Resistance of High-Temperature Cuprate Superconductors

Cuprate superconductors have many different atoms per unit cell. A large fraction of cells (5–25%) must be modified ('doped') before the material superconducts. Thus it is not surprising that there is little consensus on the superconducting mechanism, despite almost 200 000 papers (Mann 2011 Nature 475 280). Most astonishing is that for the simplest electrical property, the resistance, 'despite sustained theoretical efforts over the past two decades, its origin and its relation to the superconducting mechanism remain a profound, unsolved mystery' (Hussey et al 2011 Phil. Trans. R. Soc. A 369 1626). Currently, model parameters used to fit normal state properties are experiment specific and vary arbitrarily from one doping to the other. Here, we provide a quantitative explanation for the temperature and doping dependence of the resistivity in one self-consistent model by showing that cuprates are intrinsically inhomogeneous with a percolating metallic region and insulating regions. Using simple counting of dopant-induced plaquettes, we show that the superconducting pairing and resistivity are due to phonons

Latent Room-Temperature Tc_c in Cuprate Superconductors

The ancient phrase, "All roads lead to Rome" applies to Chemistry and Physics. Both are highly evolved sciences, with their own history, traditions, language, and approaches to problems. Despite all these differences, these two roads generally lead to the same place. For high temperature cuprate superconductors however, the Chemistry and Physics roads do not meet or even come close to each other. In this paper, we analyze the physics and chemistry approaches to the doped electronic structure of cuprates and find the chemistry doped hole (out-of-the-CuO$\mathrm{_2}$-planes) leads to explanations of a vast array of normal state cuprate phenomenology using simple counting arguments. The chemistry picture suggests that phonons are responsible for superconductivity in cuprates. We identify the important phonon modes, and show that the observed T$\mathrm{_c} \sim 100$ K, the T$\mathrm{_c}$-dome as a function of hole doping, the change in T$\mathrm{_c}$ as a function of the number of CuO$\mathrm{_2}$ layers per unit cell, the lack of an isotope effect at optimal T$\mathrm{_c}$ doping, and the D-wave symmetry of the superconducting Cooper pair wavefunction are all explained by the chemistry picture. Finally, we show that "crowding" the dopants in cuprates leads to a pair wavefunction with S-wave symmetry and T$\mathrm{_c}\approx280-390$ K. Hence, we believe there is enormous "latent" T$\mathrm{_c}$ remaining in the cuprate class of superconductors.Comment: 100 pages, 61 figure

Universal Properties of Cuprate Superconductors: T_c Phase Diagram, Room-Temperature Thermopower, Neutron Spin Resonance, and STM Incommensurability Explained in Terms of Chiral Plaquette Pairing

We report that four properties of cuprates and their evolution with doping are consequences of simply counting four-site plaquettes arising from doping, (1) the universal T_c phase diagram (superconductivity between ~0.05 and ~0.27 doping per CuO_2 plane and optimal T_c at ~0.16), (2) the universal doping dependence of the room-temperature thermopower, (3) the superconducting neutron spin resonance peak (the “41 meV peak”), and (4) the dispersionless scanning tunneling conductance incommensurability. Properties (1), (3), and (4) are explained with no adjustable parameters, and (2) is explained with exactly one. The successful quantitative interpretation of four very distinct aspects of cuprate phenomenology by a simple counting rule provides strong evidence for four-site plaquette percolation in these materials. This suggests that inhomogeneity, percolation, and plaquettes play an essential role in cuprates. This geometric analysis may provide a useful guide to search for new compositions and structures with improved superconducting properties

Accurate Band Gaps for Semiconductors from Density Functional Theory

An essential issue in developing semiconductor devices for photovoltaics and thermoelectrics is to design materials with appropriate band gaps plus the proper positioning of dopant levels relative to the bands. Local density (LDA) and generalized gradient approximation (GGA) density functionals generally underestimate band gaps for semiconductors and sometimes incorrectly predict a metal. Hybrid functionals that include some exact Hartree-Fock exchange are known to be better. We show here for CuInSe_2, the parent compound of the promising CIGS Cu(In_xGa_(1-x))Se_2 solar devices, that LDA and GGA obtain gaps of 0.0-0.01 eV (experiment is 1.04 eV), while the historically first global hybrid functional, B3PW91, is surprisingly better than B3LYP with band gaps of 1.07 and 0.95 eV, respectively. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a mean average deviation (MAD) of only 0.09 eV, which is substantially better than all modern hybrid functionals

Spinons and holons for the one-dimensional three-band Hubbard models of high-temperature superconductors

The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = ± J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential

The magnetic and electronic structure of vanadyl pyrophosphate from density functional theory

We have studied the magnetic structure of the high symmetry vanadyl pyrophosphate ((VO)_(2)P_(2)O)7, VOPO), focusing on the spin exchange couplings, using density functional theory (B3LYP) with the full three-dimensional periodicity. VOPO involves four distinct spin couplings: two larger couplings exist along the chain direction (a-axis), which we predict to be antiferromagnetic, J_(OPO) = −156.8 K and J_O = −68.6 K, and two weaker couplings appear along the c (between two layers) and b directions (between two chains in the same layer), which we calculate to be ferromagnetic, J_layer = 19.2 K and J_chain = 2.8 K. Based on the local density of states and the response of spin couplings to varying the cell parameter a, we found that J_(OPO) originates from a super-exchange interaction through the bridging –O–P–O– unit. In contrast, J_O results from a direct overlap of 3d_(x^2 − y^2) orbitals on two vanadium atoms in the same V_(2)O_8 motif, making it very sensitive to structural fluctuations. Based on the variations in V–O bond length as a function of strain along a, we found that the V–O bonds of V–(OPO)_(2)–V are covalent and rigid, whereas the bonds of V–(O)_(2)–V are fragile and dative. These distinctions suggest that compression along the a-axis would have a dramatic impact on J_O, changing the magnetic structure and spin gap of VOPO. This result also suggests that assuming J_O to be a constant over the range of 2–300 K whilst fitting couplings to the experimental magnetic susceptibility is an invalid method. Regarding its role as a catalyst, the bonding pattern suggests that O_2 can penetrate beyond the top layers of the VOPO surface, converting multiple V atoms from the +4 to +5 oxidation state, which seems crucial to explain the deep oxidation of n-butane to maleic anhydride