Anisotropy and Strong-Coupling Effects on the Collective Mode Spectrum of Chiral Superconductors: Application to Sr2_2RuO4_4

Recent theories of Sr$_2$RuO$_4$ based on the interplay of strong interactions, spin-orbit coupling and multi-band anisotropy predict chiral or helical ground states with strong anisotropy of the pairing states, with deep minima in the excitation gap, as well as strong phase anisotropy for the chiral ground state. We develop time-dependent mean field theory to calculate the Bosonic spectrum for the class of 2D chiral superconductors spanning $^3$He-A to chiral superconductors with strong anisotropy. Chiral superconductors support a pair of massive Bosonic excitations of the time-reversed pairs labeled by their parity under charge conjugation. These modes are degenerate for 2D $^3$He-A. Crystal field anisotropy lifts the degeneracy. Strong anisotropy also leads to low-lying Fermions, and thus to channels for the decay of the Bosonic modes. Selection rules and phase space considerations lead to large asymmetries in the lifetimes and hybridization of the Bosonic modes with the continuum of un-bound Fermion pairs. We also highlight results for the excitation of the Bosonic modes by microwave radiation that provide clear signatures of the Bosonic modes of an anisotropic chiral ground state.Comment: 11 pages with 8 figures. Presented as an invited talk as SCES14, Grenoble, France, July 201

Linear optical response from the odd parity Bardasis-Schrieffer mode in locally non-centrosymmetric superconductors

On the recent report of a magnetic field induced first order transition between an even-parity superconductivity and an odd-parity superconductivity in $\mathrm{CeRh_{2}As_{2}}$, the microscopic physics is still under investigation. However, if, in the vicinity of this transition, the coupling strengths of the even and odd pairing channels are comparable, a particle-particle excitonic collective mode referred to as the Bardasis-Schrieffer (BS) mode should generically exist below the pair-breaking continuum. This BS mode can couple to the light and thus affect the optical response of the superconductor, as it arises from a pairing channel with the parity opposite to that of the ground state pairs. Here, by using a generic bilayer model Hamiltonian for the electronic degree of freedom, which is globally centrosymmetric despite each layer being locally non-centrosymmetric, we study the change of the excitation gap of the BS mode with respect to the out-of-plane magnetic fields and demonstrate that its coupling to the light is possible even in the linear response regime. The linear coupling is attributed to the presence of multiple electronic bands, which is a generic feature of a bilayer system. Our result shows the microwave absorption as the signature of the BS mode, and hence a smoking gun signature of the parity-switching at the transition between two superconducting phases.Comment: 17 pages, 7 figures, 1 tabl

A non-perturbative field theory approach for the Kondo effect: Emergence of an extra dimension and its implication for the holographic duality conjecture

Implementing Wilsonian renormalization group transformations in an iterative way, we develop a non-perturbative field theoretical framework, which takes into account all-loop quantum corrections organized in the $1/N$ expansion, where $N$ represents the flavor number of quantum fields. The resulting classical field theory is given by an effective Landau-Ginzburg theory for a local order parameter field, which appears in one-dimensional higher spacetime. We claim that such all-loop quantum corrections are introduced into an equation of motion for the order parameter field through the evolution in the emergent extra dimension. Based on this non-perturbative theoretical framework, we solve the Kondo effect, where the quantum mechanics problem in the projective formulation is mapped into a Landau-Ginzburg field theory for the hybridization order parameter field with an emergent extra dimension. We confirm the non-perturbative nature of this field theoretical framework. Intriguingly, we show that the Wilsonian renormalization group method can explain non-perturbative thermodynamic properties of an impurity consistent with the Bethe ansatz solutions. Finally, we speculate how our non-perturbative field theoretical framework can be connected with the AdS$_{d+2}$/CFT$_{d+1}$ duality conjecture.Comment: Completely rewritte