A Why is the nearest hopping kept real in Haldane model?

lichen1983312
Messages
85
Reaction score
2
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?
 
Physics news on Phys.org
In the Haldane model of graphene the hopping strength can be complex with a phase coming from the Aharonov-Bohm effect in the presence of a magnetic field. If one moves a particle around a closed contour, then the phase difference between the final and initial states is proportional to the magnetic flux enclosed by the contour ##\phi =\frac{e}{h} \iint \mathbf B \cdot \mathbf S = \frac{e}{h} \oint \mathbf A \cdot \mathbf {\mathcal l}##.
Consider three sites a, b and c. The hopping strength between these three sites is ##t_{ab}##, ##t_{bc}## and ##t_{ca}##. If a particle hops from a to b and then to c, then the hopping strength around the loop is: $$t_{ab}t_{bc}t_{ca}=\left | t_{ab}t_{bc}t_{ca} \right | e^{i(\phi_{ab} + \phi_{bc} + \phi_{ca})}$$
The phase picked up by the electron is: $$\phi_{ab} +\phi_{bc} + \phi_{ca} = \frac{e}{h} \iint \mathbf B \cdot \mathbf S$$
If B is nonzero inside the triangle formed by these three sites, the phase for these hoppings are nonzero. On the other hand; no net field means no phase change.
 
From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent...
Hi. I have got question as in title. How can idea of instantaneous dipole moment for atoms like, for example hydrogen be consistent with idea of orbitals? At my level of knowledge London dispersion forces are derived taking into account Bohr model of atom. But we know today that this model is not correct. If it would be correct I understand that at each time electron is at some point at radius at some angle and there is dipole moment at this time from nucleus to electron at orbit. But how...
Back
Top