Interaction-dominated transport and Coulomb drag in bilayer graphene

We theoretically investigate interaction effects in transport phenomena in bilayer graphene (BLG). For the minimal conductivity in pristine BLG, we find that the conductivity assumes a constant interaction-limited value for $T\to 0$, with the first correction being $\propto \sqrt{T}$. We furthermore study the Coulomb drag resistivity between two BLGs in the whole range from deep within the Fermi-liquid regime all the way to the charge neutrality (CN) point. While in the Fermi-liquid regime drag behaves very similarly to drag in a standard two-dimensional electron gas, in the vicinity of CN we find that the drag resistivity crucially depends on the ratio between inelastic and elastic scattering, as recently found in the case of monolayer graphene.

Figure 1

Interaction-dominated single-layer conductivity. The leading temperature behavior is of the unusual $\sqrt{T}$ type. In the limit $T\to 0$, $\sigma$ converges to a finite value, $\sigma (T\to 0)=27.4\frac{e^2}{h}$, which is just of theoretical interest, as our approach is not valid at very low temperatures.

Figure 2

Drag resistivity for $\frac{q_{\mathrm{TF}}^2}{mT}=100$ and $d{q}_{\mathrm{TF}}=1$ (solid line), $d{q}_{\mathrm{TF}}=2$ (dashed line), and $d{q}_{\mathrm{TF}}=5$ (dotted line). The single-layer conductivities ${\sigma }_a$ and ${\sigma }_p$ are disorder dominated ($g=1000$). Then the maximum is located at $\mu \sim 2T$.

Figure 3

Drag resistivity for a series of different values of $g$ in the idealized zero-distance limit, $d{q}_{\mathrm{TF}}=0$ ($\frac{q_{\mathrm{TF}}^2}{mT}=100$). The single-layer conductivities ${\sigma }_a$ and ${\sigma }_p$ range from interaction dominated for $g\ll 1$, with a maximum at $\mu /T<2$, to disorder dominated for $g\gg 1$, in which case the maximum is located at $\mu \approx 2T$. For $g=0$ the maximum pushes to 0. For $\mu \gtrsim 2T$ the curves become independent of $g$ and collapse to a single one; see Sec. 5b.

Figure 4

Drag resistivity for $\frac{q_{\mathrm{TF}}^2}{mT}=100$ and reasonable distances $d{q}_{\mathrm{TF}}=10$. The single-layer conductivities ${\sigma }_a$ and ${\sigma }_p$ here are mostly interaction dominated. This can be seen from the fact that the maximum is located at $\mu <2T$, in contrast to the disorder-dominated case (Fig. 2). For $\mu \gtrsim 2T$ the curves become independent of $g$ and collapse to a single one; see Sec. 5b.