Edge currents and nanopore arrays in zigzag and chiral graphene nanoribbons as a route toward high-$ZT$ thermoelectrics

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Edge currents and nanopore arrays in zigzag and chiral graphene nanoribbons as a route toward high- $Z T$ thermoelectrics

Po-Hao Chang and Branislav K. Nikolić

Phys. Rev. B 86, 041406(R) – Published 16 July 2012

Abstract

We analyze electronic and phononic quantum transport in zigzag or chiral graphene nanoribbons (GNRs) perforated with an array of nanopores. Since local charge current profiles in these GNRs are peaked around their edges, drilling nanopores in their interior does not affect edge charge currents while drastically reducing the phonon heat current in sufficiently long wires. The combination of these two effects can yield highly efficient thermoelectric devices with maximum figure of merit $Z T ≃ 5$ , at both liquid nitrogen and room temperature, achieved in $\sim$ 1 $μ$ m long zigzag GNRs with nanopores of variable diameter and spacing between them. Our analysis is based on the nonequilibrium Green's function formalism combined with the $π$ -orbital tight-binding Hamiltonian including up to third-nearest-neighbor hopping for an electronic subsystem, or with an empirical fifth-nearest-neighbor force-constant (5NNFC) model for a phononic subsystem. Additionally, we demonstrate that different empirical FC models typically overestimate the phonon conductance when compared to first-principles results.

Received 25 January 2012

DOI:https://doi.org/10.1103/PhysRevB.86.041406

Authors & Affiliations

Po-Hao Chang and Branislav K. Nikolić^*

Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716-2570, USA

^*bnikolic@udel.edu

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Vol. 86, Iss. 4 — 15 July 2012

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Images

Figure 1
Schematic view of (a) 20-ZGNR (composed of 20 zigzag chains) and (b) (8,1)-CGNR with a chiral angle $θ = 5 . 8^{\circ}$ . The size of the nanopores, assumed to be drilled in the GNR interior away from its zigzag or chiral edges, and the distance between them is illustrated by plotting two repeated supercells of each GNR. The length of these GNRs in the actual calculations is set to $L ≃ 1.2$ $μ$ m, which supports 300 nanopores.Reuse & Permissions
Figure 2
Spatial profiles of local charge currents in (a) 20-ZGNR and (c) (8,1)-CGNR with nanopores for electronic transport close ( $E_{F} = - 0.43$ eV) to the DP. The corresponding current profiles over the transverse cross section of nanoribbons are shown in (b) and (d) for both infinite homogeneous GNRs and GNRs with nanopores. Note that the sum of bond currents (Ref. 15) $J_{nm} / V$ , which describe charge flow from site $n$ to site $m$ of the honeycomb lattice if hopping $t_{n}^{m} \neq 0$ is nonzero between the two sites, gives the conductance $G = I / V$ ( $I$ is the total current in the leads and $V \to 0$ is small bias voltage driving the linear-response transport).Reuse & Permissions
Figure 3
The zero-bias electronic transmission $T_{el} (E)$ for (a) infinite homogeneous 20-ZGNR or finite length 20-ZGNR with a periodic array of identical nanopores shown in Fig. 1a, and (c) infinite homogeneous (8,1)-CGNR or finite length (8,1)-CGNR with a periodic array of identical nanopores shown in Fig. 1b. (b) and (d) show the thermopower at two different temperatures corresponding to finite length 20-ZGNR with nanopores in (a) or finite length (8,1)-CGNR with nanopores in (c), respectively.Reuse & Permissions
Figure 4
(a) The phonon transmission function $T_{ph} (ω)$ and (b) the corresponding phonon thermal conductance $κ_{ph}$ for an infinite homogeneous 20-ZGNR or 20-ZGNR with a periodic array of identical nanopores shown in Fig. 1a. (c) The phonon transmission function and (d) the corresponding phonon thermal conductance $κ_{ph}$ for an infinite homogeneous (8,1)-CGNR or (8,1)-CGNR with a periodic array of identical nanopores shown in Fig. 1b.Reuse & Permissions
Figure 5
The thermoelectric figure of merit $Z T$ vs energy at two different temperatures for (a), (b) ZGNR + nanopores and (c), (d) CGNR + nanopores. In (a) and (c) we assume a periodic array of identical nanopores, as illustrated in Fig. 1, while in (b) and (d) the nanopore diameter and the distance between neighboring pores is a uniform random variable. The curves plotted in (b) and (d) are computed for a single sample.Reuse & Permissions
Figure 6
The phonon thermal conductance as a function of temperature for 8-ZGNR with and without a single nanopore (of diameter $D = 0.59$ nm) computed by coupling NEGF formalism to empirical 4NNFC (Ref. 25) or empirical 5NNFC (Ref. 26) models, Brenner EIP (Ref. 27), and DFT (using the basis of local DZP orbitals and the PBE exchange-correlation functional). The FC matrix in the case of Brenner EIP and DFT methodology was computed using the gpaw package (Ref. 28).Reuse & Permissions

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