One of the first theoretical proposals for understanding high temperature superconductivity in the cuprates was Anderson's RVB theory using a Gutzwiller projected BCS wave function as an approximate ground state. Recent work by Paramekanti, Randeria and Trivedi has shown that this variational approach gives a semi-quantitative understanding of the doping dependences of a variety of experimental observables in the superconducting state of the cuprates. In this paper we revisit these issues using the "renormalized mean field theory" of Zhang, Gros, Rice and Shiba based on the Gutzwiller approximation in which the kinetic and superexchange energies are renormalized by different doping-dependent factors g t and g S respectively. We point out a number of consequences of this early mean field theory for experimental measurements which were not available when it was first explored, and observe that it is able to explain the existence of the pseudogap, properties of nodal quasiparticles and approximate spin-charge separation, the latter leading to large renormalizations of the Drude weight and superfluid density. We use the Lee-Wen theory of the phase transition as caused by thermal excitation of nodal quasiparticles, and also obtain a number of further experimental confirmations. Finally, we remark that superexchange, and not phonons, are responsible for d-wave superconductivity in the cuprates.

The single rung t-J ladder is analyzed in a mean field theory using Gutzwiller renormalization of the matrix elements to account for strong correlation. The spin liquid (RVB) state at half-filling evolves into a superconducting state upon doping. The order parameter has a modified d-wave character. A lattice of weakly coupled ladders should show a superconducting phase transition. PACS: 71.27.+a, 74.20.Mn, 75.10.Jm There is a striking difference between the properties of a chain and a ladder (double chain) antiferromagnetic (AF) s=1/2 Heisenberg model. Whereas the chain has power law decay of the AF-correlations, the ladder has a purely exponential decay and a finite energy gap in the spin excitation spectrum, i.e. a spin gap (see for example Ref.1). If, as is the case for other spin gap systems, the spin gap persists to finite doping, then the possibilities for superconducting fluctuations are greatly enhanced in ladder systems [2]. Recently we pointed out that the compound Sr 2 Cu 4 O 6 offers the possibility of realizing a lattice of weakly coupled ladders [3,4].

Magnetic skyrmions are topologically non-trivial spin textures that manifest themselves as quasiparticles in ferromagnetic thin films or noncentrosymmetric bulk materials. So far attention has focused on skyrmions stabilized either by the Dzyaloshinskii–Moriya interaction (DMI) or by dipolar interaction, where in the latter case the excitations are known as bubble skyrmions. Here we demonstrate the existence of a dynamically stabilized skyrmion, which exists even when dipolar interactions and DMI are absent. We establish how such dynamic skyrmions can be nucleated, sustained and manipulated in an effectively lossless medium under a nanocontact. As quasiparticles, they can be transported between two nanocontacts in a nanowire, even in complete absence of DMI. Conversely, in the presence of DMI, we observe that the dynamical skyrmion experiences strong breathing. All of this points towards a wide range of skyrmion manipulation, which can be studied in a much wider class of materials than considered so far.