-red) are distinguished by the leading momentum transfer of the magnetic susceptibility $\chi^{\text{DW}}(\boldsymbol{q})$ ($K$: IVC-AFM order, $\Gamma$: valley-polarized order and $M$: striped-IVC). The black dashed curve defines the boundary of the IVC-AFM order. Solid brown points indicate the size of the correlated gap at half-filling $\nu=-1$ as predicted by Hartree-Fock. The DOS is plotted in the background to indicate the position of the VHs. FRG calculations are done below the grey dashed lines, indicating the experimentally relevant parameter regime.