Enhancing thermoelectric properties of graphene quantum rings

We study the thermoelectric properties of rectangular graphene rings connected symmetrically or asymmetrically to the leads. A side-gate voltage applied across the ring allows for the precise control of the electric current flowing through the system. The transmission coefficient of the rings manifest Breit-Wigner line shapes and/or Fano line shapes, depending on the connection configuration, the width of nanoribbons forming the ring and the side-gate voltage. We find that the thermopower and the figure of merit are greatly enhanced when the chemical potential is tuned close to resonances. Such enhancement is even more pronounced in the vicinity of Fano-like antiresonances which can be induced by a side-gate voltage independently of the geometry. This opens a possibility to use the proposed device as a tunable thermoelectric generator.

Figure 1

(a) Schematic diagram of the graphene nanoring connected to two armchair nanoribbons. A side-gate voltage can be applied across the ring. The connection can be (b) asymmetric or (c) symmetric.

Figure 2

Transmission and thermoelectric coefficients in the absence of the side-gate voltage $(V_G=0)$ for symmetric (dashed lines) and asymmetric (solid lines) rings. (a) Transmission coefficient, (b) Seebeck coefficient, and (c) figure of merit for a nanoribbon width of $N=49$. (d) Transmission coefficient, (e) Seebeck coefficient, and (f) figure of merit for a nanoribbon width of $N=51$.

Figure 3

Figure of merit $ZT$ as a function of the chemical potential $\mu$ and the side-gate voltage $V_G$ for the asymmetric rings with (a) $N=49$ and (b) $N=51$. The dotted lines mark the cross sections shown in Fig. 4.

Figure 4

(a) Transmission coefficient, (b) Seebeck coefficient, and (c) figure of merit for the cross section marked in Fig. 3 that corresponds to a nanoribbon width of $N=49$ and a side-gate voltage drop $V_G=46\mathrm{mV}.$ (d) Transmission coefficient, (e) Seebeck coefficient, and (f) figure of merit for the cross section marked in Fig. 3 that corresponds to a nanoribbon width of $N=51$ and a side-gate voltage drop $V_G=50\mathrm{mV}$.

Figure 5

Upper panels show the transmission coefficient as a function of energy for $N=49$ with $V_G=46\mathrm{mV}$ (left), and $N=51$ with $V_G=50\mathrm{mV}$ (right). Lower panels show the corresponding figure of merit as a function of the chemical potential. Gray solid lines with filling correspond to samples with ideal edges $(p=0)$, while red dashed lines and blue solid lines correspond to edge-disordered ones with $p=0.02$ and $p=0.05$, respectively.