The superconducting dome for holographic doped Mott insulator with hyperscaling violation

We reconsider the holographic model featuring a superconducting dome on the temperature-doping phase diagram with a modified view on the role of the two charges. The first type charge with density $$\rho _{A}$$ ρ A make the Mott insulator, and the second one with $$\rho _{B}$$ ρ B is the extra charge by doping, so that the complex scalar describing the cooper pair condensation couples only with the second charge. We point out that the key role in creating the dome is played by the three point interaction $$-c \chi ^{2} F_{\mu \nu }G^{\mu \nu }$$ - c χ 2 F μ ν G μ ν . The Tc increases with their coupling. We also consider the effect of the quantum critical point hidden under the dome using the geometry of hyperscaling violation. Our results show that the dome size and optimal temperature increase with z whatever is $$\theta $$ θ , while we get bigger $$\theta $$ θ for larger (smaller) dome depending on $$z>2$$ z > 2 ($$z<2$$ z < 2 ). We also point out that the condensate increases for bigger value of $$\theta $$ θ but for smaller value of z.

Trion formation and unconventional superconductivity in a three-dimensional model with short-range attraction

A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schrödinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane nearest-neighbor attraction. By comparing the energy of three-fermion bound clusters (trions) with the energy of one pair plus one free particle, a trion formation threshold is accurately determined, and the region of pair stability is mapped out. It is found that the “close-packed” density of fermion pairs, which is associated with a maximum pair condensation temperature in this model, is the highest in a strongly anisotropic case. It is also argued that pair superconductivity with the highest critical temperature is always close to trion formation, which makes the system prone to phase separation and local charge ordering.

Topological Order in Physics

In general, we know that there are four states of matter solid, liquid, gas and plasma. But there are much more states of matter. For e. g. there are ferromagnetic states of matter as revealed by the phenomenon of magnetization and superfluid states defined by the phenomenon of zero viscosity. The various phases in our colorful world are so rich that it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. Topological phenomena define the topological order at macroscopic level. Topological order need new mathematical framework to describe it. More recently it is found that at microscopic level topological order is due to the long range quantum entanglement, just like the fermions fluid is due to the fermion-pair condensation. Long range quantum entanglement leads to many amazing emergent phenomena, such as fractional quantum numbers, non- Abelian statistics ad perfect conducting boundary channels. It can even provide a unified origin of light and electron i.e. gauge interactions and Fermi statistics. Light waves (gauge fields) are fluctuations of long range entanglement and electron (fermion) are defect of long range entanglements.The Himalayan Physics Vol. 6 & 7, April 2017 (108-111)

Critical temperature of pair condensation in a dilute Bose gas with spin–orbit coupling

We study the Bardeen–Cooper–Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin–orbit coupling (SOC). In the dilute limit at low temperature, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose–Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density.