Topological Weyl Superconductor to Diffusive Thermal Hall Metal Crossover in the B-Phase of UPt3_3

The recent phase sensitive measurements in the superconducting $B$-phase of UPt$_3$ provide strong evidence for the triplet, chiral $k_z(k_x \pm ik_y)^2$ pairing symmetries, which endow the Cooper pairs with orbital angular momentum projections $L _z= \pm 2$ along the $c$-axis. In the absence of disorder such pairing can support both line and point nodes, and both types of nodal quasiparticles exhibit nontrivial topology in the momentum space. The point nodes, located at the intersections of the closed Fermi surfaces with the $c$-axis, act as the double monopoles and the antimonopoles of the Berry curvature, and generalize the notion of Weyl quasiparticles. Consequently, the $B$ phase should support an anomalous thermal Hall effect, the polar Kerr effect, in addition to the protected Fermi arcs on the (1,0,0) and the (0,1,0) surfaces. The line node at the Fermi surface equator acts as a vortex loop in the momentum space and gives rise to the zero energy, dispersionless Andreev bound states on the (0,0,1) surface. At the transition from the $B$-phase to the $A$-phase, the time reversal symmetry is restored, and only the line node survives inside the $A$-phase. As both line and double-Weyl point nodes possess linearly vanishing density of states, we show that weak disorder acts as a marginally relevant perturbation. Consequently, an infinitesimal amount of disorder destroys the ballistic quasiparticle pole, while giving rise to a diffusive phase with a finite density of states at the zero energy. The resulting diffusive phase exhibits $T$-linear specific heat, and an anomalous thermal Hall effect. We predict that the low temperature thermodynamic and transport properties display a crossover between a ballistic thermal Hall semimetal and a diffusive thermal Hall metal.Comment: 8 pages, 1 figure; replaced by the version accepted by Phys. Rev.

Coexistence of ferromagnetism and superconductivity near quantum phase transition: The Heisenberg- to Ising-type crossover

A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transition is analysed and the generic phase diagram is obtained. This scenario is then applied to the case of itinerant ferromagnet ZrZn2, which sheds light on the proposed phase diagram of this compound. Possible explanation of superconductivity in UGe2 is also discussed.Comment: 5 pages, 3 figure

Ising-nematic order in the bilinear-biquadratic model for the iron pnictides

Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations in directions perpendicular and parallel to the ordering wave-vector even above the magnetic transition temperature $T_N$, we study the frustrated Heisenberg model with a biquadratic spin-spin exchange interaction. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the $C_4$ symmetry even into the paramagnetic region $T_N<T<T_{\sigma}$ which we refer to as the Ising-nematic phase. In addition to the Heisenberg spin interaction, we include the biquadratic coupling $K (\mathbf{S}_i\cdot \mathbf{S}_j)^2$ and study its effect on the dynamical temperature range $T_{\sigma}-T_N$ of the Ising-nematic phase. We find that this range reduces dramatically when even small values of the interlayer exchange $J_c$ and biquadratic coupling $K$ are included. To supplement our analysis, we benchmark the results obtained using the DM method against those from different non-linear spin-wave theories, including the recently developed generalized spin-wave theory (GSWT), and find good qualitative agreement among the different theoretical approaches as well as experiment for both the spin-wave dispersions and the dynamical structure factors

Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain

We study the spin $S=1$ Heisenberg chain, with nearest neighbor, next nearest neighbor ($\alpha$) and biquadratic ($\beta$) interactions using a combination of the density matrix renormalization group (DMRG), an analytic variational matrix product state wavefunction, and non-Abelian bosonization. We study the effect of frustration ($\alpha>0$) on the Haldane phase with $-1\leq \beta < 1$ which reveals a rich phase diagram. For $-1<\beta<\beta^\ast$, we establish the existence of a spontaneously dimerized phase for large $\alpha>\alpha_c$, separated from the Haldane phase by the critical line $\alpha_c(\beta)$ of second-order phase transitions connected to the Takhtajan--Babudjian integrable point $\alpha_c(\beta=-1)=0$. In the opposite regime, $\beta>\beta^\ast$, the transition from the Haldane phase becomes first-order into the next nearest neighbor (NNN) AKLT phase. Based on field theoretical arguments and DMRG calculations, we conjecture that these two regimes are separated by a multicritical point ($\beta^\ast, \alpha^\ast$) of a different universality class, described by the $SU(2)_4$ Wess--Zumino--Witten critical theory. From the DMRG calculations we estimate this multicritical point to lie in the range $-0.2<\beta^\ast<-0.15$ and $0.47<\alpha^\ast < 0.53$. We find that the dimerized and NNN-AKLT phases are separated by a line of first-order phase transitions that terminates at the multicritical point. Inside the Haldane phase, we show the existence of two incommensurate crossovers: the Lifshitz transition and the disorder transition of the first kind, marking incommensurate correlations in momentum and real space, respectively. We show these crossover lines stretch across the entire $(\beta,\alpha)$ phase diagram, merging into a single incommensurate-to-commensurate transition line for negative $\beta\lesssim \beta^\ast$ outside the Haldane phase.Comment: 25 pages, 24 figures, updated with published versio

Composite pairing in a mixed valent two channel Anderson model

Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce "symplectic Hubbard operators": an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-coherent mixing of the empty and doubly occupied configurations of the mixed valent ion. This effect redistributes the f-electron charge within the unit cell. Our theory predicts a sharp superconducting shift in the nuclear quadrupole resonance frequency associated with this redistribution. We calculate the magnitude and sign of the predicted shift expected in CeCoIn_5.Comment: 13 pages, 5 figure

Spin Ferroquadrupolar Order in the Nematic Phase of FeSe

We provide evidence that spin ferroquadrupolar (FQ) order is the likely ground state in the nonmagnetic nematic phase of stoichiometric FeSe. By studying the variational mean-field phase diagram of a bilinear-biquadratic Heisenberg model up to the 2nd nearest neighbor, we find the FQ phase in close proximity to the columnar antiferromagnet commonly realized in iron-based superconductors; the stability of FQ phase is further verified by the density matrix renormalization group. The dynamical spin structure factor in the FQ state is calculated with flavor-wave theory, which yields a qualitatively consistent result with inelastic neutron scattering experiments on FeSe at both low and high energies. We verify that FQ can coexist with $C_4$ breaking environments in the mean-field calculation, and further discuss the possibility that quantum fluctuations in FQ act as a source of nematicity.Comment: 8 pages, 7 figures, Erratum adde