Orbital Effect on Carbyne Based Sensor

Carbyne material with sp-hybridized atoms has been considered as a one dimensional structure with unique properties which has been widely used in nanotechnology. In the presented work the effect of electron overlap energy in the form of electron interaction with in the unit cell and nearest neighbors is explored. In addition, the band structure variation under proposed interaction in one dimensional carbyne is investigated. The effect of overlap energy variation inside and outside the unit cell on the band gap is intended. Under proposed structure the effective mass and density of states parameters are explored. It is demonstrated that by increasing the interaction between s and p orbitals in the unit cell, the band gap increases. However, the band gap is decreased by increasing the interaction between s and p orbitals out the unit cell which can be sued as a sensing mechanism.


Introduction
Innovative category of carbon allotropes arranged in one dimensional chain with strong chemical action called carbyne with bulk production has been reported [1][2][3]. Its electrical property rarely compare to the other carbon based 1D structures such as nano-tubes and nanoribbons has been explored [1][2][3]. Carbyne sp-hybridization is observed when one s and one p orbital in the same main shell of an atomic structure mixed to make two new equivalent orbitals.
The new orbitals are called sp-hybridized orbitals [4] that can explain the linear structure in the molecule [5][6][7][8]. One of the factors that facilitate the overlap between two atomic orbital is the distance between the orbitals [8][9] which manipulates the energy gap and changes the specified state of the system to another. In this study, band gap variation in SP 2 carbyne structures [10] is as shown in figure 1 is focused.  Figure 2 depicts the chain of the unit cell, each unit cell has two atoms A and B. Note that each atom has three orbitals (SP 2 ) and their molecular interaction is also considered.

Model and formalism
So, the general form of the Hamiltonian matrix is: In accordance to Schrödinger's equation, the energy Eigen value can be calculated as: Wave function of system is given by Eq. (4).
Where I is the unit matrix. After solving the above equation, we get a fourth order equation as follows: After solving the fourth order equation and considering that the amount of energy in the band gap 0 E between the carbon atoms is 1 and the lattice parameter is 0.142, the energy equation is given in the form below : According to above equation, the total energy is depended on the energy in the cell unit (t) and energy out of the unit cell ( t′ ). The relation (12)    By comparing the curves, it is found that the increase in the interaction between the s and p orbitals inside the unit cell (t) will increase the gap between the energy strips, meaning that the energy strips go away.Since the sp -hybridization leads to the stability of the compound. These hybridization orbitals increase the electron density in the graft region to make the sigma band, and leading to a pair of hybrid springs for spin in opposite directions. According to the theory of strips, molecular orbitals differ from the atomic orbits that make them up. The allowed energy states are divided into close states and shape of the orbits changes. These split freely. In the semiconductors, the capacity band (at 0  K ) is full, but due to the low bandwidth of the band, the electrons can travel to the conducting band and move freely by gaining a little energy (for example, through heat) [11]. According to these contents, increasing the band gap causes the material to be nonconductor. In Figures 4(a-c), t is constant and equal to 3 and the value of t′ increases. This effect will be investigated as a sensing phenomenon in our time in the next research.
), respectively. It is noteworthy that the waves are non-dispersive for large effective masses [14,15]. The variation of energy curvature in the presence of impurities can be employed on the impurity sensing mechanism based on the capacitance measurement by voltage variation [19,20].

Conclusion
The behavior of matter can determined by the basic energy calculation based on the structure investigation. In the presented work, the orbital effect on carbyne band gap is investigated based on the structure energy calculation. It is demonstrated that the increasing interaction between s and p orbitals in the unit cell, makes the band gap affected which powers impurity detection systems come to account. On the other hand, the band gap is decreased by increasing the interaction between s and p orbitals out the unit cell. Also the effective mass variation for different values of orbital interaction in one unit cell and between the different unit cells is investigated. The calculation of effective mass versus wave vector indicates that as t t ′ ≠ , the non-dispersive wave is signified at Dirac point ( 0 = x K ). Figure 1 SP2 bonded carbyne atoms [10].

Figure 2
The geometry of the model.  Legend for gure 4 can be found in the manuscript le. Legend for gure 5 can be found in the manuscript le.