pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
pdf, 9 MiB - Infoscience - EPFL
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142 CHAPTER 6. ORBITAL CURRENTS IN THE CUPRATES<br />
0.30<br />
Current circulation<br />
0.15<br />
0.00<br />
V=2.5 eV<br />
V=2 eV<br />
V=1.25 eV<br />
-0.4<br />
-0.2<br />
0.0<br />
0.2<br />
0.4<br />
hole doping n<br />
h<br />
0.6<br />
0.8<br />
1.0<br />
Figure 6.7: Circulation of the orbitals current around one triangle plaquette<br />
within the mean-field calculations. We show the circulation for different values of<br />
the Coulomb repulsion. The current has same amplitude on the oxygen-oxygen<br />
links and on copper-oxygen links. The symmetry of the circulating phases at<br />
V =2. and V =2.5 isθ 2 like.<br />
Where the creation and annihilation operators c † i and c i create and annihilate<br />
holes with spin σ in the orbital centered at the lattice point labeled by i, t ij is<br />
the amplitude for hopping from site j to site i, ɛ i is the energy level of the orbital<br />
at site i, µ is the chemical potential and U ij is the interaction energy of two holes<br />
with opposite spin on the same site i = j, and of two holes on neighboring sites<br />
i ≠ j. To obtain the generalized, non-local, Bogoliubov De Gennes equations we<br />
first make a mean field approximation for the pairing field [142]:<br />
∆ ij = −U ij 〈c iσ c j−σ 〉 (6.7)<br />
The tight-binding lattice has nearest neighbor hopping interactions (t ij ), as well<br />
as a coupling between particle and hole space, via a superconducting order parameter<br />
(∆ ij ). If the interactions are purely on-site (U ii ) repulsions then the<br />
pairing potential will be purely local (∆ ii ). On the other hand when the interaction<br />
is non-local (U ij ,i ≠ j) the pairing potential ∆ ij will also be non-local.<br />
Another mean field decoupling that takes into account the effect of the U interactions<br />
by having a hopping renormalization is also considered (decoupling in the<br />
particle-hole channel) :<br />
〉<br />
χ ij = U ij<br />
〈c † iσ c jσ<br />
(6.8)