Fluctuation-induced currents in suspended graphene nanoribbons: Adiabatic quantum pumping approach

Graphene nanoribbons (GNRs) are thin strips of graphene with unique properties due to their structure and nanometric dimensions. They stand out as basic components for the construction of different types of nanoelectromechanical systems (NEMS), including some very promising sensors and pumps. However, various phenomena, such as unintended mechanical vibrations, can induce undesired electrical currents in these devices. Here, we take a quantum mechanical approach to analyze how currents induced by fluctuations (either thermal or of some other kind) in suspended GNRs contribute to the electric current. In particular, we study the pumping current induced by the adiabatic variation of the Hamiltonian of the system when a transverse vibration (flexural mode) of a GNR suspended over a gate is excited. Our theoretical approach and results provide useful tools and rules of thumb to understand and control the charge current induced by fluctuations in GNR-based NEMS, which is important for their applications in nanoscale sensors, pumps, and energy harvesting devices.

Figure 1

(a) Scheme of the studied system: A suspended GNR between two metallic contacts freely oscillating, at a distance $d_0$, over a gate with gate voltage $V_g$. We only consider the lowest frequency (acoustic) modes for the transversal vibration of the GNRs in a classical approximation and assume a rectangular membrane model to describe them. The shown mode corresponds to $(n_x,n_y)=(1,0)$. (b) Other examples of normal modes with (from left to right): $(n_x,n_y)=(1,1), (2,0)$, and $(2,1)$. (c), (d) Logarithm of the scaled emissivity ${\tilde{I}}_k$ in the low-temperature limit as a function of $n_x$ and $n_y$ for square nanoribbons with armchair (aGNR) and zigzag (zGNR) edges. ${\tilde{I}}_k$ has units of 1/eV and is proportional to the maximum value of the pumping current during a period. The size of the ribbons is $L=449a$ (with $a=0.246\mathrm{nm}$) and the Fermi energy is ${\varepsilon }_{\text{F}}=0.1\mathrm{eV}$.

Figure 2

Examples of GNRs with zigzag (zGNR) and armchair (aGNR) edges (blue and orange sites) connected to two semi-infinite contacts on the left and right (red sites). Note that the contacts are also made of GNRs of the same width and type. The green rectangles show how a row is defined for each type of GNR (to be used in Sec. 3b).

Figure 3

Scaled emissivity ${\tilde{I}}_{(1,0)}$ in units of 1/eV, as a function of the Fermi energy ${\varepsilon }_{\text{F}}$ for square GNRs with $L=449a$.

Figure 4

Contribution of each row of atoms [calculated using Eq. (24)] to the scaled emissivity ${\tilde{I}}_{(1,0)}$, for square GNRs of side $L=449a$, and ${\varepsilon }_{\text{F}}=0.001\mathrm{eV}$. The value of $y$ is the position of the row, in units of $a$. See Fig. 2 for examples of rows for each type of GNR.

Figure 5

Scaled emissivity ${\tilde{I}}_{(1,0)}$ as a function of the system's size $L$ for square GNRs, with ${\varepsilon }_{\text{F}}=0.1\mathrm{eV}$. The linear fits in dotted lines, show the approximate quadratic dependence between ${\tilde{I}}_{(1,0)}$ and $L$. ${\tilde{I}}_{(1,0)}={10}^{-2.01}{L}^{2.11}$ for aGNR and ${\tilde{I}}_{(1,0)}={10}^{-2.97}{L}^{2.09}$ for zGNRs.