Graphane with carbon dimer defects: Robust in-gap states and a scalable two-dimensional platform for quantum computation

We study the energy level structures of the defective graphane lattice, where a carbon dimer defect is created by removing the hydrogen atoms on two nearest-neighbor carbon sites. Robust defect states emerge inside the bulk insulating gap of graphane. While for the stoichiometric half-filled system there are two doubly degenerate defect levels, there are four nondegenerate and spin-polarized in-gap defect levels in the system with one electron less than half filling. A universal set of quantum gates can be realized in the defective graphane lattice, by triggering resonant transitions among the defect states via optical pulses and ac magnetic fields. The sizable energy separation between the occupied and the empty in-gap states enables precise control at room temperature. The spatial locality of the in-gap states implies a qubit network of extremely high areal density. Based on these results, we propose that graphane as a unique platform could be used to construct the future all-purpose quantum computers.

Figure 1

Band structures and lattice structures. (a) The band structures of the pristine graphane for $U=6\mathrm{eV}$. The horizontal dotted lines label the valence band top and conduction band bottom. The vertical dotted lines label the high symmetry points in the Brillouin zone, $\mathbf{\Gamma }=(0,0), \mathbf{K}=(\frac{1}{2},\frac{\sqrt{3}}{2})\frac{4\pi }{3a}$, and $\mathbf{M}=(\frac{\sqrt{3}}{2},\frac{1}{2})\frac{2\pi }{\sqrt{3}a}$. Each band is twofold degenerate. $E=0\mathrm{eV}$ labels the position of the chemical potential. (b) A $12\times 8$ graphane lattice with a carbon dimer defect enclosed by a blue ellipse. The larger yellow (smaller red) balls represent the carbon (hydrogen) atoms.

Figure 2

Energy distribution of the quasiparticle states. A $30\times 30$ graphane lattice with one carbon dimer defect (two hydrogen vacancies on two NN carbon sites) is considered. $U=6\mathrm{eV}$. (a) and (c) are for the half-filled system. (b) and (d) are for the system with one electron less than the half-filled system. (c) and (d) are enlarged plots close to the bulk band gap. The six symbols in (c) and (d), $E_0$ to $E_5$, are the names defined for the six states right above the corresponding symbols. The horizontal dashed lines at $E=0\mathrm{eV}$ label the positions of the chemical potential.

Figure 3

Total number of electrons ($N_e$) as a function of the chemical potential ($\mu$) in a $30\times 30$ graphane lattice with one carbon dimer defect. $U=6\mathrm{eV}$. The self-consistent mean-field calculations (at 300 and 100 K) are performed in the presence of a static magnetic field $B_0$, which gives a Zeeman energy of ${\mu }_0{B}_0=0.001\mathrm{eV}$, with ${\mu }_0$ the Bohr magneton.

Figure 4

Dependence of the in-gap defect states on the Hubbard interaction $U$. A single carbon dimer defect is created inside a $30\times 30$ graphane lattice. The subindices of the energies follow the definitions of Figs. 2 and 2. (a) is for the half-filled system. The curves for $n+1=2$ and $n+1=4$ coincide, which are zero for all $U$. (b)–(d) are for the system with one electron less than the half-filled system. The inset of (d) is the schematic energy level structure of the defect states, for $U\le 9\mathrm{eV}$. It also shows the four possible transitions, corresponding to the four energy intervals on Fig. 4, among the four defect states. $\gamma$ and $B_1$ represent the optical field and the ac magnetic field, respectively.