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Non-magnetic Impurities in Spin Gap Systems

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 Added by Akira Furusaki
 Publication date 1996
  fields Physics
and research's language is English




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The effect of non-magnetic impurities is discussed for both the two-leg Heisenberg ladder system and other spin liquids with excitation gap. It is shown that the random depletion of spins introduces a random Berry phase term to the non-linear sigma model. The classical nature of the antiferromagnetic correlation is enhanced by the topological decoherence, and the staggered susceptibility shows more singular behavior at low temperatures than the uniform antiferromagnetic Heisenberg chain.



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Quasiparticle states in Dirac systems with complex impurity potentials are investigated. It is shown that an impurity site with loss leads to a nontrivial distribution of the local density of states (LDOS). While the real part of defect potential induces a well-pronounced peak in the density of states (DOS), the DOS is either weakly enhanced at small frequencies or even forms a peak at the zero frequency for a lattice in the case of non-Hermitian impurity. As for the spatial distribution of the LDOS, it is enhanced in the vicinity of impurity but shows a dip at a defect itself when the potential is sufficiently strong. The results for a two-dimensional hexagonal lattice demonstrate the characteristic trigonal-shaped profile for the LDOS. The latter acquires a double-trigonal pattern in the case of two defects placed at neighboring sites. The effects of non-Hermitian impurities could be tested both in photonic lattices and certain condensed matter setups.
Following the discovery of topological insulators, there has been a renewed interest in superconducting systems that have strong spin-orbit (SO) coupling. Here we address the fundamental question of how the spin properties of a otherwise spin-singlet superconducting ground state evolve with increasing SO impurity density. We have mapped out the Zeeman critical field phase diagram of superconducting Al films that were deposited over random Pb cluster arrays of varying density. These phase diagrams give a direct measure of the Fermi liquid spin renormalization, as well as the spin orbit scattering rate. We find that the spin renormalization is a linear function of the average Pb cluster-to-cluster separation and that this dependency can be used to tune the spin susceptibility of the Al over a surprisingly wide range from 0.8$chi_0$ to 4.0$chi_0$, where $chi_0$ is the non-interacting Pauli susceptibility.
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We calculate the plasmon dispersion in quasi-one-dimensional quantum wires, in the presence of non-magnetic impurities, taking into consideration the memory function formalism and the role of the forward scattering. The plasma frequency is reduced by the presence of impurities. We also calculate, analytically, the plasmon dispersion in the Born approximation, for the scattering of the electrons by the non-magnetic impurities. We compare our result with the numerical results of Sarma and Hwang.
The influence of La non magnetic impurities on the spin dynamics of CeCoIn$_{5}$ was studied by inelastic neutron scattering. In La-substituted systems, the spin resonance peak (observed at $Omega_{res}=0.55 meV$ in the pure system) is shifted to lower energies but the ratio $Omega_{res}/k_{B}T_{c}$ remains unchanged. The excitation broadens till it reaches 0.3 meV equal to the value of the quasi-elastic signal in the normal state. The evolution of La substitution is compared with the evolution of the magnetic resonance in Ni and Zn substituted YBa$_{2}$Cu$_{3}$O$_{7}$.
We demonstrate that electrostatic interactions between helical electrons at the edge of a quantum spin Hall insulator and a dynamical impurity can induce quasi-elastic backscattering. Modelling the impurity as a two-level system, we show that transitions between counterpropagating Kramers-degenerate electronic states can occur without breaking time-reversal symmetry, provided that the impurity also undergoes a transition. The associated electrical resistance has a weak temperature dependence down to a non-universal temperature scale. Our results extend the range of known backscattering mechanisms in helical edge modes to include scenarios where electron tunnelling out of the system is absent.
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