The most intriguing observation of cuprate experiments is most likely the metal-insulator-crossover (MIC), seen in the underdome region of the temperature-doping phase diagram for copper-oxides under a strong magnetic field, when superconductivity is suppressed. This MIC, which results in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, nonlinear entropy, insulating ground state, nematicity-and stripe-phases and Fermi pockets, reveals the nonconventional dielectric property of the pseudogap-normal phase. Since conventional superconductivity appears from a conducting normal phase, the understanding of how superconductivity arises from an insulating state becomes a fundamental problem and thus the keystone for all of cuprate physics. Recently, in interpreting the physics of visualization in scanning tunneling microscopy (STM) real space nanoregions (NRs), which exhibit an energy gap, we have succeeded in understanding that the minimum size for these NRs provides pseudogap and superconductivity pairs, which are single bosons. In this work, we discuss the intra-particle magnetic spin and charge fluctuations of these bosons, observed recently in hidden magnetic order and STM experiments. We find that all the mentioned MIC phenomena can be obtained in the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of sample percolating NRs of single fermions into those of single bosons.
For the derivation of the dilute Bose-Einstein condensate density and its phase, we have developed the perturbative approach for the solution of the stationary state couple Gross-Pitaevskii hydrodynamic equations. The external disorder potential is considered as a small parameter in this approach. We have derived expressions for the total density, condensate density, condensate density depletion and superfluid velocity of the Bose-Einstein condensate in an infinite length ring with disorder potential having a general form. For the delta correlated disorder, the explicit analytical forms of these quantities (except the superfluid velocity) have been obtained. Keywords:Bose-Einstein condensate in ring, Gross-Pitaevskii hydrodynamic equations, disorder potential, condensate density, condensate density depletion, delta correlated disorder. Received: 2 February 2015The Gross-Pitaevskii equation [1,2]:is a powerful approach for the description of the Bose-Einstein condensate of the dilute ultracold atomic Bose gases [3], which have been recently observed in many experiments on cooling of atoms in magnetic traps and laser radiation (see references on experimental papers in [3]). In Eq.(1), the term proportional to g describes the contact interaction between two atoms in the s-scattering approximation.With the existence of the external potential U (x) (confining trap or disorder potential) and a fluidity flow, the condensate wave function ψ (x, t) = n (x, t)e iS(x,t) becomes a function not only of the condensate density n (x, t), but also of its phase S (x, t). For that case, it is rather convenient to describe a system by the couple hydrodynamic equations for the condensate density and its phase, originating from the Gross-Pitaevskii equation:Here, m is the mass of an atom, the superfluid velocity is expressed by formula v s =h∇S (x, t) /m and for simplicity, we have omitted arguments in expressions for n (x, t), S (x, t), v s (x, t). For the stationary case, when time derivatives of the condensate density and the superfluid velocity are equal to zero, Eq. (2) reduces to:
In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal -insulator (fermion-boson)-crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [Abdullaev B., et al. arXiv:cond-mat/0703290], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to the PG pair intra charge and spin fluctuations. We will try to obtain an answer to the question; why ground state of YBCO is Fermi liquid oscillating and of Bi-2212 is insulating? We will also clarify the physics of the recently observed MIC results of Lalibert et al. [arXiv:1606.04491] and explain the long-discussed transition of the electric charge density from doping to doping+1 dependence at the critical doping. We predict that at the upturns this density should have the temperature dependences n ∼ T 3 n 2 for T → 0, where n 2 is density for dopings close to the critical value. We understood that the upturns before and after the first critical doping have the same nature. We will find understanding of all above mentioned phenomena within PG pair physics.Keywords: high critical temperature superconductivity, cuprate, metal-insulator-crossover, temperature-doping phase diagram, resistivity temperature upturn, insulating ground state, nematicity and stripe phases, Fermi pockets evolution.
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