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I am leaning the Haldane model :
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.61.2015
Haldane imaged threading magnetic flux though a graphene sheet, and the net flux of a unit cell is zero.
He argued that since the loop integral ##\exp [ie/\hbar \oint {A \cdot dr} ]## along a path of nearest bonds vanishes, the nearest hopping is not changed.
However, I cannot see the connect between the vanishing loop integral and the unchanged nearest hopping, can anybody help?
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.61.2015
Haldane imaged threading magnetic flux though a graphene sheet, and the net flux of a unit cell is zero.
He argued that since the loop integral ##\exp [ie/\hbar \oint {A \cdot dr} ]## along a path of nearest bonds vanishes, the nearest hopping is not changed.
However, I cannot see the connect between the vanishing loop integral and the unchanged nearest hopping, can anybody help?