A High Performance Single-Molecule Switch Designed by Changing

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C: Energy Conversion and Storage; Energy and Charge Transport

A High Performance Single-Molecule Switch Designed by Changing Parity of Electronic Wavefunctions via Intramolecular Proton Transfer Zi-Qun Wang, Ming-Zhi Wei, Mi-Mi Dong, Gui-Chao Hu, Zong-Liang Li, Chuan-Kui Wang, and Guang-Ping Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03761 • Publication Date (Web): 19 Jul 2018 Downloaded from http://pubs.acs.org on July 20, 2018

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The Journal of Physical Chemistry

A High Performance Single-Molecule Switch Designed by Changing Parity of Electronic Wavefunctions via Intramolecular Proton Transfer Zi-Qun Wang,† Ming-Zhi Wei,†,‡ Mi-Mi Dong,† Gui-Chao Hu,†,¶ Zong-Liang Li,† Chuan-Kui Wang,∗,† and Guang-Ping Zhang∗,†,¶ †Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, School of Physics and Electronics, Shandong Normal University, Jinan 250358, China. ‡School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China. ¶Institute of Materials and Clean Energy, Shandong Normal University, Jinan 250014, China. E-mail: [email protected]; [email protected]

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Abstract

Molecular switches, as one of functional molecular components, play a vital role in nanoscale logic circuits. Here, effect of intramolecular proton transfer on current of single-molecule devices consisting of a keto or enol molecule sandwiched between two magnetic zigzag graphene nanoribbon (zGNR) electrodes is theoretically investigated. The keto and enol tautomers interconvert into each other by intramolecular proton transfer. The results show that the current of the keto molecular device is hardly observed, whereas that of the enol molecular device is significantly enhanced, demonstrating a high efficient switching effect with the ON/OFF ratio up to 3.4 × 102 . Moreover, spin currents of the device with an enol isomer display giant bipolar rectification with the largest rectification ratio of 1.4×105 when the two zGNR electrodes are antiparallely spin-polarized. The underlying mechanism is attributed to parity matching principle of electronic wavefunctions in the core molecule and zGNR electrodes. The intramolecular proton transfer completely changes the parity of the electronic wavefunctions of the core molecule, and the electron tunneling channels around the Fermi energy are thus largely modified, resulting in a significant ON/OFF switching ratio. This work develops a strategy for designing high performance single-molecule switches.

1. Introduction Organic single-molecule device, which has been attracting a great deal of attention over the past decades, is considered as one of the promising candidates to achieve the miniaturization of traditional electronic devices. 1–5 Since Aviram and Ratner first proposed the concept of molecular rectifier consisting of a donor-bridge-acceptor molecule in 1974, 6 a vast amount of functional molecular devices, such as molecular wires, 7–11 switches, 12–17 rectifiers, 6,18–26 and field effect transistors, 27–31 have been experimentally and theoretically designed and synthesized. It has been found that the functionality of molecular devices is affected by a lot of 2


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factors, for example, the intrinsic molecular characteristic, 32 electrode material, 33 contact configurations between the molecule and electrodes, 34,35 molecular anchoring group, 18,25,36 and even the external environment. 15 Especially, when molecular devices comprise magnetic electrodes or magnetic organic molecules, spin-dependent transport properties maybe show some interesting phenomena like spin filtering 15,37 and magnetoresistance effect. 38–40 Magnetic molecular devices belong to the burgeoning field of molecular spintronics, which aim to manipulate the spin degree of freedom to store information with high capacity, perform calculation with high speed and run with low power. Zigzag graphene nanoribbons (zGNRs), which are tailored from graphene nanosheets (GNSs) along zigzag edges, are excellent lowdimensional magnetic materials and extensively used in the design of magnetic molecular devices owing to its high carrier mobility, tunable carrier concentration and low spin-orbit coupling. 15,41–44 Recently, Supur et al. have successfully fabricated molecular junctions consisting of graphene nanoribbons, which provides a promising experimental approach to realize nanoribbon-based molecular junctions. 45 In addition, the Bloch wavefunctions of symmetric zGNRs have either odd or even parity. For symmetric molecular devices with GNR electrodes, a consistency for parities of electronic wavefunctions in the left GNR electrode, the core molecule, and the right GNR electrode is an essential prerequisite for forming a good electron transport channel due to the parity conservation required for the wavefunctions of tunneling electrons. 46 Therefore, the parity properties of electronic wavefunctions can be used to modulate the performance of GNR based molecular devices, which is hardly available in metal-molecule-metal devices. For example, taking advantage of this rule, Song et al. have demonstrated that the rectification ratio of single-molecule diodes designed based on GNR electrodes can be enhanced by four orders of magnitude through combing undoped zGNR and doped aGNR (armchair graphene nanoribbon) electrodes. 33 As one kind of useful functional molecular devices, molecular switches that exhibit two distinct conducting states with high or low conductance and can be triggered by stimuli such as illumination, 12 redox reaction, 13,14 mechanical operations, 15 and cis-trans transfor-

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mation, 47 have drawn a lot of research interest. Recently, Weckbecker et al. have proposed a new approach to realize conductance switching via intermolecular proton transfer. 48 In this approach, the core molecule will interconvert between keto and enol forms by intermolecular proton transfer, which have different conjugation properties and hence large difference in conductance. Meanwhile, they illustrated this method by a representative molecule 6,11-dioxo5,6,11,12-tetrahydrobenzo[b]phenazine-1,4,7,10-tetracarbonitrile (DO-THBbPA-TCN) sandwiched between two GNS electrodes. The numerical results showed a clear switching effect with a ON/OFF switching ratio of ∼ 28. However, this ON/OFF value is far from that required for real application. It is also noted that the keto and enol molecules investigated by Weckbecker et al. are symmetric and their frontier molecular orbitals have either odd or even parity. But the rule of parity conservation for the wavefunctions of tunneling electrons did not work since they used two GNSs instead of GNRs as electrodes. In principle, utilizing the rule of parity conservation for the wavefunctions of tunneling electron also can facilitate the ON/OFF switching ratio since it can largely enhance the rectification performance of single-molecule diodes. 33 In this term, the effect of intramolecular proton transfer on conductance of DO-THBbPA-TCN molecule has been revisited when the molecule is sandwiched between two symmetric zGNR electrodes by using the density functional theory (DFT) combined with non-equilibrium Green’s function (NEGF) method. 49 The numerical results show a significant enhancement in the switching performance with the ON/OFF switching ratio up to 3.4 × 102 . Further analysis confirms that the high switching ratio indeed originates from the parity matching between the left zGNR electrode, the core molecule, and the right zGNR electrode. In addition, the molecular devices manifest giant bipolar rectifying effect when the magnetic zGNR electrodes are antiparallely spin-polarized, which can also be understood in terms of different parities for the spin-resolved subbands of zGNR electrodes above and below Fermi energy (EF ). The rest of the paper is organized as follows. The theoretical model and computational details are briefly presented in part 2, and part 3 is devoted to the results and discussion. Finally, a conclusion is given in part 4.

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Figure 1: Schematic of investigated molecular junctions, where the keto and enol molecules are covalently fused into the zGNR electrodes. The left and right electrodes are denoted by the red and blue rectangles, respectively.

2. Theoretical model and computational details As depicted in Figure 1, the modeled single-molecule devices are comprised of three parts: the left zGNR electrode (marked by the red rectangle), the right zGNR electrode (marked by the blue rectangle), and the central region (i.e., the device part). Corresponding structural formula (see Figure S1 ) and coordinate information of the devices can be found in Supporting Information. To avoid spurious interaction between neighboring images in the calculations, a vacuum of about 15 Å is used along the x and y directions of the modeled single-molecule junctions, respectively (which is not displayed in Figure 1). The central region consists of the core DO-THBbPA-TCN molecule and some interacting layers of zGNR electrodes, where interactions between the core molecule and two zGNR electrodes are screened. As pointed out by Weckbecker et al., the DO-THBbPA-TCN molecule has two tautomers, namely, the keto form and the enol form (henceforth keto and enol for simplicity), which can be interconverted to each other through the intramolecular proton transfer process triggered by electrostatic field. 48 Since the zGNR is magnetic, there are two spin-polarization configurations for the zGNR electrodes, that is, parallel spin-polarization (denoted as P) and antiparallel spinpolarization (denoted as AP). Therefore, four single-molecule devices in total are obtained

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in our investigation, which are labeled as keto-P, keto-AP, enol-P, and enol-AP, respectively. From Figure 1, one can see clearly that the geometric structure of each single-molecule junction is symmetric with respected to its z axis. The geometric structure of each singlemolecule junction was first optimized in the ab initio package Atomistix ToolKit (ATK). 50,51 During the optimization, a vacuum of about 15 Å is used along the z direction of the supercell to avoid spurious interaction between neighboring images. All atoms in the central region are fully relaxed until the residual force is smaller than 0.03 eVÅ−1 . In the geometric optimization and the following electron transport calculations, the spin-dependent generalized gradient approximation (SGGA) with the Perdew-Burke-Ernzerh (PBE) parameterization is employed. An energy cutoff of 200 Ryd is used to determine the real space grids and a 1 × 1 × 100 mesh is used for the k -point sampling in the Brillouin zone. As shown in Figure S2 in Supporting Information, the test calculations on the basis set show nearly the same transmission spectra for keto-P under zero bias voltage for the single-ζ polarized (SZP) and double-ζ polarized (DZP) basis sets, where there is only a small energy shift of 0.04 eV for the spin-down transmission peak at around 0.2 eV. To balance calculation accuracy and efficiency, the SZP basis set is thus employed. The spin-resolved electron transport properties are studied using the state-of-the-art DFT based NEGF method, which has been efficiently implemented in ATK package. 49–51 The spindependent current through the single-molecule devices is calculated by Landauer-Büttiker formula 52 e Iσ = h

Z Tσ (E, V )[f (E − µL ) − f (E − µR )]dE,

(1)

where σ =↑ / ↓ represents spin orientation (spin up/spin down) of electron. f (E − µL/R ) is the Fermi-Dirac distribution function for electrons in the left/right electrode, and µL/R = EF ∓ eV /2 is chemical potential of the left/right electrode. In the calculations, the EF is set to zero. Tσ (E, V ) is spin-dependent transmission spectra for spin σ, which is defined as

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Figure 2: Spin-resolved I-V curves for (a) keto-P, (b) enol-P, (c) keto-AP, and (d) enol-AP. The insets in (a) and (c) are the zoomed-in plots of I-V curves for keto-P and keto-AP.

Tσ (E, V ) = Tr[Γσ,L (E, V )Gσ (E, V )Γσ,R G†σ (E, V )],

(2)

where Gσ (E, V ) is Green’s function of the central region, and Γσ,L/R (E, V ) represents the coupling between the left/right electrode and the central region.

3. Results and discussion The calculated spin-dependent current-voltage (I-V ) curves in the range of [−0.8 V, 0.8 V] for keto and enol devices with P and AP spin-polarized configurations are shown in Figure 2. First, let’s discuss the case where the two magnetic zGNR electrodes are parallely spinpolarized. For the keto-P device, from Figure 2(a), one can hardly see any current through the device all over the investigated bias range. Meanwhile, the zoomed-in inset of Figure

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2(a) shows nonlinear spin-resolved I-V curves. Both the spin-up and spin-down currents first increase with the bias voltage and then decrease when the bias voltage is further increased, manifesting negative differential resistance (NDR) features. The I-V curves under negative bias voltage are nearly symmetric with those under positive bias voltage. However, the largest values of the current for spin-up and spin-down component are only 69.6 nA at 0.4 V and 35.3 nA at 0.2 V, respectively. When the two hydrogen atoms are transferred from the dihydropyrazine ring to the benzoquinone ring, the molecule changes into enol from keto, and the corresponding spin-resolved I-V curves are displayed in Figure 2(b). It is noted that there is a large enhancement in the conductance for enol-P device. Specifically, the maximum values of spin-up and spin-down current reach up to as large as 2.7 µA and 1.8 µA at −0.8 V, respectively, which are about 250 and 818 times larger than the corresponding counterparts for keto-P, showing a remarkable switching effect due to the intramolecular proton transfer. Then, we turn to the case where the two magnetic zGNR electrodes are antiparallely spinpolarized. Similarly to the case of keto-P, the keto-AP device is also blocked in the range of investigated bias voltage. However, as shown in the zoomed-in inset of Figure 2(c), the spin components of the current show bipolar rectifying effect. That is to say, the spin-up electron can only tunnel through the device under negative bias voltage while it is blocked under the positive bias voltage, which leads to an obvious rectifying effect with the forward rectification direction along the negative bias voltage. At the same time, the spin-down current also manifests a clear rectifying effect but with a reversed rectification direction, where the forward rectification direction is completely reversed to the positive bias voltage. When it turns to the case of enol-AP, the main feature for the spin-resolved I-V curves is almost the same with those of keto-AP, namely, bipolar rectifying effect is evidently seen for the spin currents of keto-AP. Meanwhile, conductance of the device is again largely enhanced compared with that of keto-AP with the largest values of 4.06 µA at −0.8 V and 2.8 µA at 0.8 V for spin-up and spin-down current, respectively. Thus, a significant switching effect is again demonstrated when the zGNR electrodes are antiparallely spin-polarized.

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Figure 3: (a) The variation of switch ratio SR as a function of bias voltage for the P and AP configurations. (b) and (c) are the spin-resolved rectification ratio RR or inverted rectification ratio 1/RR versus keto-AP and enol-AP, respectively. To evaluate the change of current induced by proton transfer, switch ratio SR(V ) = |I↑enol (V ) + I↓enol (V )|/|I↑keto (V ) + I↓keto (V )| is defined. For zero bias, spin-dependent transmission coefficient Tσ (EF , 0 V ) is accordingly used for the switch ratio SR = |T↑enol + T↓enol |/|T↑keto +T↓keto |. On the other hand, in order to characterize the rectifying performance of each single-molecule device, spin-resolved rectification ratio RR↑/↓ (V ) = |I↑/↓ (V )/I↑/↓ (−V )| and spin-resolved inverted rectification ratio 1/RR↑/↓ (V ) = |I↑/↓ (−V )/I↑/↓ (V )| are respectively calculated. A value of RR (1/RR) larger than 1 indicates that the rectification direction is along the positive (negative) bias voltage. From Figure 3(a), one can see clearly that the SR of the single-molecule device varies obviously as a function of the external bias voltage. For the P configuration, the value of SR increases monotonically with the increase of the magnitude of positive and negative bias voltages. The SR has its minimum of 2.6 at 0 V, while it rises up to 184 at 0.8 V and even can get up to as large as 341 at −0.8 V, which demonstrates a remarkable switching effect when the molecule is transformed from keto to enol induced by intramolecular proton transfer. Differently, for the AP configuration, one can still expect a relative large SR ∼ 102 at moderate bias voltage. And the maximum value of SR for AP configuration is 332 at −0.8 V, which is slightly smaller compared with that of P configuration but still far larger than the value of ca. 28 reported by Weckbecker et al. 48 This suggests that significant switching effect can be achieved when the rule of parity conservation for the wavefunctions of tunneling electron is fully taken advantage of. 9



Figure 4: Spin-resolved transmission spectra as a function of bias voltage for (a) keto-P, (b) enol-P, (c) keto-AP, and (d) enol-AP. The dash lines indicate chemical potentials of the left and right electrodes. As shown in Figure 2(a) and 2(b), the spin-resolved I-V curves for both keto-P and enolP show nearly symmetric features suggesting very weak rectifying effect. The largest value of RR for spin-up current of keto-P is only 1.5 at 0.4 V while the maximum value of 1/RR for spin-down current of enol-P is only 2.5 at 0.6 V. When it turns to the case where the two zGNR electrodes are antiparallely spin-polarized, there are evident bipolar rectifying effects for both keto-AP and enol-AP as shown in Figure 3(b) and 3(c). For keto-AP, the largest value of 1/RR gets up to 5.8 × 103 at 0.4 V for the spin-up current and the maximum value of spin-down RR can reach as large as 8.3 × 103 at 0.4 V. More interestingly, the rectifying performance for enol-AP is further largely enhanced with the RR or 1/RR improved by two orders of magnitude compared with those of keto-AP. Specifically, the largest value of 1/RR for enol-AP is 1.4 × 105 at 0.6 V for the spin-up current and the maximum value of RR for the spin-down current can reach as large as 0.9 × 105 at 0.4 V, which suggests a remarkable enhancement of the rectifying performance by means of intramolecular proton transfer. To understand the high efficient switching effect induced by the intramolecular proton transfer and the bipolar rectifying effect, evolutions of transmission spectra under bias voltage

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are explored and shown in Figure 4. Corresponding transmission spectra in logarithmic scale are also given in Figure S3 in Supporting Information. From Figure 4(a), it is clearly seen that there is a very sharp spin-up transmission peak locating at 0.39 eV below EF for keto-P at zero bias voltage. On the contrary, there is a sharp spin-down transmission peak around 0.22 eV above EF when the bias voltage is zero. However, the intensities of these two transmission peaks are quickly suppressed when either a positive or a negative bias voltage is applied. Thus, an invisible current is observed for keto-P in the investigated bias voltage range. For enol-P, as seen from Figure 4(b), there are two spin-up transmission peaks with a relative larger broadening, which respectively reside at −0.4 eV and 0.27 eV at 0 V. The transmission peak at −0.4 eV is sharply lowered when a moderate bias voltage is applied. However, the intensity and energy location of the transmission peak at 0.27 eV above EF is nearly unchanged as the magnitude of bias voltage is increased. And then it enters the bias window around ±0.4 V contributing to the spin-up current, which leads to a threshold bias of ca. 0.4 V and an almost symmetric feature for the spin-up current as seen in Figure 2(b). Similarly, there are also two spin-down transmission peaks that locate at −0.4 eV and 0.3 eV under zero bias voltage, respectively. However, their evolutions under bias voltage are completely opposite to the spin-up ones. That is to say, the spin-down current is almost contributed from the transmission peak at −0.4 eV. Hence, a significant switching effect is displayed. When it turns to keto-AP where the two zGNR electrodes are antiparallely spinpolarized, there is hardly any visible transmission peak in the investigated bias voltage range. Therefore, the current through the keto-AP device is on the magnitude of nanoampere. However, for enol-AP, two transmission peaks around 0.3 eV and −0.4 eV are observed for each spin component. For the spin-up case shown in Figure 4(d1), these two transmission peaks are quickly suppressed under positive bias voltage while they are included in the bias window at larger negative bias voltages. As a result, rectifying effect with a rectification ratio of ∼ 105 is found for the spin-up current and the forward direction of rectification is along the negative bias voltage. In contrast, the two spin-down transmission peaks shown in

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Figure 5: (a) Spin-resolved Bloch wavefunctions of π and π ∗ subbands at Γ-point. (b) Spatial distributions of spin-resolved MPSH molecular orbitals for keto-P, enol-P, keto-AP, and enol-AP. The isovalue for the wavefunction plots is 0.01. Figure 4(d2) have an opposite evolution compared with that for the spin-up ones, which leads to a reversed rectification direction along the positive bias voltage for the spin-down current. On the other hand, the large spin-up current under negative bias voltage and spin-down current under positive bias voltage contribute to a significant ON/OFF switching effect for enol-AP/keto-AP induced by the intramolecular proton transfer. As pointed out in our previous study, the electron transport through GNR based singlemolecule devices, of which the geometric structures are symmetric with respect to the z axis, can be well understood by analysing the parity of wavefunctions for tunneling electrons. 33 It is found that a good channel for electron transport requires a consistency in the parity

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Figure 6: Spin-resolved energy bands of the left electrode (left panel), the right electrode (right panel), and transmission spectra (middle panel) for (a1)-(a3) keto-P, (b1)-(b3) enol-P, (c1)-(c3) keto-AP, and (d1)-(d3) enol-AP at 0.0 V, ±0.8 V. π (π∗) subbands are indicated by dash (solid) lines. Dash lines in the middle panel are bias windows and colored triangles denote the MPSH eigenvalues. of electronic wavefunctions in all parts of the device (i.e., the left GNR electrode, the core molecule, and the right GNR electrode). Bloch wavefunctions of the two subbands around EF at Γ-point for the unit cell of zGNR electrodes and the wavefunctions for the core molecule obtained by diagonalizing the molecular projected self-consistent Hamiltonian (MPSH) are displayed in Figure 5. Also, the spin-resolved energy bands of each electrode and transmission spectra at bias voltages of V = 0.0, ±0.8 V are plotted in Figure 6, from which one can see that the spin-up and spin-down energy bands are split. As shown in Figure 5(a), it is found that the Bloch wavefunctions for both spin-up and spin-down π (π ∗ ) subbands have odd

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(even) parity under the yz midplane mirror operation. Also, the highest occupied molecular orbital (HOMO) of keto-P has an even parity while the lowest unoccupied molecular orbital (LUMO) has an odd parity (see Figure 5(b)). For the case of spin up displayed in Figure 6(a1), both the HOMO and LUMO (labelled as triangles in the middle panel) align with the spin-up π ∗ subband at zero bias voltage. However, the spin-up electrons can only be allowed to tunnel through the device via HOMO due to the consistency of the parities for HOMO and spin-up π ∗ subband. For the case of spin-down, both the HOMO and LUMO align with the spin-down π subband at zero bias voltage. Similarly, one can tell that the spin-down electrons are only allowed to tunnel through LUMO due to the parity conservation rule for tunneling wavefunction. However, when a bias voltage is applied, taking the cases of −0.8 V and 0.8 V for examples as shown in Figure 6(a2) and 6(a3), the energy bands of the left zGNR electrode have a displacement with respect to those of the right zGNR electrode, which breaks the consistency of the parities for wavefunctions in the left and right zGNRs electrodes at the energies of spin-up HOMO and spin-down LUMO. Hence, transmission peaks contributed by the spin-up HOMO and spin-down LUMO are also strongly suppressed once there is a moderate bias voltage applied across the device. When the keto is transformed into enol induced by intramolecular proton transfer, as shown in Figure 5(b), the parities of HOMO and LUMO are changed. That is to say, the HOMO of enol-P has an odd parity while the LUMO has an even parity. For the case of spin up, the HOMO (LUMO) aligns with the spin-up π (π ∗ ) subband at zero bias voltage as depicted in Figure 6(b1). Therefore, there are two broad spin-up transmission peaks locating around −0.4 eV and 0.27 eV mediated by HOMO and LUMO, respectively. Meanwhile, there is a very similar situation for the case of spin down, where two spin-down transmission peaks are also observed at around −0.4 eV and 0.27 eV contributed from HOMO and LUMO. However, once a bias voltage is applied on the device, similar to the case of keto-P, the spin-up transmission peak at −0.4 eV and the spin-down transmission peak at 0.27 eV are severely lowered due to the discrepancy of parities for subbands of two zGNR electrodes

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arising from the displacement between the corresponding subbands as shown in Figure 6(b2) and (b3). Consequently, only the transmission peaks mediated by the spin-up LUMO and the spin-down HOMO remain under positive and negative bias voltages, which can be easily checked in Figure 5(b). When it turns to the AP configuration where the two zGNR electrodes are antiparallely spin-polarized, spin characteristics of the energy bands for the right zGNR electrode are completely reversed compared to the case of P configuration. In this case, by applying the parity analysis for wavefunctions of tunneling electrons, it is clearly that there are no transmission peaks around EF for keto-AP neither under zero bias voltage nor when a bias voltage is applied shown in Figure 6(c). That is why keto-AP manifests a blocked feature all over the bias voltage investigated. For the enol-AP, the HOMO has an odd parity while the LUMO has an even parity, which are opposite to those of keto-AP. Meanwhile, HOMO aligns with the π subbands and LUMO aligns with the π ∗ subbands of both zGNR electrodes, which results in two broad transmission peaks residing at −0.4 eV and 0.3 eV respectively for both spin up and spin down (see Figure 6(d1)). When a moderate positive bias voltage is applied, the two spin-up transmission peaks are severely suppressed due to the alignment of the spin-up π ∗ subband of the left zGNR electrode with the spin-up π subband of the right zGNR electrode around the EF . Therefore, only the two spin-down transmission peaks contribute to the current under positive bias voltage. On the contrary, under a moderate negative bias voltage, the spin-down π subband of the left zGNR electrode aligns with the spin-down π ∗ subband of the right zGNR electrode around the EF , which leads to the two spin-down transmission peaks severely suppressed. Hence, the current of enol-AP under negative bias voltage is almost contributed from the spin-up transmission peaks. Now, it is clearly that the electron transport properties can also be well understood by analysing the parity of wavefunctions for tunneling electrons. To further demonstrate that parity conservation for the wavefunctions of tunneling elec-

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Figure 7: (a) Spin-resolved transmission eigenstates (from left contribution) for keto-P under zero bias voltage at the energies of -0.39 eV and 0.22 eV, which correspond to the spin-up and spin-down transmission peaks in Figure. 6(a1), respectively. (b) Spin-resolved transmission eigenstates (from left contribution and right contribution) for keto-P under 0.8 V at the energies of spin-up HOMO and spin-down LUMO. The isovalue for the plots is chosen as 0.3. tron indeed governs the electronic transport in the GNR based devices with symmetric geometric structures, transmission eigenstates are additionally investigated, which are the eigenstates of the transmission matrix and are a linear combination of the scattering eigenstates through the device. For simplicity, only the transmission eigenstates for keto-P at 0 V and 0.8 V are displayed in Figure 7. One can easily see that the spatial distribution of the spin-up transmission eigenstate at 0.22 eV localizes only on the left zGNR electrode due to the discrepancy in parities of wavefunctions for spin-up LUMO and spin-up π ∗ subband, which confirms the fact that no transmission peak contributed from spin-up LUMO at 0.22 eV has been observed in Figure 6(a1). However, the spin-down LUMO aligns with the spindown π subband causing a delocalized transmission eigenstates at 0.22 eV (see Figure 7(a))

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and hence a spin-down transmission peak at 0.22 eV shown in Figure 6(a1). When it turns to the energy of -0.39 eV, a spin-up transmission eigenstate delocalized all over the device and a spin-down transmission eigenstate localized on the left zGNR electrode have been presented due to the change to even parity for the wavefunctions of spin-up and spin-down HOMOs. When a positive bias voltage is applied across the device, taking the case of 0.8 V as an example, as shown in Figure 6(a2), the spin-down LUMO (spin-up HOMO) aligns with the spin-down (spin-up) π ∗ subband of the left zGNR electrode and the spin-down (spin-up) π subband of the right zGNR electrode. Therefore, as seen from Figure 7(b), the transmission eigenstate from left contribution or right contribution is truncated at the contact between the keto molecule and the left (right) zGNR electrode because the parities of the wavefunctions for LUMO (HOMO) and the π ∗ (π) subband of the left (right) zGNR electrode are different. To verify the parity rule as a general one for devices with symmetric structures with respect to the z axis, other keto and enol devices have also been investigated, where infinite GNS electrodes (Figure S4(a) in Supporting Information) and asymmetric zGNR electrodes (Figure S4(b) in Supporting Information) are used. The I-V curves and SR as a function of bias voltage for these devices are given in Figure S5 in Supporting Information. It can be easily found that SR of devices with GNS electrodes and devices with asymmetric zGNR electrodes is significantly reduced, which suggests that the parity rule does not hold in the devices with asymmetric structures. In addition, we also check effects of the width of zGNR electrodes on the parity rule. Keto and enol devices with other symmetric zGNR electrodes are tested (Figure S4(d) in Supporting Information). The spin-resolved transmission spectra under zero bias voltage (Figure S6 in Supporting Information) suggest that the parity rule always holds when the width of the zGNR electrodes changes.

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4. Conclusions In summary, by using the first-principles method, current of molecular junctions with a keto or enol tautomer sandwiched between two magnetic zGNR electrodes is studied, and effect of intramolecular proton transfer on the current is investigated. A significant switching property with the ON/OFF ratio up to 3.4 × 102 is revealed. Meanwhile, bipolar rectification with giant rectification ratio of 1.4 × 105 for the enol-AP device is also observed. Current of the investigated molecular junctions is closely related to the parity of electronic wavefunctions in both the core molecule and two zGNR electrodes, and parity conservation of the wavefunctions is required for tunneling electrons across the whole device. As the intramolecular proton transfer occurs, parities of electronic wavefunctions for frontier molecular orbitals in the core molecule are completely changed, and hence the electron tunneling channels around the Fermi energy are significantly modified, leading to a significant ON/OFF switching ratio. Moreover, the remarkable rectifying behavior of each spin-resolved current for the enol-AP device is observed. This work presents a method to construct high performance molecular switch by taking advantage of parity of electronic wavefunctions.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Figures S1-S5 (PDF)

Acknowledgements Support from the National Natural Science Foundation of China (Grant Nos. 11704230 and 11374195), China Postdoctoral Science Foundation (Grant No. 2017M612321), and the Taishan Scholar Project of Shandong Province are gratefully acknowledged.

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A High Performance Single-Molecule Switch Designed by Changing

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