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Register a new userGauge-invariant microscopic kinetic theory of superconductivity: application to electromagnetic response of Nambu-Goldstone and Higgs modes
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We show that the gauge-invariant kinetic equation of superconductivity provides an efficient approach to study the electromagnetic response of the gapless Nambu-Goldstone and gapful Higgs modes on an equal footing. We prove that the Fock energy in the kinetic equation is equivalent to the generalized Wards identity. Hence, the gauge invariance directly leads to the charge conservation. Both linear and second-order responses are investigated. The linear response of the Higgs mode vanishes in the long-wave limit. Whereas the linear response of the Nambu-Goldstone mode interacts with the long-range Coulomb interaction, causing the original gapless spectrum lifted up to the plasma frequency as a result of the Anderson-Higgs mechanism, in consistency with the previous works. The second-order response exhibits interesting physics. On one hand, a finite second-order response of the Higgs mode is obtained in the long-wave limit. We reveal that this response, which has been experimentally observed, is attributed solely to the drive effect rather than the widely considered Anderson-pump effect. On the other hand, the second-order response of the Nambu-Goldstone mode, free from the influence of the long-range Coulomb interaction and hence the Anderson-Higgs mechanism, is predicted. We find that both Anderson-pump and drive effects play important role in this response. A tentative scheme to detect this second-order response is proposed.
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Within a gauge-invariant microscopic kinetic theory, we study the electromagnetic response in the superconducting states. Both superfluid and normal-fluid dynamics are involved. We predict that the normal fluid is present only when the excited superconducting velocity $v_s$ is larger than a threshold $v_L=|Delta|/k_F$. Interestingly, with the normal fluid, we find that there exists friction between the normal-fluid and superfluid currents. Due to this friction, part of the superfluid becomes viscous. Therefore, a three-fluid model: normal fluid, non-viscous and viscous superfluids, is proposed. For the stationary magnetic response, at $v_s<v_L$ with only the non-viscous superfluid, the Meissner supercurrent is excited and the gap equation can reduce to Ginzburg-Landau equation. At $v_s{ge}v_L$, with the normal fluid, non-viscous and viscous superfluids, in addition to the directly excited Meissner supercurrent in the superfluid, normal-fluid current is also induced through the friction drag with the viscous superfluid current. Due to the normal-fluid and viscous superfluid currents, the penetration depth is influenced by the scattering effect. In addition, a modified Ginzburg-Landau equation is proposed. We predict an exotic phase in which both the resistivity and superconducting gap are {em finite}. As for the optical response, the excited ${v_s}$ oscillates with time. When $v_s<v_L$, only the non-viscous superfluid is present whereas at $v_s{ge}v_L$, normal fluid, non-viscous and viscous superfluids are present. We show that the excited normal-fluid current exhibits the Drude-model behavior while the superfluid current consists of the Meissner supercurrent and Bogoliubov quasiparticle current. Due to the friction between the superfluid and normal-fluid currents, the optical conductivity is captured by the three-fluid model. ......
We report on results of our theoretical study of the c-axis infrared conductivity of bilayer high-Tc cuprate superconductors using a microscopic model involving the bilayer-split (bonding and antibonding) bands. An emphasis is on the gauge-invariance of the theory, which turns out to be essential for the physical understanding of the electrodynamics of these compounds. The description of the optical response involves local (intra-bilayer and inter-bilayer) current densities and local conductivities. The local conductivities are obtained using a microscopic theory, where the quasiparticles of the two bands are coupled to spin fluctuations. The coupling leads to superconductivity and is described at the level of generalized Eliashberg theory. Also addressed is the simpler case of quasiparticles coupled by a separable and nonretarded interaction. The gauge invariance of the theory is achieved by including a suitable class of vertex corrections. The resulting response of the model is studied in detail and an interpretation of two superconductivity-induced peaks in the experimental data of the real part of the c-axis conductivity is proposed. The peak around 400/cm is attributed to a collective mode of the intra-bilayer regions, that is an analogue of the Bogolyubov-Anderson mode playing a crucial role in the theory of the longitudinal response of superconductors. For small values of the bilayer splitting, its nature is similar to that of the transverse plasmon of the phenomenological Josephson superlattice model. The peak around 1000/cm is interpreted as a pair breaking-feature that is related to the electronic coupling through the spacing layers separating the bilayers.
Structural phase transitions described by Mexican hat potentials should in principle exhibit aspects of Higgs and Goldstone physics. Here, we investigate the relationship between the phonons that soften at such structural phase transitions and the Higgs- and Goldstone-boson analogues associated with the crystallographic Mexican hat potential. We show that, with the exception of systems containing only one atom type, the usual Higgs and Goldstone modes are represented by a combination of several phonon modes, with the lowest energy phonons of the relevant symmetry having substantial contribution. Taking the hexagonal manganites as a model system, we identify these modes using Landau theory, and predict the temperature dependence of their frequencies using parameters obtained from density functional theory. Separately, we calculate the additional temperature dependence of all phonon mode frequencies arising from thermal expansion within the quasi-harmonic approximation. We predict that Higgs-mode softening will dominate the low-frequency vibrational spectrum of InMnO$_3$ between zero kelvin and room-temperature, whereas the behavior of ErMnO$_3$ will be dominated by lattice expansion effects. We present temperature-dependent Raman scattering data that support our predictions, in particular confirming the existence of the Higgs mode in InMnO$_3$.
We argue that Raman study of Fe-pnictides is a way to unambiguously distinguish between various superconducting gaps proposed for these materials. We show that $A_{1g}$ Raman intensity has a true resonance peak below $2Delta$ for extended s-wave superconducting gap, $Delta(mathbf{k}) = Delta (cos k_x + cos k_y)/2$ in the folded Brillouin zone. No such peak emerges for a pure s-wave gap, a d-wave gap, and another extended s-wave gap with $Delta(mathbf{k}) = Delta cos{frac{k_x}{2}} cos{frac{k_y}{2}}$ proposed by several groups.
Unambiguous evidence for the microscopic coexistence of ferromagnetism and superconductivity in UCoGe ($T_{rm Curie} sim 2.5$ K and $T_{rm SC}$ $sim$ 0.6 K) is reported from $^{59}$Co nuclear quadrupole resonance (NQR). The $^{59}$Co-NQR signal below 1 K indicates ferromagnetism throughout the sample volume, while nuclear spin-lattice relaxation rate $1/T_1$ in the ferromagnetic (FM) phase decreases below $T_{rm SC}$ due to the opening of the superconducting(SC) gap. The SC state was found to be inhomogeneous, suggestive of a self-induced vortex state, potentially realizable in a FM superconductor. In addition, the $^{59}$Co-NQR spectrum around $T_{rm Curie}$ show that the FM transition in UCoGe possesses a first-order character, which is consistent with the theoretical prediction that the low-temperature FM transition in itinerant magnets is generically of first-order.
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