Effective Hamiltonians and dilution effects in kagome and related antiferromagnets

What is the zero-temperature ordering pattern of a Heisenberg antiferromagnet with large spin length $S$ (and possibly small dilution), on the kagome lattice, or others built from corner-sharing triangles and tetrahedra? First, I summarize the uses of effective Hamiltonians to resolve the large ground-state degeneracy, leading to long-range order of the usual kind. Secondly, I discuss the effects of dilution, in particular to {\it non}-frustration of classical ground states, in that every simplex of spins is optimally satisfied. Of three explanations for this, the most complete is Moessner-Chalker constraint-counting. Quantum zero-point energy may compete with classical exchange energy in a diluted system, creating frustration and enabling a spin-glass state. I suggest that the regime of over 97% occupation is qualitatively different from the more strongly diluted regime.Comment: 11 pages; invited talk at "HFM 2000" (Waterloo, June 2000); submitted to Can. J. Phy

Boson features in STM spectra of cuprate superconductors: Weak-coupling phenomenology

We derive the shape of the high-energy features due to a weakly coupled boson in cuprate superconductors, as seen experimentally in Bi_2 Sr_2 Ca_1 Cu_2 O_8+x (BSCCO) by Lee et al. [Nature (London) 442, 546 (2006)]. A simplified model is used of d-wave Bogoliubov quasiparticles coupled to Einstein oscillators with a momentum-independent electron-boson coupling and an analytic fitting form is derived, which allows us (a) to extract the boson mode's frequency and (b) to estimate the electron-boson coupling strength. We further calculate the maximum possible superconducting gap due to an Einstein oscillator with the extracted electron-boson coupling strength, which is found to be less than 0.2 times of the observed gap indicating at the observed boson's non-dominant role in the superconductivity's mechanism. The extracted momentum-independent electron-boson coupling parameter (that we show a posteriori to indeed be in the weak-coupling regime) is then to be interpreted as an (band-structure detail dependent weighted) average over the Brillouin zone of the actual momentum-dependent electron-boson coupling in BSCCO.Comment: 6.5 page

Hole on a stripe in a spinless fermion model

In the spinless fermion model on a square lattice with infinite nearest-neighbor repulsion, holes doped into the half-filled ordered state form stripes which, at low doping, are stable against phase separation into an ordered state and a hole-rich metal. Here we consider transport of additional holes along these stripes. The motion of a single hole on a stripe is mapped to a one-dimensional problem, a variational wavefunction is constructed and the energy spectrum is calculated and compared to energies obtained by exact diagonalization.Comment: 7 Pages, 6 figures; Revised version accepted for publication in Europhysics Letter

Temperature-dependent "phason" elasticity in a random tiling quasicrystal

Both ``phason'' elastic constants have been measured from Monte Carlo simulations of a random-tiling icosahedral quasicrystal model with a Hamiltonian. The low-temperature limit approximates the ``canonical-cell'' tiling used to describe several real quasicrystals. The elastic constant K2 changes sign from positive to negative with decreasing temperature; in the ``canonical-cell'' limit, K2/K1 appears to approach -0.7, about the critical value for a phason-mode modulation instability. We compare to the experiments on i-AlPdMn and i-AlCuFe.Comment: 5 pages, 2 Postscript figures, LaTeX, uses revtex4, submitted to PR