Modeling of electrotransport properties of Li-intercalated graphene film

In this work, within the framework of density functional theory combined with the method of nonequilibrium Green’s functions the density of states, transmission spectrum, current-voltage characteristics, and differential conductivity of Li-intercalated graphene (LiC6) have been determined. It is shown that in the energy range of -1.3÷-1.05 eV the quasiparticle transport through the nanostructure is disable. The features of IV- and dI/dV-characteristics of LiC6 in the form of decreasing of resistance in the range of -0.4÷0.4 V were revealed, and in the interval of 0.4÷1.4 V formation of negative differential resistance area, related to scattering of quasiparticles. It is established, that LiC6 nanodevice has 12÷13 ballistic channels and has the maximum amount of conductance 12÷13G0 , where Go is the conductance quantum.


Introduction
Recently, to reduce the size, mass, and energy consumption of electronic techniques, electrophysical properties of different nanoscale contacts are being investigated to be used as active and passive elements in electric circuits and to replace traditional elements (see, for example, [1,2]). New directions of electronics based on exotic materials are being developed to create a new generation of electronic devices and appliances, such as superconductor [3][4][5], organic [6], single-electronics [7,8], spintronics [9] and others. In this respect, one of the most promising nanomaterials for such nanocontacts is graphene, which is an allotropic modification of carbon in the form of a twodimensional monatomic layer [10,11]. After the discovery of graphene, the search for new twodimensional materials was started, and some quasi-two-dimensional materials with unusual electronic properties were created [12][13][14]. In theoretical works [15][16][17], the possible superconducting properties of the calcium-and lithium-doped graphene film have been considered. However, there is considerable disagreement in explaining the electronic properties of these two-dimensional materials. In work [18] it is noted that for the appearance of superconductivity is responsible non-phonon mechanism of formation of Coopers pairs of electrons due to the weak repulsion between them, leading to spiral type d-pairing, and in work [19] usual phonon mechanism of electron pairing in schannel is considered, and within the framework of Eliashberg theory is estimated the critical temperature of LiC6 nanostructure, equal to ~8 K.
Even though the superconductivity in the LiC6 monolayer has not been confirmed experimentally yet, a significant change in the electronic properties of the Li-intercalated graphene compared to the "pure" graphene are observed. In this work, the electrotransport characteristics of Li-intercalated graphene are simulated and analyzed within the framework of the electron density functional theory (DFT) in combination with the non-equilibrium Green's function (NEGF) method.

Geometry
The geometry of the Li-intercalated graphene nanodevice is shown in Figure 1. The length of the nanodevice is ~51.15 Å. The electrodes are an extension of the Li-intercalated graphene with a length of ~8.525 Å. The Li-graphene surface with a size of ~34.1×17.23 Å consists of 255 carbon atoms and 40 lithium atoms. To describe the interatomic interaction and optimize the nanostructure, Brenner [20] and ReaxFF_CHONSSiLi_2013 [21] potentials have been used. During the nanodevice geometry optimization, the parameters of the atomic configuration were relaxed until the forces at all atoms became lower than a given threshold value of 0.05 eV/Å. carbon atom lithium atom Figure 1. The geometry of a Li intercalated graphene nanodevice.

Fundamental equations
Computer simulation of electrotransport characteristics of Li-graphene nanodevice was carried out in the framework of DFT + NEGF in local density approximation (LDA). Modeling of electrotransport characteristics of the nanodevice was realized in program Atomistix ToolKit with Virtual NanoLab [21]. (Fundamental equations of this method are described in detail in our previous works [22,23]). The current-voltage-characteristic (CVC) of the nanostructure was determined by solving the Landauer equation which indicates the fundamental coupling of the electric current I with the transmittance spectrum ( ) TE: where e is electron charge, h is Planck's constant, E is energy, ( ) ( ) † † tr tr G , † G is lagged and leading Green's functions. The differential conductivity of the nanostructure was obtained by calculating the self-consistent current at a number of applied biases and performing numerical differentiation.

Results
The density of states (DOS) of the LiC6 nanodevice is shown in Figure 2.

( )
TEof the LiC6 nanodevice with increasing bias voltage from -2 V to 2 V in 0.2 V steps is shown in Figure 3a,b. As the bias voltage increases, the intensity of the transmission spectrum increases. At positive energy, the transmission capacity of quasiparticles through the nanostructure in consideration is higher than at negative energy. In the energy range -1.3÷ -1.05 eV the probability of quasiparticles passing through the nanostructure is small. As can be seen, the features of DOS appear in the transmission spectrum of the considered nanostructure at the same energy values, as these values are directly proportional The current voltage characteristic (CVC) and the differential conductivity of the LiC6 nanodevice are shown in Figure 4a,b. In the voltage range of -0.4÷0.4 V in LiC6 nanodevice a rapid linear increase of current to 0.11 mA is observed. It is supposed that the decreasing of the film resistance in the stated interval of voltage appears because of the increasing of number of energy levels near to the Fermi energy. Further increasing of bias voltage from 0.4 to 1.4 V will lead to quasi-linear decrease of current due to scattering of quasiparticles. Notice that a significant decrease in current in this voltage range forms a negative differential resistance (NDR) region on the CVC. These changes are reflected  (Figure 4b). The LiC6 nanodevice demonstrates 12÷13 ballistic channels and has a maximum conductance value of ~12÷13G0, where 2 0 = G e h is the conductance quantum. a) b) Figure 4. The current -voltage -(a) and dI/dV-characteristics (b) of LiC6 nanodevices: 1 -LiC6, 2graphene (for comparison).

Conclusion
In summary, the main electrotransport characteristics of Li-intercalated graphene (DOS, transmission spectrum, CVC) and differential conductivity have been determined within the framework of DFT + NEGF. It is found that in the energy interval -1.3÷-1.05 eV the transport of quasiparticles through the nanostructure is disable. The features of IV-and dI/dV-characteristics are determined: decreasing of resistance in the range of -0.4÷0.4V leading to the linear increase of current, appearance of NDR region in the range of 0.4÷1.4V because of quasiparticles scattering. It is established that the electronic conductivity of LiC6 near the Fermi energy is higher in comparison with graphene.