Controllable Superconductivity in Suspended van der Waals Materials

Abstract

Tunable superconductors provide a versatile platform for advancing next-generation quantum technologies. Here, we demonstrate controllable superconductivity in suspended NbSe2 thin layers, achieved through local strain and thermal modulation of the superconducting state. Our results show that suspended NbSe2 structures enable strain modulation of the critical temperature by up to approximately 0.92 K (about 12.5% of the critical temperature) and allow the realization of gate-tunable superconducting critical currents. We further demonstrate configurable hysteretic transport characteristics exhibiting multistability and negative differential resistance, providing easily reconfigurable, spatially dependent superconducting states. These phenomena are well explained by calculations of electron-phonon coupling using density functional theory, together with time-dependent Ginzburg-Landau dynamics coupled to the thermal diffusion equation. Our work provides profound insight into strain and thermal modulation of van der Waals superconductors and opens new opportunities for tunable on-chip superconductor devices, integrated superconducting circuits, and quantum simulators.

Figures (3)

• Figure 1: Controllable suspended NbSe$_2$ superconductor concept with strain and thermal modulation. (a) The schematic of a suspended controllable NbSe$_2$ superconductor. The NbSe$_2$ flake with flake width $w_f$ is transferred onto a SiO$_2$ substrate containing prepatterned 4 electrodes and an opening (indicated by purple color) that defines the suspended area with suspended width $w_s$. The suspended area can be modulated by tensile strain when applying a gate voltage $V_g$ for controllable superconductivity (Left inset). When applying the bias current $I$, the heat generated by current dissipation will interact with the superconducting state (Right inset). (b) Strain-tunable superconductivity. Left panel indicates that the calculated electron-phonon coupling strength as a function of frequency in strain of 0%, 0.25% and 0.5% with the corresponding stable electron-phonon coupling strengths of $\sim$ 1.02, 0.99, and 0.92, respectively. The right panel shows that the calculated superconducting gap $\Delta_{nk}(w = 0)$ as a function of temperature under strain of 0%, 0.25%, and 0.5%. The corresponding critical temperatures are $T_c$, 0.98 $T_c$, and 0.88 $T_c$, respectively, where $T_c$ is the critical temperature of the unstrained NbSe$_2$. (c) Controllable superconductor with thermal coupling. The simulated $I$-$V$ curve and the order paratmeter heatmap of the suspended NbSe$_2$ with a suspended width $w_s=$ 8.8 $\xi$ marked as purple dashed boxes.
• Figure 2: Controllable superconductivity with strain. (a) Optical micrograph of a suspended NbSe$_2$ device with multiple electrodes. The purple area outlines a $\sim$600 nm-deep cavity etched into a 1000 nm-thick SiO$_2$ layer; Yellow strips are Au electrodes. (b) Resistance–temperature ($R$–$T$) curves of a collapsed and partially suspended NbSe$_2$ structure. Critical temperatures are extracted by fitting a sum of three logistic components. The inset indicates the four-terminal measurement configuration. (c) $R$–$T$ curves of a fully suspended NbSe$_2$ device under $V_g=0$, 60, and 80 V. The inset indicates the four-terminal measurement configuration. (d) Fitted $T_c$ change $\Delta T_c$ versus $V_g$ for the device in (c). (e) $R$–$T$ curves from a geometry where the four-terminal path spans both suspended and SiO$_2$-supported regions, measured under $V_g=0$, 40, 60, 80, and 100 V. The inset indicates the four-terminal measurement configuration. (f) Fitted critical temperature changes and critical current versus $V_g$ for the device in (e). The behaviour arises from the combination of electrically tunable suspended superconductivity, where $\Delta T_{c1}$ is modulated by the gate voltage $V_g$, and electrically independent non-suspended superconductors, where $\Delta T_{c2}$ remains nearly constant with respect to $V_g$.
• Figure 3: Controllable superconductivity with thermal modulation. (a) $I$--$V$ curves of suspended NbSe$_2$ at $3~\mathrm{K}$ showing thermal hysteresis: red line shows single-step hysteresis for Device 1 with flake width $w_f\approx 8~\upmu\mathrm{m}$, suspended width $w_s\approx 3~\upmu\mathrm{m}$, and thickness $\sim 13~\mathrm{nm}$ (Supplementary Fig. S1a), and blue line shows two-step hysteresis for Device 2 with flake width $w_f \approx 25~\upmu\mathrm{m}$, suspended width $w_s\approx 2~\upmu\mathrm{m}$, and thickness $\sim 11~\mathrm{nm}$ (Supplementary Fig. S1b). (b) TDGL simulations for $64~\xi$-long flakes interacting with a suspended width of $w_s=8.8~\xi$; the resulting $I$--$V$ curves for widths of $w_f=4~\xi$ and $w_f=12~\xi$ are shown in red and blue, respectively. (c) $I$--$V$ curves of suspended NbSe$_2$ at $3~\mathrm{K}$ exhibiting multistep hysteresis for Device 3 with flake width $w_f \approx 8~\upmu\mathrm{m}$, suspended width $w_s\approx 3~\upmu\mathrm{m}$, and thickness $\sim 13~\mathrm{nm}$ (Supplementary Fig. S1c). (d) Temperature-dependent $I$--$V$ curves for a device with flake width $w_f \approx 25~\upmu\mathrm{m}$, suspended width $w_s\approx 4~\upmu\mathrm{m}$, and thickness $\sim 11~\mathrm{nm}$ (Supplementary Fig. S1d); insets highlight regions of negative differential resistance. (e) TDGL coupled to the thermal diffusion equation: simulated order parameter $|\psi|$ for suspended with of $w_s=6.4~\xi$, flake width of $w_f=24~\xi$, illustrating states I--III corresponding to distinct $I$--$V$ regimes. (f) TDGL+thermal-diffusion simulated $I$--$V$ curve with stages I--III marked, corresponding to the spatial maps in (e).