Notes:

1. This poster summarizes a paper published in Phys. Rev. B 59 (23), pp. 15143-15159 (1999); you can find the .pdf file here .
2. What makes a poster useful is having a person nearby, ready to explain it. If you have any questions, please contact me.
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Summary of pages:

• Page 1 contains the Abstract or Why you should read this poster . Page 2 describes the Generation of spin flux . We believe the spin-flux generation to be a very non-trivial consequence of the long range nature of the Coulomb repulsion and the spin 1/2 of the electron. This poster's main message is that in the presence of spin-flux, a finite doping of the cuprate planes leads to the appearance of a quantum liquid of meron-vortices, as opposed to a charged stripe in the absence of the spin-flux. This liquid of charged vortices has many attractive features, as detailed below.




• Pages 3 and 4 describe the Hamiltonian and Approximations used. Page 3 details the differences between the spin-flux model and the conventional model (related to the hopping part of the Hubbard Hamiltonian), while page 4 describes the Hartree-Fock Approximation used to deal with the on-site repulsion.




• Pages 5 and 6 refer to The Undoped Parent Compound . More specifically, Page 5 shows a comparison between self consistent energies and staggered spins for the spin-flux and conventional model, while Page 6 compares their quasiparticle dispersion relations to those measured experimentally through ARPES. The conclusion is that for the undoped parent compound, the spin-flux model fares better than the conventional one: its energy is lower and the agreement with the ARPES is much better.




• Pages 7 and 8 deal with the possible types of Elementary Excitations upon Doping , i.e. the question of what happens if you add one single hole to the antiferromagnetic plane. Two types of excitations may appear, namely the meron-vortex , which is a charged boson (see page 7 ), or a spin-bag (or spin-polaron), which is a charged fermion (see page 8 ).


The next logical question is which one of these two types of excitations is the relevant one. We treat this problem, neglecting the pair interactions, on page 9 . By comparing their excitation energies, we see that in the conventional model the spin-bag is the low-energy excitation for all values of U/t, in the small and intermediate doping region. However, in the spin-flux model we see that for intermediate values of U/t and small and intermediate dopings, the meron-vortices may become the low-energy excitations. Page 10 shows that the role of the pair interactions is to increase the region of stability of meron-vortices, since they have a topological tendency of coupling in meron-antimeron pairs, and this lowers their energy considerably. One very important point is that attraction between vortices varies logarithmically with the distance, so this topological pairing of vortices cannot be broken even in the presence of full long-range Coulomb interaction between the charged cores.

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• The next two pages refer to finite doping concentrations of holes, and show that the self-consistent results obtained are in agreement with the conclusions arrived at in pages 9 and 10. More specifically, page 11 shows the self-consistent configurations obtained for a doping of 0.08 and U/t=5 in the spin-flux model, which consists of a liquid of pairs of meron and antimerons. Page 12 shows the self-consistent configurations obtained for a doping of 0.15 and U/t=5 in the conventional model, which contains a charged stripe.




• On page 13 we show the comparison between the energies of the self-consistent configurations obtained for the spin-flux and the conventional models, for U/t=5. For small and intermediate dopings (corresponding to large electron concentrations) the more stable model is the spin-flux model, and the configurations obtained are liquids of meron-antimeron pairs. For large dopings the conventional model becomes stable. Page 14 lists some of the main points of the emerging picture, as well as some critique.




• Finally, pages 15 and 16 show some response functions of the liquid of meron vortices, namely its conductivity on page 15 and its static magnetic factor on page 16 . These are in rough agreement with those measured experimentally.

Why is this very appealing?

1. the existence of the meron-antimeron pairs, which may be the answer for the preformed pairs thought to exist in the cuprates. There is very strong bonding, of topological nature, between a vortex and an antivortex. Such a pair should be stable even in the presence of full 1/r Coulomb repulsion between the charged cores.
2. the charged merons and antimerons are bosons . A liquid of such charged bosons must be a non-Fermi-liquid metal, since the charge carriers are not fermions. However, for higher dopings this liquid becomes unstable, and a transition to the conventional model describing a Fermi liquid takes place.
3. the meron-antimeron pair creation upon doping provides a good scenario for understanding the destruction of the long range antiferromagnetic order at very low dopings, of about 0.02. From the picture on page 10 we can see that the spin of about 100 sites is indeed rotated out of the background orientation near a tightly bound meron-antimeron pair, containing two holes. However, short range antiferromagnetic correlations are preserved, since the rotated spins are locally antiferromagnetically ordered.
4. this evolution of the magnetic state, from long range order to short range correlations as the doping is increased, reflects in the magnetic structure factor, which has the incommensurate splitting seen experimentally (see page 16 ).
5. this picture may explain the unusual optical conduction of the cuprates. The broad mid-infrared peak that develops upon doping is associated with excitations on the gap levels trapped inside the vortex cores. This contribution is shown on page 15 . The missing part is the "Drude-like" tail, which is due to the overall translational motion of the charged vortices under the influence of the electric field (this motion is frozen in our static model). This picture explains why the broad mid-infrared peak is observed quite unchanged below the superconducting transition, while the Drude-tail collapses in a delta-function: superconductivity is related to how the charged vortices move, in other words how their flow becomes a superflow.




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