Transport through Graphene on ${\mathrm{SrTiO}}_3$

We report transport measurements through graphene on ${\mathrm{SrTiO}}_3$ substrates as a function of magnetic field $B$, carrier density $n$, and temperature $T$. The large dielectric constant of ${\mathrm{SrTiO}}_3$ very effectively screens long-range electron-electron interactions and potential fluctuations, making Dirac electrons in graphene virtually noninteracting. The absence of interactions results in an unexpected behavior of the longitudinal resistance in the $N=0$ Landau level and in a large suppression of the transport gap in nanoribbons. The “bulk” transport properties of graphene at $B=0\mathrm{T}$, on the contrary, are completely unaffected by the substrate dielectric constant.

Figure 1

(a) Square resistance of graphene on ${\mathrm{SrTiO}}_3$ as a function of gate voltage, measured for different temperatures between 50 K and 250 mK; the arrow points in the direction of lowering temperature. Inset: Optical microscope image with software enhanced contrast (left); the final device with contacts attached (right; scale bar is $3\mu \mathrm{m}$ long). (b) Optical contrast of mono-, bi-, and trilayer graphene on ${\mathrm{SrTiO}}_3$. (c) Ratio of the carrier density measured by Hall effect at $V_g=2\mathrm{V}$ at temperature $T$ over the carrier density at $T=250\mathrm{mK}$: this ratio is proportional to the dielectric constant of the substrate $ϵ(T)$ and decreases by almost 1 order of magnitude when $T$ is increased from 250 mK to 50 K, as expected.

Figure 2

(a) Square resistance of graphene on ${\mathrm{SrTiO}}_3$ measured at different temperatures between 250 mK and 50 K, as a function of carrier density (extracted from Hall effect measurements). (b) Conductivity $\sigma$ of graphene on ${\mathrm{SrTiO}}_3$ as a function of $n$ (in log scale) at different temperatures, showing the low density region where $\sigma$ is independent of $n$ [by extrapolating the $\sigma (n)$ curve measure at large density—dotted line—we estimate the width of this region to be approximately $\delta n=(6.0\pm 0.5)\times {10}^{11}{\mathrm{cm}}^{-2}$, independent of temperature]. (c) (blue line) Fitting the experimental data to the dependence of $\sigma (n)$ by taking into account resonant scattering [Eq. (1) of main text] gives a very good agreement with values for the parameters ($n_i=2.9\times {10}^{11}{\mathrm{cm}}^{-2}$ $R=0.22\mathrm{nm}$) very close to those obtained for graphene on ${\mathrm{SiO}}_2$.

Figure 3

(a) Longitudinal square resistance $R$ as a function of $V_g$ at $B=15\mathrm{T}$, measured at different temperatures between 250 mK and 50 K. The height of the resistance peak at the charge neutrality ($N=0$ Landau level) decreases significantly with lowering $T$, whereas the height of the peaks centered around the subsequent $N=\pm 1$ Landau shows a slight increase in resistance with lowering $T$ [see (c); $N=0$ (circles), $N=+1$ (squares), and $N=-1$ (triangles)]. (b) The Hall conductivity measured at 50 K ($B=15\mathrm{T}$) shows very well-developed plateaus at $\pm 2,\pm 6e^2/h$, as is characteristic for Dirac fermions in graphene.

Figure 4

(a) Differential conductance $G$ (in units of $e^2/h$), of a graphene nanoribbon, as a function of the source-drain and gate voltage, $V_{sd}$ and $V_g$. (b) Differential conductance as a function of $V_{sd}$ for three specific $V_g$ values, corresponding to the dotted lines in (a). The interval enclosed by the dashed lines gives the size of the transport gap, which is approximately 2 meV for each polarity of $V_{sd}$ (1 order of magnitude smaller than for an identical ribbon on ${\mathrm{SiO}}_2$).