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Register a new userConsequences of current conservation in systems with partial magnetic order
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We discuss the consequences of spin current conservation in systems with SU(2) spin symmetry that is spontaneously broken by partial magnetic order, using a momentum-space approach. The long-distance interaction is mediated by Goldstone magnons, whose interaction is expressed in terms of the electron Greens functions. There is also a Higgs mode, whose excitation energy can be calculated. The case of fast magnons obeying linear dispersion relation in three spatial dimensions admits nonperturbative treatment using the Gribov equation, and the solution exhibits singular behaviour which has an interpretation as a tower of spin-1 electronic excitations. This occurs near the Mott insulator state. The electrons are more free in the case of slow magnons, where the perturbative corrections are less singular at the thresholds. We then turn our attention to the problem of high-Tc superconductivity, through the discussion of the stability of the antiferromagnetic ground state in two spatial dimensions. We argue that this is caused by an effective mixing of the Goldstone and Higgs modes, which in turn is caused by an effective Goldstone-boson condensation. The instability of the antiferromagnetic system is analyzed by studying the non-perturbative behaviour of the Higgs boson self-energy using the Dyson-Schwinger equations.
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From general considerations of spin-symmetry breaking associated with (anti-)ferromagnetism in metallic systems with Coulomb repulsion, we obtain interesting and simple all-order rules involving the ratios of the densities of states. These are exact for ferromagnetism under reasonable conditions, and nearly exact for anti-ferromagnetism. In the case of ferromagnetism, the comparison with the available experimental and theoretical numbers yields favourable results.
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in $mathbb{P}^{n+2}$ satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space $W$ of dimension $n+2$, classify $n$-tuples of skew-symmetric 2-forms $A^{alpha} in Lambda^2(W)$ such that [ phi_{beta gamma}A^{beta}wedge A^{gamma}=0, ] for some non-degenerate symmetric $phi$.
Magnetic spin fluctuations is one candidate to produce the bosonic modes that mediate the superconductivity in the ferrous superconductors. Up until now, all of the LaOFeAs and BaFe2As2 structure types have simple commensurate magnetic ground states, as result of nesting Fermi surfaces. This type of spin-density-wave (SDW) magnetic order is known to be vulnerable to shifts in the Fermi surface when electronic densities are altered at the superconducting compositions. Superconductivity has more recently been discovered in alpha-Fe(Te,Se), whose electronically active antifluorite planes are isostructural to the FeAs layers found in the previous ferrous superconductors and share with them the same quasi-two-dimensional electronic structure. Here we report neutron scattering studies that reveal a unique complex incommensurate antiferromagnetic order in the parent compound alpha-FeTe. When the long-range magnetic order is suppressed by the isovalent substitution of Te with Se, short-range correlations survive in the superconducting phase.
Most theoretical studies of topological superconductors and Majorana-based quantum computation rely on a mean-field approach to describe superconductivity. A potential problem with this approach is that real superconductors are described by number-conserving Hamiltonians with long-range interactions, so their topological properties may not be correctly captured by mean-field models that violate number conservation and have short-range interactions. To resolve this issue, reliable results on number-conserving models of superconductivity are essential. As a first step in this direction, we use rigorous methods to study a number-conserving toy model of a topological superconducting wire. We prove that this model exhibits many of the desired properties of the mean-field models, including a finite energy gap in a sector of fixed total particle number, the existence of long range Majorana-like correlations between the ends of an open wire, and a change in the ground state fermion parity for periodic vs. anti-periodic boundary conditions. These results show that many of the remarkable properties of mean-field models of topological superconductivity persist in more realistic models with number-conserving dynamics.
In high-transition temperature (high-Tc) copper oxides, it is generally believed that antiferromagnetism plays a fundamental role in the superconducting mechanism because superconductivity occurs when mobile electrons or holes are doped into the antiferromagnetic parent compounds. The recent discovery of superconductivity in the rare-earth (R) iron-based oxide systems [RO1-xFxFeAs] has generated enormous interest because these materials are the first noncopper oxide superconductors with Tc exceeding 50 K. The parent (nonsuperconducting) LaOFeAs material is metallic but shows anomalies near 150 K in both resistivity and dc magnetic susceptibility. While optical conductivity and theoretical calculations suggest that LaOFeAs exhibits a spin-density-wave (SDW) instability that is suppressed with doping electrons to form superconductivity, there has been no direct evidence of the SDW order. Here we use neutron scattering to demonstrate that LaOFeAs undergoes an abrupt structural distortion below ~150 K, changing the symmetry from tetragonal (space group P4/nmm) to monoclinic (space group P112/n) at low temperatures, and then followed with the development of long range SDW-type antiferromagnetic order at ~134 K with a small moment but simple magnetic structure. Doping the system with flourine suppresses both the magnetic order and structural distortion in favor of superconductivity. Therefore, much like high-Tc copper oxides, the superconducting regime in these Fe-based materials occurs in close proximity to a long-range ordered antiferromagnetic ground state. Since the discovery of long
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