Time-dependent equation for the magnetic order parameter near the quantum critical point in multiband superconductors with a spin density wave

Abstract

Using a simple two-band model for Fe-based pnictides and the generalized Eilenberger equation, we present a microscopic derivation of a time-dependent equation for the amplitude of the spin density wave near the quantum critical point where it turns to zero. This equation describes the dynamics of the magnetic---$m$, as well as the superconducting order parameter---$\Delta$. It is valid at low temperatures $T$ and small $m$ ($T,m\ll \Delta$) in a region of coexistence of both order parameters, $m$ and $\Delta$. The boundary of this region is found in the space of the nesting parameter $\{{\mu }_0,{\mu }_{\varphi }\}$ where ${\mu }_0$ describes the relative position of the electron and the hole pockets on the energy scale, and ${\mu }_{\varphi }$ accounts for the ellipticity of the electron pocket. At low $T$ the number of quasiparticles is small due to the presence of the energy gap $\Delta$, and therefore the quasiparticles do not play a role in the relaxation of $m$. This circumstance allows one to derive the time-dependent equation for $m$ in contrast to the case of conventional superconductors for which the time-dependent Ginzburg--Landau equation can be derived near $T_{\text{c}}$ only in some special cases (high concentration of paramagnetic impurities. In the stationary case the derived equation is valid at arbitrary temperatures. We find a solution of the stationary equation which describes a domain wall in the magnetic structure. In the center of the domain wall the superconducting order parameter has a maximum, which means a local enhancement of superconductivity. Using the derived time-dependent equation for $m$, we investgate also the stability of a uniform commensurate SDW and obtain the values of $\{{\mu }_0,{\mu }_{\varphi }\}$ at which the first order transition into the state with $m=0$ takes place or the transition to the state with an inhomogeneous SDW occurs.

11 pages, 7 figures Published version

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Cited by in corpus (4)

• Theory of light-induced resonances with collective Higgs and Leggett modes in multiband superconductors
• Dynamics of Order Parameters near Stationary States in Superconductors with a Charge-Density Wave
• Anomalous diamagnetic response in multi-band superconductors with time-reversal broken symmetry
• Spin Current in Junctions composed of Multi-band Superconductors with a Spin-density Wave