† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11874242, 21933002, and 11704230), China Postdoctoral Science Foundation (Grant No. 2017M612321), and the Taishan Scholar Project of Shandong Province of China.
The idea of replacing traditional silicon-based electronic components with the ones assembled by organic molecules to further scale down the electric circuits has been attracting extensive research focuses. Among the molecularly assembled components, the design of molecular logic gates with simple structure and high Boolean computing speed remains a great challenge. Here, by using the state-of-the-art nonequilibrium Green’s function theory in conjugation with first-principles method, the spin transport properties of single-molecule junctions comprised of two serially connected transition metal dibenzotetraaza[14]annulenes (TM(DBTAA), TM = Fe, Co) sandwiched between two single-walled carbon nanotube electrodes are theoretically investigated. The numerical results show a close dependence of the spin-resolved current-voltage characteristics on spin configurations between the left and right molecular kernels and the kind of TM atom in TM(DBTAA) molecule. By taking advantage of spin degree of freedom of electrons, NOR or XNOR Boolean logic gates can be realized in Fe(DBTAA) and Co(DBTAA) junctions depending on the definitions of input and output signals. This work proposes a new kind of molecular logic gates and hence is helpful for further miniaturization of the electric circuits.
Logic gates, which can take single- or two-input signals and then generate a binary output signal, are elementary blocks of extensively used digital integrated circuits. Enhancing the circuit integration by scaling down the electronic components can effectively improve the performance of integrated circuits. On the other hand, as the traditional electronic components are continually approaching to nano or even sub-nano scale, further miniaturization of silicon-based electronic components faces extremely formidable challenges due to limitations in current processing technology and prominent influence of quantum effect. As one of promising solutions, utilizing molecules as building blocks to design functional electronic devices, which are potential candidates to substitute traditional silicon-based components, has been drawing a great deal of research attention.[1–4] So far, as a result of advances in experimental approaches and theoretical methods,[5–8] a large number of functional molecular devices have been successfully designed and synthesized, such as molecular wires,[9,10] molecular rectifiers,[11–13] molecular transistors,[14,14] molecular sensors,[16,17] and molecular switches.[18–21] However, assembly of logic gates from these molecular device still encounters huge difficulties since there is lack of mature integration approaches in the field of molecular electronics. On the contrary, the idea of directly using a single molecule or a set of combined molecules to design logic gates has been put forward and lots of works have demonstrated its feasibility.[22–26] For example, using a dithienylethene molecule as the functional kernel, Meng et al. have realized two-input OR and three-input AND-OR single-molecule logic gates, which take optical and electrochemical stimuli as input signals.[22] Zhang et al. have fabricated an AND single-molecule logic gate by two serially connected molecular kernels, of which the conductance can be controlled by illumination and pH, respectively.[23] Nevertheless, a common issue for the above synthesized molecular logic gates is that the Boolean computing relies on changes of geometric structures of functional molecular kernels induced by the switch of input signals. This will take considerable time and thus cause delayed response of output signals.
Spin degree of freedom is an important intrinsic property for electrons. The ability of controlling transport behavior of electron spin provides a significant way to develop high-performance electronic components.[27–34] Naturally, electron spin can also be utilized in designing molecular logic gates. Specifically, input/output signals of a logic gate can be carried by electron spin (i.e., spin-up and spin-down). In this case, fast switch of the spin of electrons under external fields (e.g., magnetic field) enables high-speed Boolean computing. Taking advantage of this concept, a few single-molecule logic gates based on spin degree of freedom of electrons have been designed.[35–37] Recently, by connecting manganese phthalocyanine molecules to carbon nanotube electrodes with different connection manners, Zhao et al. have put forward three molecular logic gates, where NOT, AND, and OR Boolean operations can be realized.[35] Meanwhile, Zeng et al. have proposed an easy approach to achieve AND molecular logic gates by covalently merging magnetic transition metal porphyrin molecules into the edges of a graphene nanoribbon.[36] Differently, by defining the thermal-induced spin-down current as the output signal, Gao et al. have also demonstrated that an AND logic gate can be achieved in manganese-oligoporphyrin based molecular junction, which is driven by temperature difference instead of bias voltage on the left and right electrodes.[37]
As another intriguing organic macrocyclic compound, dibenzotetraaza[14]annulene (denoted DBTAA) is now attracting more and more focuses. Similar to porphyrin molecule, a series of transition metal atoms (TMs) can be accommodated in the cavity of DBTAA molecules, endowing this tetradentate compound with different magnetic properties.[38,39] In 2015, Wu et al. built single-molecule junctions composed of TM(DBTAA) molecules sandwiched between two zigzag graphene nanoribbons and investigated the corresponding spin-dependent transport properties. Perfect spin-filtering effect can be observed for junctions with Fe(DBTAA) molecules.[40] More recently, using carbon atomic chains (CACs) to connect two Fe(DBTAA) molecules, Zeng et al. have found spin-filtering efficiency and magnetoresistance fluctuate against odd and even number of carbon atoms in the CACs.[41] These works demonstrate that TM(DBTAA) molecules can effectively generate spin polarized current in a single-molecule device and are promising candidates for designing molecular logic gates. In this work, we have constructed single-molecule junctions by sandwiching two serially connected TM(DBTAA) (TM = Fe, Co) molecules between (4,4) single-walled carbon nanotube (SWCNT) electrodes via CACs. Spin-resolved electron transport properties of these single-molecule junctions under parallel- and antiparallel-spin polarizations for the two TM(DBTAA) molecular kernels are theoretically investigated. Based on calculated spin-resolved current–voltage (I–V) curves, it is revealed that Fe(DBTAA) and Co(DBTAA) junctions can act as NOR or XNOR molecular logic gates relying on the definitions of the output signal. In the following parts of this article, theoretical model and computational details are given in Section
Schematic illustration of the studied single-molecule junctions is depicted in Fig.
The geometric structures of the constructed molecular junctions are first optimized in Atomistix ToolKit package (ATK).[49,50] A 15 Å vacuum is applied along the x, y, and z directions of the central region to eliminate spurious interaction from neighboring images during optimization stage. Each atom is not relaxed until the residual force is less than 0.05 eV/Å. The subsequent calculations of spin transport properties of each junction are also implemented in ATK by using the state-of-the-art nonequilibrium Green’s function (NEGF) method in combination with density functional theory (DFT).[8] In our calculations, the spin-polarized generalized gradient approximation (SGGA) with the Perdew–Burke–Ernzerhof (PBE) parameterization is used for the exchange-correlation functional. A 200 Ryd energy cutoff is employed to determine real space grids and a double-ζ polarized (DZP) basis set is chosen to expand valence-electron wavefunctions. A 1 × 1 × 100 k-point sampling in the Brillouin zone is utilized for the electrode calculations. The spin-resolved current is calculated according to the Landauer–Büttiker formula[51]
![](cpb_29_6_067202/cpb_29_6_067202_ieqn1.gif)
The Mulliken population of spin-up and spin-down electrons for the left and right TM atoms and total energies of TM(DBTAA)-P/AP junctions are shown in Table
![]() | Table 1. The Mulliken population of spin-up (↑) and spin-down (↓) electrons for the left and right TM atoms (respectively denoted TML and TMR) and total energies (in units of eV) of TM(DBTAA)-P/AP junctions, where TM = Fe, Co. . |
The spin-resolved current–voltage (I–V) curves for TM(DBTAA) molecular junctions under P and AP spin configurations are investigated in the bias region of [–0.5 V, 0.5 V] and are displayed in Fig.
![]() | Fig. 2. Spin-dependent I–V curves for (a) Fe(DBTAA) and (b) Co(DBTAA) molecular junctions under P and AP spin configurations. |
From the above discussion, it is easy to find that spin-down current of the investigated TM(DBTAA) junctions can be switched between ON and OFF states by manipulating the spin configurations of the two TM atoms. Such response of spin current to spin configurations in the junctions has a potential for realizing logic operations. From this viewpoint, it is worthy to inspect if the designed TM(DBTAA) junctions can act as logic gates. For this, we assume the spin polarization of the left and right TM(DBTAA) molecules in the junction as input signal, where spin-down and spin-up polarizations of the TM atom are defined as 0 and 1, respectively. Meanwhile, the low and high levels of spin-up current at 0.5 V are respectively used to represent output signals 0 and 1. According to the above definition for the input and output signals, the truth table for Fe(DBTAA) and Co(DBTAA) junctions is consequently obtained and presented in Table
![]() | Table 2. Truth table for TM(DBTAA) (TM = Fe, Co) junctions as logic gates, where input signals are defined by spin polarization of the left and right TM atoms and output signals are defined by the spin-up current. . |
In fact, one junction may realize different Boolean logic functions by adopting different definitions of input and output signals. Table
![]() | Table 3. Truth table for TM(DBTAA) (TM = Fe, Co) junctions as logic gates, where input signals are defined by spin polarization of the left and right TM atoms and output signals are defined by the total current. . |
The above discussion suggests that the spin-dependent electron transport properties of the investigated junctions are closely related to the kinds of embedded TM atoms and their spin configurations. In order to relate the spin-resolved I–V curves of the TM(DBTAA) junctions to TM atoms and their spin configurations, spin-dependent transmission spectra for each junction have been explored, as shown in Fig.
![]() | Fig. 3. Spin-dependent transmission spectra for (a) Fe(DBTAA)-P/AP and (b) Co(DBTAA)-P/AP junctions at 0 V and 0.5 V. The dashed lines denote the bias window. |
When it turns to Co(DBTAA) junctions, as shown in Fig.
Origins of the spin-resolved transmission peaks around EF are further rationalized by the spin-resolved PDOS, where the contributions of the left and right TM(BDTAA) molecules to the total DOS under zero bias voltage are analyzed. Also, spin-resolved frontier molecular orbitals obtained by molecular projected self-consistent Hamiltonian (MPSH) analysis are inspected to understand the contributions of spin electronic states to electron tunneling channels. From Fig.
![]() | Fig. 5. Spatial distributions of frontier molecular orbitals for each TM(BDTAA) junction with P and AP spin configurations. |
When the spin polarization of the right TM atom reverses and spin configuration turns to be antiparallel, it is clearly seen from Figs.
In summary, by using the DFT based NEGF method, spin transport properties of single-molecule junctions, which are comprised of two serially connected magnetic TM(DBTAA) (TM = Fe, Co) molecules embedded between two SWCNT electrodes, have been investigated for both P and AP spin configurations. The calculated results reveal that spin configurations and the kind of TM atoms play important roles in determining the I–V characteristics of TM(DBTAA) junctions. Specifically, the spin polarizations of the I–V curves for Fe(DBTAA) and Co(DBTAA) junctions are very similar for both P and AP configurations. That is, for P spin configuration, only spin-down electrons are allowed to flow through the junctions while spin-up ones are prohibited. For AP spin configuration, both spin-up and spin-down currents are blocked. Large spin-down current under P spin configuration stems from the delocalization of spin-down electronic states among two molecular kernels and the bridging CAC. However, when it turns to AP spin configuration, both the spin-up and spin-down electronic states around EF are localized due to the complete mismatch between electronic states of the left and right molecular kernels for each spin component. It is found that, under P spin configuration, when the TM atom changes from Fe to Co, the charge transport mechanism of the junction is transformed from non-resonant to resonant tunneling regime, therefore resulting in a much larger spin-down current for Co(DBTAA)-P than Fe(DBTAA)-P. This can be ascribed to the fact that the conducting channel above EF is much more closer to EF for Co(DBTAA)-P than for Fe(DBTAA)-P. More interestingly, by defining different input and output signal criteria, it is found that Fe(DBTAA) and Co(DBTAA) junctions can work as NOR or XNOR molecular logic gate. Our work here proposes a new kind of molecular logic gates by taking advantage of the spin degree of freedom of electrons, which is helpful for further miniaturizing the electric circuits.
Supplementary data related to this article can be found in the
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