A glimpse of physics --- not read worthy

Hopefully, by now I have firmly established that I am not a good writter. People like us wishes hard to express and even sits tight to write too, but when we think what to write all kinds of idea jumble in our mind, but none of them crystalize to a rigid story. The "flame of hope" is still burning the same, neither scintillated high nor quenched to zero.

Here is an odd idea to fill some blank space here. I wrote a narration on our recent research work to publish somewhere, but never tried to do so later. In professional world it is highly unprofessional, but my indolence is not obedient. So let us read that bizarre account in a mood of gossip.


Superconductivity : From its rationale to unintelligibility

Superconductivity (causing resistanceless current) was discovered in 1911 by H. K. Onnes and was explained with remarkable accuracy by Bardeen, Cooper and Schrieffer (BCS) in 1957. This theory provides the origin of the effective electron-electron attraction (forming Cooper pair) due to the lattice vibration (phonon) which causes the superconductivity, but it neglects the electron-electron Coulomb repulsion, has been very successful (along with Landau's Fermi liquid theory) in explaining various fascinating properties of conventional superconductivity. But this theory fails to provide a plausible understanding of the high-temperature superconductors discovered by Bednorz and Müller in 1986 by doping a parent Mott insulator in cuprates, containing cupper oxide plain(s).

In both hole and electron doping, away from half-filling (at half filling the system is an Mott insulator) the system becomes antiferromagnet which vanishes at certain doping (Quantum Critical Point) depending on the type of dopants and the superconductivity evolves near or after the quantum critical point for electron or hole doping respectively. The possible presence of a large Coulomb interaction(s) in the cuprates has the potential to destroy conventional spherical symmetry of the s-wave superconducting pairing symmetry (BCS). Therefore, an understanding of the symmetry of the pairing and its evolution with hole and electron doping, in the presence of competing magnetic instability(s) is a key to unraveling the mechanism of high-temperature superconductivity in the cuprates.

Our work addresses two issues of great current interest: (1) Do antiferromagnetism and superconductivity locally coexist in electron-doped cuprates and (2) How does the pairing symmetry evolve in these cuprates? Even though for the hole doped cuprates it is generally believed that d-wave pairing survives up to the edge of antiferromagnetism, experimental results for determining the superconducting pairing symmetry have been contradictory in electron doped cuprates. In particular, penetration depth, a characteristic length of the system into which the magnetic field can penetrate, measurements in low temperature show behavior characteristic of s-wave and/or d-wave pairing symmetry in different doping regions.

In an s-wave superconductor the penetration depth varies exponentially with temperature in the small temperature region, which is the direct consequence of the presence of nonzero gap minimum in the underlying spectrum. However when a zero gap is present and thus Cooper pairs can be broken more easily, the penetration depth varies linearly with temperature.

Our study gives insight into the observed doping and momentum dependence of the superconducting pairing in electron doped cuprates. Conventional d-wave pairing has the momentum symmetry such that the corresponding superconducting gap decreases monotonically from its maximum value at the boundary of the Fermi Surface to zero at the diagonal. In contrary the s-wave gap has a nonzero minimum at the diagonal. In the underdoping state the strong antiferromagnetic fluctuation suppresses the spectral weight from the diagonal region of the Fermi Surface, and hence even a d-wave pairing shows a nonzero superconducting gap at the diagonal, in other words, the d-wave pairing in underdoping region behaves like s-wave superconducting gap.

We are the first to directly calculate the absolute value of the superfluid density (proportional to the number of contributing superconducting electrons) and compare with experimental results. Our calculation predicts the experimental value of the superfluid density very well near optimal doping (at this doping the superconductivity reaches maximum), but away from optimal doping, we find that the experimental superfuild density deviates from its BCS value. We have also studied the doping dependence of the nonmonotonic momentum behavior of the superconducting pairing first time and found that the maximum of the d-wave gap moves away from the antinodal direction toward nodal as we increase electron doping. We also provide a natural explanation of the movement of the maximum of the d-wave pairing symmetry from the Fermi Surface boundary towards the diagonal with increasing doping.