Interacting electrons in graphene nanoribbons in the lowest Landau level

We study the effect of electron-electron interaction and spin on electronic and transport properties of gated graphene nanoribbons (GNRs) in a perpendicular magnetic field in the regime of the lowest Landau level (LL). The electron-electron interaction is taken into account using the Hartree and Hubbard approximations, and the conductance of GNRs is calculated on the basis of the recursive Greens function technique within the Landauer formalism. We demonstrate that, in comparison to the one-electron picture, electron-electron interaction leads to the drastic changes in the dispersion relation and structure of propagating states in the regime of the lowest LL showing a formation of the compressible strip and opening of additional conductive channels in the middle of the ribbon. We show that the latter are very sensitive to disorder and get scattered even if the concentration of disorder is moderate. In contrast, the edge states transport is very robust and cannot be suppressed even in the presence of a strong spin-flipping.

Figure 1

A schematic layout illustrating a system consisting of a graphene nanoribbon of the width $w=20$ nm which is located on an insulating substrate at the distance $d=300$ nm apart from a metallic back gate. The whole system is subjected to a perpendicular magnetic field $B=150$ T.

Figure 2

(a)–(c) Charge density distributions, and (d)–(f) band structure of a graphene nanoribbon in a perpendicular magnetic field $B=150$ T. (a, d) one-electron approximation, $e{V}_g/t_0=0$; (b, e) self-consistent calculations for $e{V}_g/t_0=0.1$ and (c), (f) $e{V}_g/t_0=0.5$. Red and blue curves marked by $\uparrow$ and $\downarrow$ correspond to the charge densities of spin-up and spin-down electrons, respectively, $n_{\uparrow }\left(y\right),n_{\downarrow }\left(y\right)$. Charge densities are averaged over three successive sites. Green curves correspond to the total density distribution $n\left(y\right)=n_{\uparrow }\left(y\right)+n_{\downarrow }\left(y\right)$. Dashed lines define the Fermi energy position. Yellow fields correspond to the energy interval $[-2\pi k_{B}T,2\pi k_{B}T]$; temperature $T=4.2$ K.

Figure 3

Conductance of the GNR as a function of the filling factor $\nu$ calculated in the presence of different types of disorder: (a) short-range impurities with strength $\delta =4t_0,$ (b) fluctuation of the normal to the surface component of the magnetic field due to the warping; (c) spin-flip effect. The red (solid) line on all plots corresponds to an ideal ribbon (i.e., without disorder). The arrows (e) and (f) indicate the filling factors for which the corresponding band structures are plotted in Figs. 2e and 2f, respectively. The inset in (b) illustrates the landscape of a corrugated GNR. A typical wavelength of the ripples is about 8 nm, while the height fluctuates within 1 nm. $T=4.2$ K.