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Register a new userResonating Valence Bond Theory of Superconductivity: Beyond Cuprates
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G. Baskaran
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Resonating valence bond (RVB) theory of high Tc superconductivity, an electron correlation based mechanism, began as an insightful response by Anderson, to Bednorz and Mullers discovery of high Tc superconductivity in cuprates in late 1986. Shortly a theoretical framework for quantum spin liquids and superconductivity was developed. This theory adresses a formidable strong coupling quantum manybody problem, in modern times. It is built on certain key experimental facts: i) survival of a dynamical Mott localization in a metallic state, ii) proliferation of bond singlets and iii) absence of fermi liquid quasi particles. After summarising RVB theory I will provide an aerial view of, mostly, new superconductors where I believe that, to a large degree RVB mechanism is at work and indicate prospects for even higher Tcs.
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We investigate the entanglement properties of resonating-valence-bond states on two and higher dimensional lattices, which play a significant role in our understanding of various many-body systems. We show that these states are genuinely multipartite entangled, while there is only a negligible amount of two-site entanglement. We comment on possible physical implications of our findings.
A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong onsite Hunds interactions develop intra-atomic tRVBs between the t$_{2g}$ orbitals. On doping, the presence of two iron atoms per unit cell allows these inter-orbital triplets to coherently delocalize onto the Fermi surface, forming a fully gapped triplet superconductor. This mechanism gives rise to a unique staggered structure of onsite pair correlations, detectable as an alternating $pi$ phase shift in a scanning tunnelling Josephson microscope.
We study the potential energy surface of the ozone molecule by means of Quantum Monte Carlo simulations based on the resonating valence bond concept. The trial wave function consists of an antisymmetrized geminal power arranged in a single-determinant that is multiplied by a Jastrow correlation factor. Whereas the determinantal part incorporates static correlation effects, the augmented real-space correlation factor accounts for the dynamics electron correlation. The accuracy of this approach is demonstrated by computing the potential energy surface for the ozone molecule in three vibrational states: symmetric, asymmetric and scissoring. We find that the employed wave function provides a detailed description of rather strongly-correlated multi-reference systems, which is in quantitative agreement with experiment.
The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix method.
We apply a variational wave function capable of describing qualitatively and quantitatively the so called resonating valence bond in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekule and Dewar contributions to the chemical bond of the benzene molecule, and we establish the corresponding resonating valence bond energy of these well known structures ($simeq 0.01$eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene and show that this picture remains only within a small resonance length of few atomic units.
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