Heat transfer at the van der Waals interface between graphene and ${\mathrm{NbSe}}_2$

Graphene has been widely used to construct low-resistance van der Waals (vdW) contacts to other two-dimensional (2D) materials. However, a rise of graphene's electron temperature under a current flow has not been seriously considered in many applications. Owing to its small electronic heat capacity and electron-phonon coupling, graphene's electron temperature can be increased easily by the application of current. The heat generated within the graphene is transferred to the contacted 2D materials through the vdW interface and potentially influences their properties. Here, we compare the superconducting critical currents of an ${\mathrm{NbSe}}_2$ flake for two different methods of current application: with a Au/Ti electrode fabricated by thermal evaporation and with a graphene electrode contacted to the ${\mathrm{NbSe}}_2$ flake through a vdW interface. The influence of the heat transfer from the graphene to ${\mathrm{NbSe}}_2$ is detected through the change of the superconductivity of ${\mathrm{NbSe}}_2$. We found that the critical current of ${\mathrm{NbSe}}_2$ is significantly reduced when the current is applied with the graphene electrode compared to that from the conventional Au/Ti electrode. Further, since the electron heating in graphene exhibits ambipolar back-gate modulation, we demonstrate the electric field modulation of the critical current in ${\mathrm{NbSe}}_2$ when the current is applied with graphene electrode. These results are attributed to the significant heat transfer from the graphene electrode to ${\mathrm{NbSe}}_2$ through the vdW interface.

Figure 1

(a) Optical micrograph of the fabricated device. (b),(c) Schematic illustration of the graphene/${\mathrm{NbSe}}_2$ device structure with different current application geometries. Arrows indicate the flow of current. (b) Current application with graphene electrode. (c) Current application with Au/Ti metal electrode. (d) Diagram of heat flow in the device. $p$ denotes the injected power density to the electrons of the graphene due to Joule heating, ${\mathrm{G}}_{\mathrm{e}}^{\mathrm{vdW}}$ is the heat conduction through electron at the graphene/${\mathrm{NbSe}}_2$ vdW interface, ${\mathrm{G}}_{\mathrm{ep}}^{\mathrm{Gr}}$ is the heat conduction from electrons to phonons in graphene, ${\mathrm{G}}_{\mathrm{p}}^{\mathrm{vdW}}$ is the heat conduction through phonons at graphene/${\mathrm{NbSe}}_2$ vdW interface, ${\mathrm{G}}_{\mathrm{ep}}^{\mathrm{NS}}$ is the heat conduction between electrons to phonons in ${\mathrm{NbSe}}_2$, and the heat conduction from graphene or ${\mathrm{NbSe}}_2$ to $\mathrm{Si}{\mathrm{O}}_2$/Si substrate heat bath via phonons. (e) Schematic illustration of graphene/${\mathrm{NbSe}}_2$ vdW interface.

Figure 2

(a) Current-voltage ($I-V$) curves for different measurement configurations; current application with the graphene (Gr.) electrode or application with the metal electrode at $V_{\mathrm{G}}=-50\mathrm{V}$. Data obtained from temperatures $T=2.0$ and 7.8 K are presented. Measurements are performed under zero magnetic fields. (b) Critical current $I_{\mathrm{c}}$ values for the current application with the graphene electrode at 2.0 K with different voltage probe configuration. (c) Critical current $I_{\mathrm{c}}$ values for the current application with the metal electrode at 2.0 K and $V_{\mathrm{BG}}=-50\mathrm{V}$ with different voltage probe configurations.

Figure 3

(a) $I-V$ curves at 2.0 K at various back-gate voltages $V_{\mathrm{BG}}$ measured with current application with the graphene (Gr.) electrode. The curves are offset for clarity and dashed lines indicate offset values. (b) $I-V$ curves at 2.0 K at various $V_{\mathrm{BG}}$ measured with current application with the metal electrode. The curves are offset for clarity and dashed lines indicate offset values. (c) $V_{\mathrm{BG}}$ dependence of critical current $I_{\mathrm{c}}$ for current application with the graphene contact. (d) $V_{\mathrm{BG}}$ dependence of the two-terminal resistance of the graphene measured at 2.0 K. (Inset) Illustration of the measurement configuration. (e) $V_{\mathrm{BG}}$ dependence of critical current $I_{\mathrm{c}}$ for current application with the metal contact.

Figure 4

(a) The measurement geometry of the voltage probes. (b) $I-V$ curves at 2.0 K at various backgate voltages $V_{\mathrm{BG}}$ measured with current application with the graphene electrode. The curves are offset for clarity and dashed lines indicate offset values. (c) Current $I$ dependence of the power $P$ injected to the device measured at different $V_{\mathrm{BG}}$. The curves are offset for clarity and dashed lines indicate offset values. (d) Plot of $I$ values for constant injected powers of $P=25$, 50, and 75 μW. In comparison, $V_{\mathrm{BG}}$ dependence of $I_{\mathrm{c}}$ is plotted with circles.

Figure 5

(a)–(c) I-V curves obtained at different temperatures of 2.0, 4.8, 5.8, and 7.8 K for current application with the graphene electrode at different $V_{\mathrm{BG}}$ values of (a) −50, (b) −15, and (c) 0 V. (d)–(f) P-V curves obtained at different temperatures of 2.0, 4.8, 5.8, and 7.8 K for current application with the graphene electrode at different $V_{\mathrm{BG}}$ values of (d) −50, (e) −15, and (f) 0 V. Critical power $P_{\mathrm{c}}$ values for positive $P$ are indicated by arrows. (g) Critical power $P_{\mathrm{c}}$ with respect to the temperature $T$ obtained for different values of $V_{\mathrm{BG}}$.

Figure 6

(a)–(d) Data obtained from a bilayer graphene (BLG)/51-nm-thick ${\mathrm{NbSe}}_2$ device. (a) Optical micrograph. (b) $I-V$ curves at 2.0 K at various back-gate voltages $V_{\mathrm{BG}}$ measured with current application with the bilayer graphene electrode. (c) $V_{\mathrm{BG}}$ dependence of critical current $I_{\mathrm{c}}$ for current application with the bilayer graphene contact at 2.0 K. (d) $V_{\mathrm{BG}}$ dependence of the resistance of the bilayer graphene measured at 2.0 K. (e)–(h) Data obtained from the eight-layer graphene(8LG)/40-nm-thick ${\mathrm{NbSe}}_2$ device. (e) Optical micrograph. (f) $I-V$ curves at 2.0 K at various backgate voltages $V_{\mathrm{BG}}$ measured with current application with the eight-layer graphene electrode. (g) $V_{\mathrm{BG}}$ dependence of critical current $I_{\mathrm{c}}$ for current application with the eight-layer graphene contact at 2.0 K. (h) $V_{\mathrm{BG}}$ dependence of the resistance of the 8-layer graphene measured at 2.0 K.

Figure 7

(a) Two-terminal differential resistance $\mathit{dV}/\mathit{dI}$ of a graphene as a function of $V_{\mathrm{BG}}$ measured with the geometry shown in Fig. 3. Measurement temperature was 2.0 K and magnetic field of 8.5 T was applied perpendicular to the sample plane. [(b) and (c)] Closeup of the Fig. 7. (d) Total contact resistance contribution $R_{\mathrm{c}}$ of the Au/Ti/graphene junction, the ${\mathrm{NbSe}}_2$/graphene junction and the lead resistance of Au/Ti determined for different $V_{\mathrm{BG}}$ values.

Figure 8

(a) Current-voltage ($I-V$) curves for different voltage measurement configurations for current application with the graphene electrode at $V_{\mathrm{G}}=-50\mathrm{V}$ at 2.0 K. (b) Current-voltage ($I-V$) curves for different voltage measurement configurations for current application with the metal electrode at $V_{\mathrm{BG}}=-50\mathrm{V}$ at 2.0 K. Arrows indicate sweep direction of current $I$.