Coulomb drag of massless fermions in graphene

Using a structure consisting of two, independently contacted graphene single layers separated by an ultrathin dielectric, we experimentally measure the Coulomb drag of massless fermions in graphene. At temperatures higher than 50 K, the Coulomb drag follows a temperature and carrier density dependence consistent with the Fermi liquid regime. As the temperature is reduced, the Coulomb drag exhibits giant fluctuations with an increasing amplitude, thanks to the interplay between coherent transport in the graphene layer and interaction between the two layers.

Figure 1

Optical micrographs (top) and schematic representation (bottom) of the fabrication process of an independently contacted graphene bilayer. (a) Hall bar device fabrication on the bottom graphene layer, followed by the Al${}_2$O${}_3$ interlayer dielectric deposition. (b) Top graphene layer isolation on a separate substrate, followed by transfer onto the bottom layer. (c) Top layer Hall bar realization by etching, lithography, metal deposition, and liftoff. The yellow (inner) and red (outer) dashed contours in the optical micrograph represent the top and bottom layers, respectively. The scale bars in all panels are 10 $\mu$m.

Figure 2

(a) Layer resistivities and (b) densities vs $V_{\mathrm{BG}}$ measured at $T=4.2$ K in sample 1. Depending on $V_{\mathrm{BG}}$, both electrons or holes can be induced in the bottom layer; the top layer contains electrons in the available $V_{\mathrm{BG}}$ window, owing to unintentional doping. The symbols in panels (a) and (b) represent experimental data, while the lines represent the calculated values according to Eqs. (1) and (2). (c) Band diagram across the graphene bilayer heterostructure at $V_{\mathrm{BG}}=0$ V, and (d) at a positive $V_{\mathrm{BG}}$. Both layers are assumed to be at the charge neutrality point and aligned with the back-gate Fermi level at $V_{\mathrm{BG}}=0$. The layers are held at the ground potential, and their thicknesses exaggerated to show the Dirac cones. The applied $V_{\mathrm{BG}}$ induces voltage drops $V_{{\mathrm{SiO}}_2}$ and $V_{{\mathrm{Al}}_2{\mathrm{O}}_3}$ across the bottom and interlayer dielectrics, respectively.

Figure 3

Coulomb drag in graphene. (a) Layer resistivities (${\rho }_{T,B}$) and ${\rho }_{\mathrm{Drag}}$ vs layer densities ($n_{T,B}$) for sample 2, measured by sweeping $V_{\mathrm{BG}}$ at $T=250$ K. The bilayer probes three different regimes: hole-hole, electron-hole, and electron-electron. (b) ${\rho }_{\mathrm{Drag}}$ vs $V_{\mathrm{BG}}$ at different $T$ values, from 250 to 77 K (solid lines). Inset: maximum ${\rho }_{\mathrm{Drag}}$ vs $T^2$ in the electron-hole and electron-electron regimes. The different $x$ axes, i.e., $n_B$ and $n_T$ of panel (a) and $V_{\mathrm{BG}}$ of panel (b), apply to both panels.

Figure 4

${\rho }_{\mathrm{Drag}}$ vs $V_{\mathrm{BG}}$ measured in sample 2 for $T⩽77$ K. As $T$ is reduced, ${\rho }_{\mathrm{Drag}}$ exhibits mesoscopic fluctuations with increasing amplitude, which fully obscure the average drag at the lowest $T$. The traces are shifted for clarity; the horizontal dashed lines indicate 0 $\Omega$ for each trace.

Figure 5

${\rho }_{\mathrm{Drag}}$ vs $B$ measured at $T=0.3$ K in sample 3, showing mesoscopic fluctuations similar to Fig. 4 data. Inset: ${\rho }_{\mathrm{Drag}}$ vs $B$ data autocorrelation.