Elsevier

Carbon

Volume 142, February 2019, Pages 107-114
Carbon

Odd-even phonon transport effects in strained carbon atomic chains bridging graphene nanoribbon electrodes

https://doi.org/10.1016/j.carbon.2018.10.036Get rights and content

Abstract

Based on first-principles approaches, we study the ballistic phonon transport characteristics of finite monatomic carbon chains stretched between graphene nanoribbons, an sp1-sp2 hybrid carbon nanostructure that has recently seen significant experimental advances in its synthesis. We find that the lattice thermal conductance anomalously increases with tensile strain for the even-numbered carbon chains that adopt the alternating bond-length polyyne configuration. On the other hand, in the odd-numbered carbon chain cases, which assume the equal bond-length cumulene configuration, phonon conductance decreases with increasing strain. We show that the strong odd-even phonon transport effects originate from the characteristic longitudinal acoustic phonon modes of carbon wires and their unique strain-induced redshifts with respect to graphene nanoribbon phonon modes. The novel phonon transport properties and their atomistic mechanisms revealed in this work will provide valuable guidelines in designing hybrid carbon nanostructures for next-generation device applications such as nano-biosensors.

Introduction

Representing the ideal one-dimensional (1D) sp1-hybridized carbon systems, monoatomic carbon chains (CCs) were predicted to exhibit intriguing physical and chemical properties but their experimental investigations have been relatively slow compared to other sp2-and sp3-carbon allotropes [[1], [2], [3], [4]]. While the infinite CC or carbyne is not yet observed and its existence still remains controversial, much progress has been recently made in the experimental realization of finite CC systems. An interesting aspect of this development is that, rather than the direct synthesis of isolated molecular CCs [5,6], they were successfully prepared in the sp1-sp2 hybrid carbon structures. A notable case is the CC confined within carbon nanotubes [7,8], and the other is the CC stretched between graphene [[9], [10], [11], [12], [13], [14], [15], [16], [17]].

In particular, the graphenesingle bondCCsingle bondgraphene system assumes an ideal electrode-channel-electrode junction configuration [[9], [10], [11], [12], [13], [14], [15], [16], [17], [18]], providing unique opportunities to study the quantum transport properties of all-carbon nanodevices. The infinite CCs can adopt cumulene ( … Cdouble bondCdouble bondCdouble bondC …) or polyyne ( … Ctriple bondCsingle bondCtriple bondC …) configuration (Fig. 1a) and exhibit metallic or semiconducting properties, respectively [3,4]. In a notable example, very recently, strain-induced metal-to-insulator (i.e. cumulene-to-polyyne) transition was observed [14], confirming a recent theoretical prediction [19]. Another promising example theoretically suggested is spintronic applications such as spin filter and spin valve, which will be operated based on the spin-polarized nature of graphene zigzag edge states and can be modulated by the number of carbon atoms within CCs (cumulene or polyyne) [[20], [21], [22]].

In this work, applying an atomistic Green's function method (AGF) based on density functional theory (DFT) calculations, we investigate the strain-dependent ballistic phonon transport properties of CCs bridging graphene nanoribbon (GNR) electrodes (Fig. 1b). Although several theoretical reports on the charge and spin transport properties of GNRsingle bondCCsingle bondGNR junctions have previously appeared [[20], [21], [22], [23], [24]], study on their phonon transport properties is non-existent [25]. More generally, while ballistic electron and spin transports in nanoscale junctions have been extensively studied in the past decade or so, still much less is known about their ballistic phononic heat transport [26,27]. We here adopt the microscopic AGF theory to describe the thermal resistance across the dimensionally mismatched sp1-sp2 interfaces [[28], [29], [30]]. Moreover, in spite of the high computational cost, we will utilize first-principles atomics forces obtained through DFT because it was shown in a previous study that classical force fields significantly overestimate phonon transmissions across GNR-atomic carbon contacts [25].

In examining the ballistic phonon transport properties of various GNRsingle bondCCsingle bondGNR junction models, we particularly focus on the effects of tensile strain as well as the number of carbon atoms within CCs. Strain was predicted to be an important variable that affects the structural and electronic properties of infinite [[31], [32], [33]] as well as finite CCs [14,18,19,24,32,34]. Regarding the number of C atoms within finite CCs, while strong odd-even effects were predicted for the structural and electron transport properties of GNRsingle bondCCsingle bondGNR [20,23,24,34] as well as metalsingle bondCCsingle bondmetal junctions [35], it remains to be seen whether an oscillatory behavior also appears in phonon transport and if does what its nature is. We will show that a strong strain-dependent odd-even phonon transport effect indeed arises because phonon conductances in the even-numbered (odd-numbered) CC junctions increase (decrease) with tensile strain. The effect is found in both armchair and zigzag GNRs, indicating the robust nature of the effect. The microscopic mechanisms will be rationalized by the polyynic atomic structure of even-numbered CCs and the strong redshifting behavior of their longitudinal optical (LO) modes with respect to GNR phonon bands.

Section snippets

Density-functional theory phonon calculations

Following our earlier works on stretched molecular junctions [36,37], we carried out strain-dependent geometry optimizations within the local density approximation (LDA) of DFT implemented in the SIESTA package [38]. Dynamical matrices were obtained with the DFT forces and the small displacement method as implemented in the Phonopy code [39]. Norm-conserving pseudopotentials and double-zeta-plus-polarization quality atomic orbital basis sets were adopted. The convergence criterion for atomic

Phononic heat transport in infinite CCs

We first discuss the strain-dependent variations in the lattice thermal transport properties of infinite CCs (carbyne) and GNRs, which become the basis of analyzing the phonon transport in GNRsingle bondCCsingle bondGNR junctions. In terms of the atomic structures of infinite carbynes, we obtained within LDA 1.269 Å (1.301 Å) as the Ctriple bondC (Csingle bondC) bond length in the polyyne form and 1.285 Å as the Cdouble bondC bond length in the cumulene counterpart (Fig. 1a). Due to Peierls distortion that drives the bond-length alternation and

Conclusions

In summary, we carried out ab initio phonon transport calculations on finite monatomic CCs stretched between GNR electrodes. Representing the ultimate all-carbon junction model, these hybrid carbon nanostructures based on sp-sp2 interfaces are appealing in many aspects but the research efforts have been so far limited to their structural and electronic (and spin) transport properties. Systematically considering a series of CC channels and both zGNR and aGNR electrodes, we found that the phonon

Acknowledgement

This work was supported by the Nano-Material Technology Development Program (Nos. 2016M3A7B4024133 and 2016M3A7B4909944), Basic Research Program (No. 2017R1A2B3009872), Global Frontier Program (No. 2013M3A6B1078881), and Basic Research Lab Program (No. 2016M3A7B4909944) of the National Research Foundation funded by the Ministry of Science and ICT of Korea. Computational resources were provided by the KISTI Supercomputing Center (KSC-2016-C3-0076).

References (59)

  • J.A. Januszewski et al.

    Synthesis and properties of long [n]cumulenes (n ≥ 5)

    Chem. Soc. Rev.

    (2014)
  • X. Zhao et al.

    Carbon nanowire made of a long linear carbon chain inserted inside a multiwalled carbon nanotube

    Phys. Rev. Lett.

    (2003)
  • L. Shi et al.

    Confined linear carbon chains as a route to bulk carbyne

    Nat. Mater.

    (2016)
  • B. Standley et al.

    Graphene-based atomic-scale switches

    Nano Lett.

    (2008)
  • C. Jin et al.

    Deriving carbon atomic chains from graphene

    Phys. Rev. Lett.

    (2009)
  • A. Chuvilin et al.

    From graphene constrictions to single carbon chains

    New J. Phys.

    (2009)
  • H. Zhang et al.

    Visualizing electrical breakdown and ON/OFF states in electrically switchable suspended graphene break junctions

    Nano Lett.

    (2012)
  • A. La Torre et al.

    Strain-induced metal-semiconductor transition observed in atomic carbon chains

    Nat. Commun.

    (2015)
  • S.G. Sarwat et al.

    Scaling limits of graphene nanoelectrodes

    Nano Lett.

    (2017)
  • Y.C. Lin et al.

    Unexpected huge dimerization ratio in one-dimensional carbon atomic chains

    Nano Lett.

    (2017)
  • O. Cretu et al.

    Electrical transport measured in atomic carbon chains

    Nano Lett.

    (2013)
  • V.I. Artyukhov et al.

    Mechanically induced metal-insulator transition in carbyne

    Nano Lett.

    (2014)
  • Z. Zanolli et al.

    Quantum spin transport in carbon chains

    ACS Nano

    (2010)
  • J.A. Fürst et al.

    Atomic carbon chains as spin-transmitters: an ab initio transport study

    Epl-Europhys Lett

    (2010)
  • M.G. Zeng et al.

    Perfect spin-filter and spin-valve in carbon atomic chains

    Appl. Phys. Lett.

    (2010)
  • L. Shen et al.

    Electron transport properties of atomic carbon nanowires between graphene electrodes

    J. Am. Chem. Soc.

    (2010)
  • B. Akdim et al.

    Switching behavior of carbon chains bridging graphene nanoribbons: effects of uniaxial strain

    ACS Nano

    (2011)
  • B.K. Nikolic et al.

    First-principles quantum transport modeling of thermoelectricity in single-molecule nanojunctions with graphene nanoribbon electrodes

    J. Comput. Electron.

    (2012)
  • Y. Dubi et al.

    Colloquium: heat flow and thermoelectricity in atomic and molecular junctions

    Rev. Mod. Phys.

    (2011)
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