Random Spin-orbit Coupling in Spin Triplet Superconductors: Stacking Faults in Sr_2RuO_4 and CePt_3Si

The random spin-orbit coupling in multicomponent superconductors is investigated focusing on the non-centrosymmetric superconductor CePt_3Si and the spin triplet superconductor Sr_2RuO_4. We find novel manifestations of the random spin-orbit coupling in the multicomponent superconductors with directional disorders, such as stacking faults. The presence of stacking faults is indicated for the disordered phase of CePt_3Si and Sr_2RuO_4. It is shown that the d-vector of spin triplet superconductivity is locked to be d = k_y x - k_x y with the anisotropy \Delta T_c/T_c0 \sim \bar{\alpha}^2/T_c0 W_z, where \bar{\alpha}, T_c0, and W_z are the mean square root of random spin-orbit coupling, the transition temperature in the clean limit, and the kinetic energy along the c-axis, respectively. This anisotropy is much larger (smaller) than that in the clean bulk Sr_2RuO_4 (CePt_3Si). These results indicate that the helical pairing state d = k_y x - k_x y in the eutectic crystal Sr_2RuO_4-Sr_3Ru_2O_7 is stabilized in contrast to the chiral state d = (k_x \pm i k_y) z in the bulk Sr_2RuO_4. The unusual variation of T_c in CePt_3Si is resolved by taking into account the weak pair-breaking effect arising from the uniform and random spin-orbit couplings. These superconductors provide a basis for discussing recent topics on Majorana fermions and non-Abelian statistics.Comment: J. Phys. Soc. Jpn. 79 (2010) 08470

Bounds on Decoherence and Error

When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave function optimization required to avoid decoherence is also examined.Comment: 10 pages, plain TeX, no figure

Disordered Fulde-Ferrel-Larkin-Ovchinnikov State in d-wave Superconductors

We study the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) superconducting state in the disordered systems. We analyze the microscopic model, in which the d-wave superconductivity is stabilized near the antiferromagnetic quantum critical point, and investigate two kinds of disorder, namely, box disorder and point disorder, on the basis of the Bogoliubov-deGennes (BdG) equation. The spatial structure of modulated superconducting order parameter and the magnetic properties in the disordered FFLO state are investigated. We point out the possibility of "FFLO glass" state in the presence of strong point disorders, which arises from the configurational degree of freedom of FFLO nodal plane. The distribution function of local spin susceptibility is calculated and its relation to the FFLO nodal plane is clarified. We discuss the NMR measurements for CeCoIn_5.Comment: Submitted to New. J. Phys. a focus issue on "Superconductors with Exotic Symmetries

Spin moment over 10-300 K and delocalization of magnetic electrons above the Verwey transition in magnetite

In order to probe the magnetic ground state, we have carried out temperature dependent magnetic Compton scattering experiments on an oriented single crystal of magnetite (Fe$_3$O$_4$), together with the corresponding first-principles band theory computations to gain insight into the measurements. An accurate value of the magnetic moment $\mu_S$ associated with unpaired spins is obtained directly over the temperature range of 10-300K. $\mu_S$ is found to be non-integral and to display an anomalous behavior with the direction of the external magnetic field near the Verwey transition. These results reveal how the magnetic properties enter the Verwey energy scale via spin-orbit coupling and the geometrical frustration of the spinel structure, even though the Curie temperature of magnetite is in excess of 800 K. The anisotropy of the magnetic Compton profiles increases through the Verwey temperature $T_v$ and indicates that magnetic electrons in the ground state of magnetite become delocalized on Fe B-sites above $T_v$.Comment: 5 pages, 5 figures, to appear in Journal of Physics and Chemistry of Solid

Band structures of P-, D-, and G-surfaces

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.Comment: 21 pages, 8 figures, 3 tables, submitted to Phys. Rev.

Pseudogap in fermionic density of states in the BCS-BEC crossover of atomic Fermi gases

We study pseudogap behaviors of ultracold Fermi gases in the BCS-BEC crossover region. We calculate the density of states (DOS), as well as the single-particle spectral weight, above the superfluid transition temperature $T_{\rm c}$ including pairing fluctuations within a $T$-matrix approximation. We find that DOS exhibits a pseudogap structure in the BCS-BEC crossover region, which is most remarkable near the unitarity limit. We determine the pseudogap temperature $T^*$ at which the pseudogap structure in DOS disappears. We also introduce another temperature $T^{**}$ at which the BCS-like double-peak structure disappears in the spectral weight. While one finds $T^*>T^{**}$ in the BCS regime, $T^{**}$ becomes higher than $T^*$ in the crossover and BEC regime. We also determine the pseudogap region in the phase diagram in terms of temperature and pairing interaction.Comment: 6 pages, 4 figures, Proceedings of QFS 200

Fourth Order Perturbation Theory for Normal Selfenergy in Repulsive Hubbard Model

We investigate the normal selfenergy and the mass enhancement factor in the Hubbard model on the two-dimensional square lattice. Our purpose in this paper is to evaluate the mass enhancement factor more quantitatively than the conventional third order perturbation theory. We calculate it by expanding perturbatively up to the fourth order with respect to the on-site repulsion $U$. We consider the cases that the system is near the half-filling, which are similar situations to high-$T_c$ cuprates. As results of the calculations, we obtain the large mass enhancement on the Fermi surface by introducing the fourth order terms. This is mainly originated from the fourth order particle-hole and particle-particle diagrams. Although the other fourth order terms have effect of reducing the effective mass, this effect does not cancel out the former mass enhancement completely and there remains still a large mass enhancement effect. In addition, we find that the mass enhancement factor becomes large with increasing the on-site repulsion $U$ and the density of state (DOS) at the Fermi energy $\rho(0)$. According to many current reseaches, such large $U$ and $\rho(0)$ enhance the effective interaction between quasiparticles, therefore the superconducting transition temperature $T_c$ increases. On the other hand, the large mass enhancement leads the reduction of the energy scale of quasiparticles, as a result, $T_c$ is reduced. When we discuss $T_c$, we have to estimate these two competitive effects.Comment: 6pages,8figure

Antiferromagnetic order in the FFLO state

We investigate the antiferromagnetic (AF) order in the d-wave superconducting (SC) state at high magnetic fields. A two-dimensional model with on-site repulsion U, inter-site attractive interaction V and antiferromagnetic exchange interaction J is solved using the mean field theory. For finite values of U and J, a first order transition occurs from the normal state to the FFLO state, while the FFLO-BCS phase transition is second order, consistent with the experimental results in CeCoIn_5. Although the BCS-FFLO transition is continuous, the Ne'el temperature of AF order is discontinuous at the phase boundary because the AF order in the FFLO state is induced by the Andreev bound state localized in the zeros of FFLO order parameter, while the AF order hardly occurs in the uniform BCS state. The spatial structure of the magnetic moment is investigated for the commensurate AF state as well as for the incommensurate AF state. The influence of the spin fluctuations is discussed for both states. Since the fluctuations are enhanced in the normal state for incommensurate AF order, this AF order can be confined in the FFLO state. The experimental results in CeCoIn_5 are discussed.Comment: Proceedings of LT25 conference (Amsterdam, 2008