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I am trying to do some calculation based on a k.p model of GaN proposed by S. Chuang [Phys. Rev. B, 54, 2491]. It is a 8 by 8 Kane model with basis functions:

The 8 by 8 Hamiltonian contain first order of k is

where ##{k_ \pm } = {k_x} \pm i{k_y}##

the reciprocal space and high symmetry points is pictures as [Phys. rev. B, 53, 10173]

My question is: How is the direction of kx and ky defined in the 8 by 8 Hamiltonian?

Put is in another way. If I want to draw a E-k curve along ##\Gamma \to M##, how do I express this direction in terms of kx and ky ?

Thanks very much, please help.

The 8 by 8 Hamiltonian contain first order of k is

where ##{k_ \pm } = {k_x} \pm i{k_y}##

the reciprocal space and high symmetry points is pictures as [Phys. rev. B, 53, 10173]

My question is: How is the direction of kx and ky defined in the 8 by 8 Hamiltonian?

Put is in another way. If I want to draw a E-k curve along ##\Gamma \to M##, how do I express this direction in terms of kx and ky ?

Thanks very much, please help.