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C: Physical Processes in Nanomaterials and Nanostructures

Gate-Tunable Fano Resonances in ParallelPolyacene-Bridged Carbon Nanotubes Kunpeng Dou, Ching-Hao Chang, and Chao-Cheng Kaun J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00643 • Publication Date (Web): 29 Jan 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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The Journal of Physical Chemistry

Gate-Tunable Fano Resonances in ParallelPolyacene-Bridged Carbon Nanotubes Kun Peng Dou,†,‡,# Ching-Hao Chang,†,§,# and Chao-Cheng Kaun*,†,‖

†Research

‡College

Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan

of Information Science and Engineering, Ocean University of China, Qingdao 266100,

China §

Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan

‖Department

of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan

ABSTRACT A nanoscale device functioning in electronic transport via electrically tunable Fano resonances has huge potential for applications but is still rarely available to date. Using firstprinciples calculations, we show that a double-path molecular junction under an applied gate voltage can realize such a goal. It turns out that the crosstalk between two paths can be mapped to an ideal Fano-Anderson model - a single-path junction coupling to an isolated quantum dot. Its line shape of Fano resonance progressively evolves from an asymmetric to a symmetric BreitWigner peak when the gate voltage increases moderately. The significance of this system is illustrated by the sizable coupling strength that scales linearly with the gate voltage. Based on this

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scheme, we propose that this tunable Fano molecular junctions can serve as efficient transistors and thermoelectric energy conversion devices.

INTRODUCTION Fano resonances appear in spectra of absorption, scattering and transport,1 and their usages often advance the device, because of their tunable sharp asymmetric peaks stemming from quantum interference. For example, a tunable phonon-exciton Fano system based on a bilayer graphene has been achieved recently, which can be manipulated through electrostatic gating so that even phonon lasers can be built.2 Yet this capability has rarely been demonstrated in conducting quasi-one-dimensional junctions.3-5 One common route to trigger the Fano characteristics is attaching various side groups to a molecular wire via weakly coupling.6-8 On the other hand, the different intrinsic property of molecular devices is an important factor.9-11 For instance, Kim et al. indicated that Fano resonance exists in the single azobenzene-based molecular devices with trans conformation but it is absent in those with cis one.9 Min et al. demonstrated that different nucleobases on a graphene nanoribbon could be distinguished as different Fano dips.10-12 The asymmetric interface between the molecule and the electrode could also result in Fano resonance.13,14 The nature of Fano resonance, however, is hardly controlled in these pioneer works. Papadopoulos et al. suggested that the energy position of Fano resonance can be modified by rotating the side group (bipyridine) of the molecular wire composed by fluorene subunits.15,16 Hong et al. proposed that the width and energy position of the Fano resonance dip can be tuned by controlling the stacking distance between the vanadocene and carbon nanotube (CNT) from 2.6 Å to 3.4 Å.17 However, these manipulations may be sensitive to the changes of experimental environments, such as temperature fluctuation.


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Whereas the model-level analysis18 proposes that Fano line shapes19 in parallel-coupled double quantum dots are tunable by gating, in this work, we theoretically establish that a molecular junction with parallel paths, as shown in Figure 1a, represents a realistic device that enables precise controls of Fano resonance via gating.3-5 We prove that such a parallel structure can be analyzed in view of an ideal Fano-Anderson model that has an isolated side-coupled branch (Figure 1b). The consequent equivalent crosstalk between two paths is directly modulated by an external gate voltage, leading to Fano phenomenon. Two overriding advantages emerge in such junctions with parallel paths: (1) Fano resonance can be turned on by gating. (2) The asymmetric factor of nonlinear Fano profile can be varied linearly by gating. Both features are applicable in other parallel-path molecular junctions, allowing an efficient charge transfer between paths by increasing the gate voltage.

Figure 1 (a) Geometric structure of the junction, consisted of double polyacene (PA) molecules bridging carbon nanotubes, under an external electric field. (b) Schematic illustration of a parallelpath structure under an external electric field, being mathematically equivalent to a Fano-Anderson model.


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MODELS AND METHODS Armchair CNTs (n, n) are adopted as electrodes, where n = 4, 6, 8, and 10. Figure 1a shows the geometric structure of the junction, consisted of double polyacene (PA) molecules seamlessly bridging CNTs, under an external electric field. Both PAs are in cofacial alignment, corresponding to the maximal separation, known to be energetically favorable.20,21 Optimization calculations of each junction were performed by using density functional theory (DFT) implemented in the SIESTA package.22 An energy cut-off of 200 Ry was used. Structural relaxations were allowed until the force acting on each atom was less than 0.01 eV/Å. Then transport calculations were performed by using Nanodcal package23 based on DFT with the nonequilibrium Green’s function (NEGF) formalism. Both calculations used pseudopotentials and the double-ζ plus polarization basis set, within the local density approximation.24 Three primitive layers of each electrode were included as buffer layers in the scattering region. The Brillouin zone was sampled by 100 k-points.


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Figure 2 Evolution of transmission spectra of the PA-CNT(4,4) junction under different electric fields along y axis. The ab initio results are fitted by a transformed Fano resonance model (Ey≠0) and Breit–Wigner peaks (Ey=0).

RESULTS AND DISCUSSION Figure 2 shows the calculated transmission spectra of the junction where two PA molecules bridge CNT (4,4) electrodes under different gate electric fields. Without gating, two symmetric BreitWigner peaks situate at either side of the Fermi level (EF) due to resonant transmissions. Under gating, asymmetric Fano peaks appear and shift to lower energies relative to EF. As the vertical


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distance between the two molecular backbones is more than 5 Å and thus direct interwire coupling (π−π interactions) can be ignored,25,26 these systems can be understood by the Breit–Wigner resonance model. Importantly, a gated parallel-coupled system can be approximately transformed into the Fano-Anderson model (Figure 1b),27,28 and the proof of transformation are shown in supporting information. Without gating, the Breit–Wigner resonance model gives a precise description for results calculated from first-principles (see black and red-dashed lines in Figure 2).27 Once electric field is applied along the y direction by gating, asymmetric transmission profiles emerge, which bear a close resemblance to those of Fano resonances. This suggest that the parallel system under external electric fields can indeed be transformed into the Fano-Anderson model.27,28 The ab initio result is well reproduced by an equivalent model (Figure 1b):

T (E) 

[ E  EH1

 2H  2L   t H2 / ( E  EH 2 )]2   2H [ E  EL1  t L2 / ( E  EL2 )]2   2L

(1)

where the subscript H and L denotes the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), respectively. Orbitals with energies EH1 and EL1 are assumed to be symmetrically coupled to left and right electrodes via the coupling constant ΓH = ΓL. EH2 and EL2 are eigen-energies of the effective quantum dot and tH/tL is the effective coupling between EH1/ EH2 and EL1/ EL2.


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Figure 3 Rescaled coupling strength trescale (tH’=tH/rcnt and tL’=tL/rcnt) in effective Fano-Anderson model which are mapped from PA junctions with different CNT electrodes. We further scrutinize the interplay between Fano properties and external electric fields on double-PA bridging CNT (n, n) electrodes with different radius. A linear-like relationship is found between the rescaled term tH/tL and the electric field, as shown in Figure 3 (tH’= tH/rcnt, tL’= tL/rcnt). This is in line with Eqn. 7 in supporting information, obtained after the transformation from the parallel system to the Fano-Anderson model. Based on these results, we expect that parallel paths in CNT junction represent a good platform enabling precise tunable Fano resonances via gating. Such a platform is stable against the changes of environment (such as temperature fluctuation). In addition, the gate effect on wider parallel paths compared to PA molecules is checked, shown in Figure S2, and multiple Fano resonances (up to four) appear near EF.


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Figure 4 Evolution of PDOS on (a) the upper and (b) the lower PA molecules. Black cases, without electric field; red cases, with Ey = 0.02 V/Å; green cases, with Ey = 0.04 V/Å. (c) Evolution of the real-space projections of wave function on both paths in the junction. The blue and white dots denote the parts with opposite signs of phase. To gain a microscopic insight into this gate-tunable Fano system, we focus on projected density of states (PDOS) analyses in the energy range around HOMO of the PA molecule (PDOS analyses on LUMO part draw the same trend). In Figure 4 (a) and (b), two peaks in PDOS on the PA molecules indicate that the HOMO is divided into bonding (Hb) and antibonding (Ha) states, referring to two paths with in-phase and out-of-phase couplings (cf. blue and white dots in Figure 4(c)), respectively. The energy difference between Hb and Ha states, however, further increases by applying external electric fields. The energy of Hb shifts to lower energy and distributes mainly on the lower PA as the field increases, and the opposite trend happens in that of Ha. Existence of bonding and antibonding states that are field-tunable finally leads to Fano resonance that are gatecontrollable.18


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To further illustrate the molecular orbital gating, we perform the Bader charge analysis, which indicates that the certain number of electrons transfer from the upper PA to the lower PA under gating (cf. Figure 5). This is reminiscent of formation of the silicon surface dimer, where the upper silicon dimer atom transfers portion of electrons to the lower silicon dimer atom, then π and π* states form on the upper and lower silicon atoms, respectively.29 In the present work, no intrinsic dipole exists between the two paths, as well as the direct interwire coupling.30 Upon gating, an artificial dipole is produced between the two paths following the direction of the electric field. The dipole can be well controlled by gating. This in turn reflects in the crosstalk (t in Figure 3) between the two paths which induces the Fano effect.

Figure 5 Bader charge analysis on the upper and the lower PA molecules under electric fields. We have demonstrated the effective electrostatic modulation of orbitals in a parallel configuration and this tunable Fano system have shown its application potential in molecular field effect transistor (FETs). On the one hand, FETs should respond quickly to variations of gate


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voltage, for high-speed applications. In our system, the electric field not only shifts the molecular orbital but also introduces resonance splitting (cf. Figure 2), thus the gating efficiency is expected to be better than the normal molecular FET with linear rigid shift (0.25 eV/V and 0.22 eV/V in Ref. 31). On the other hand, to reduce power dissipation, FETs in integrated circuits have to lower the bias voltage while maintain the increase of the source-drain current at least by one order of magnitude at room temperature. The source-drain current of the double PA bridged CNT (4,4) junction at Vsd = 0.3 V can be enhanced by an order of magnitude under Ey= 0.5 V/Å, as shown in Figure S3(c). Whereas the strength of the gating field can be reached within current experimental scope (~1 V/Å),32 lengthening the PA molecule shifts the resonance closer to the Fermi level30 and may reduce the required field strength. The efficient molecular orbital gating in the tunable Fano system may help to extend the thermionic limit (60 mV/decade)33 as well. The recent proposed quantum interference effect based on the ring-shaped molecular FET requires a third electrode locally attached the molecule to introduce dephasing which is sensitive to the attached site, otherwise the transistor efficiency is reduced,34,35 and such a precise control however remains an experimental challenge. As advances in selective etching techniques36 hold promise to tailor the desirable molecular junctions with parallel paths, the well-established global gating31 is expected to demonstrate this tunable Fano-based FET. Both electric field37 and strain38,39 could assist the selective etching progress, which has been in situ real-time monitored by polarized optical microscope recently.40 Finally, the controlled steepness of Fano resonance can be explored for the high-power-output thermoelectric energy conversion.41 Previous works41-43 hint the interwoven factors arising from electrode materials, molecule lengths, end-groups and so on, drawing complexity in correlations between junction compositions and power factors. Figure S4 shows that the sharp Fano dip in the


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LUMO derived resonance can be located at the Fermi level with Vsd = 0.77V and Ey= 0.03 V/Å, giving the Seeback coefficient as high as -97.32V/K at 30K and -324.4 V/K at 100K.41 The efficiency is increased by an order than single molecular devices (biphenyl and C60) without employing interference effects.44

CONCLUSIONS We have computationally proposed a quasi-one-dimensional junction consisted of parallel PA molecules bridging CNT electrodes, which can produce gate-tunable Fano resonances. An effective Fano-Anderson model well represents the driving mechanism of the Fano resonance evolving by gating. Moreover, the sizable coupling strength in this system scales linearly with the applied gate voltage. The proposed configurations are within the current experimental scope31,36,40 and their features can be used to build efficient transistors and thermoelectric energy conversion devices.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: Model analysis; gating effect on wider parallel paths compared to PA molecules; Fano-based fieldeffect transistor and thermoelectric device (PDF). AUTHOR INFORMATION


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#K.P.D

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and C.H.C contributed equally to the work.

Corresponding Author *E-mail: [email protected] (C.C. K.). ORCID Chao-Cheng Kaun: 0000-0002-5400-4758 Kunpeng Dou: 0000-0002-2565-8015 Ching-Hao Chang: 0000-0003-0878-9328

ACKNOWLEDGMENT This work was partially supported by the Ministry of Science and Technology, Taiwan (Grant no. 107-2112-M-001-036-MY3 and no. 107-2218-E-006-050), China Postdoctoral Science Foundation (Grant No. 2017M612348) and the Young Talent Project at Ocean University of China (Grant No. 3002000-861701013151). C.H.C. acknowledges financial support from the German Research Foundation (Grant CH 2051/1-1).

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Gate-Tunable Fano Resonances in Parallel ... - ACS Publications

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