Recent studies have emphasized the importance of impurity scattering for the optical Higgs response of superconductors. In the dirty limit, an additional paramagnetic coupling of light to the superconducting condensate arises which drastically enhances excitation. So far, most work concentrated on the periodic driving with light, where the third-harmonic generation response of the Higgs mode was shown to be enhanced. In this work, we additionally calculate the time-resolved optical conductivity of single- and two-band superconductors in a two-pulse quench-probe setup, where we find good agreement with existing experimental results. We use the Mattis-Bardeen approach to incorporate impurity scattering and calculate explicitly the time-evolution of the system. Calculations are performed both in a diagrammatic picture derived from an effective action formalism and within a time-dependent density matrix formalism.
Theories and experiments on dirty superconductors are sophisticated but important for both fundamentals and applications. It becomes more challenging when magnetic fields are present, because the field distribution, the electron density of states, and the superconducting pairing potentials are nonuniform. Here we present tunneling microspectroscopic experiments on NbC single crystals and show that NbC is a homogeneous dirty superconductor. When applying magnetic fields to the sample, we observe that the zero-energy local density of states and the pairing energy gap follow an explicit scale rel…
We discuss the symmetry property of a nodal superconductor that hosts robust flat-band zero-energy states at its surface under potential disorder. Such robust zero-energy states are known to induce the anomalous proximity effect in a dirty normal metal attached to a superconductor. A recent study has shown that a topological index ${\cal N}_\mathrm{ZES}$ describes the number of zero-energy states at the dirty surface of a $p$-wave superconductor. We generalize the theory to clarify the conditions required for a superconductor that enables ${\cal N}_\mathrm{ZES}\neq 0$. Our results show that ${…
We study the effects of the Lifshitz transition from closed to open Fermi surface in dirty topological insulators with the nematic superconductivity near the critical temperature. We solve linearized Gor'kov equations and find that the nematic superconductor with an open Fermi surface has a lower critical temperature and more susceptible to the disorder than the superconductor with the closed Fermi surface. We propose that correspondence between the critical temperature and stability against the disorder is the general feature of the superconductivity. We investigate the effects of the Lifshit…
We study the structure of Abrikosov vortices in two-band superconductors for different external magnetic fields and different parameters of the bands. The vortex core size determined by the coherence lengths are found to have qualitatively different behaviour from that determined by the quasiparticle density of states spatial variation. These different vortex core length scales coincide near the upper critical field, while the discrepancy between them becomes quite significant at lower fields. Within the diffusive approximation we demonstrate several generic regimes in the field dependence of …
Optical conductivity of a dirty current-carrying superconductor
L. D. Landau Institute for Theoretical Physics（列夫·朗道理论物理研究所）；Laboratory for Condensed Matter Physics, HSE University（高等经济学院凝聚态物理实验室）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
A class of hydrogen-rich (H-rich) systems, consistent with Type II superconductivity, are known to have very high superconducting transition temperatures Tc and upper critical magnetic field Bc2 values (up to 288 K and 222 T respectively). By looking at all the experimental H-rich superconductors reported to date most are in the dirty limit, with only the highest Tc values being in the crossover to the clean regime. In this framework, there is a clear understanding of some previous unexplained behaviors: (1) A maximum in Bc2 as a function of Tc; (2) a clear change in slope in Tc as a function …
In multiband systems, such as iron-based superconductors, the superconducting states with locking and anti-locking of the interband phase differences, are usually considered as mutually exclusive. For example, a dirty two-band system with interband impurity scattering undergoes a sharp crossover between the $s_{\pm}$ state (which favors phase anti locking) and the $s_{++}$ state (which favors phase locking). We discuss here that the situation can be much more complex in the presence of an external field or superconducting currents. In an external applied magnetic field, dirty two-band supercon…
How experimentally to detect a solitary superconductivity in dirty ferromagnet-superconductor trilayers?
本文从理论上研究了F $_1$ F $_2$ S设计中铁磁（F）-超导（S）异质结构中的邻近效应。本文考虑了Usadel型方程在所谓的“脏”极限情形下的边值问题。考虑了F层中的“潜在”超导对相互作用。重点是在实验制备的所谓的孤立超导态的配方。我们还提出并讨论了孤立超导区基于F $_1$ F $_2$ S三层的超导自旋阀模型。
The ultra-fast dynamics of superconducting vortices harbors rich physics generic to nonequilibrium collective systems. The phenomenon of flux-flow instability (FFI), however, prevents its exploration and sets practical limits for the use of vortices in various applications. To suppress the FFI, a superconductor should exhibit a rarely achieved combination of properties: weak volume pinning, close-to-depairing critical current, and fast heat removal from heated electrons. Here, we demonstrate experimentally ultra-fast vortex motion at velocities of 10-15 km/s in a directly written Nb-C supercon…
We study the dissipative conductivity $σ_1$ of a dirty superconductor with a finite Dynes parameter $Γ$ under a dc-biased weak time-dependent field. The Usadel equation for the current-carrying state is solved to calculate the pair potential, penetration depth, supercurrent density, and quasiparticle spectrum. It is shown that, while the depairing current density $j_d$ for $Γ=0$ is coincident with the Kupriyanov-Lukichev theory, a finite $Γ$ decreases the superfluid density, resulting in a reduction of $j_d$. The broadening of the peaks of the quasiparticle density of states induced by a combi…
We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order as well as a spin-singlet s-wave order parameter due to the two-band degree of freedom. In a spin-singlet superconductor, $T_c$ is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in …
Disorder in two-band superconductors with repulsive interband interaction induces a frustrated competition between the phase-locking preferences of the various potential and kinetic terms. This frustrated interaction can result in the formation of an $s+is$ superconducting state, that breaks the time-reversal symmetry. In this paper we study the normal modes and their associated coherence lengths in such materials. We especially focus on the consequences of the soft modes stemming from the frustration and time-reversal-symmetry breakdown. We find that two-bands superconductors with such impuri…
FeTe$_{0.55}$Se$_{0.45}$: a multiband superconductor in the clean and dirty limit
详细的光学性质的多带铁硫族化物超导体FeTe $_{0.55}$ Se $_{0.45}$已重新检查了大量的温度以上和以下的临界温度$T_c=14$ K的光偏振在a-b平面。在$T_c$之上，正常态的光学性质最好用考虑两个独立电子子系统的双Drude模型来描述，而不是假设单个能带的简单Drude模型;我们观察到一个微弱的反应（$ω_{p,D;1}\simeq 3000$ cm $^{-1}$），其中散射速率具有很强的温度依赖性（$T \gtrsim T_c$的$1/τ_{D,1}\simeq 32$ cm $^{-1}$），以及具有大散射率（$1/τ_{D,2}\simeq 1720$ cm $^{-1}$）的强响应（$ω_{p,D;2}\simeq 14\,500$ cm $^{-1}$），其基本上与温度无关。这种材料的多波段性质排除了使用流行的广义Drude方法通常适用于单波段材料，这意味着在频率依赖的散射率$1/τ(ω)$中观察到的任何结构都是虚假的，它不能用作光学反演技术的基础，以确定电子玻色子光谱函数$α^2 F(ω)$。在$T_c$以下，使用分别应用于强响应和弱响应的两个超导光学带隙$2Δ_1\simeq 45$和$2Δ_2 \simeq 90$ cm $^{-1}$来最好地描述光学电导率。这两个波段的散射率在低温下有很大的不同，使这种材料同时处于清洁和肮脏的极限。有趣…
We study the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor, where we assume the equal-time spin-singlet s-wave pair potential in each conduction band and the hybridization between the two bands as well as the band asymmetry. In the clean limit, the phase of hybridization determines the stability of two states: called $s_{++}$ and $s_{+-}$. The interband impurity scatterings decrease $T_c$ of the two states exactly in the same manner when the Hamiltonian preserves time-reversal symmetry. We find that a superconductor wi…
This work performs a comparative numerical study of the impurity average self-frequency $\tildeω$ in an unconventional superconducting alloy with non-magnetic impurities. Two methods are used: the Levenberg-Marquardt algorithm as a non-linear minimization problem, and a fixed-point iteration procedure. The unconventional superconducting renormalized by impurities \bw is a self-consistent complex non-linear equation with two varying parameters: the impurity concentration $Γ^+$ and the strength of the impurities c, for which its numerical solution is a computational challenge. Throughout this st…
The optical properties of the new iron-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$ with $T_c \sim 29$~K have been determined. In the normal state a good description of the low-frequency response is obtained with a superposition of two Drude components of which one has a very low scattering rate (narrow Drude-peak) and the other a rather large one (broad Drude-peak). Well below $T_c \sim 29$~K, a pronounced gap feature is observed which involves a complete suppression of the optical conductivity below $\sim$ 110~cm$^{-1}$ and thus is characteristic of a nodeless superconducting state. The op…
We calculate the surface resistance of s-wave superconductors under a static external field on the basis of the quasiclassical approximation. The numerical calculations are performed both for the dirty and relatively clean cases, and the difference in the absorption spectrum between them is investigated. The amplitude mode in the dirty case, which has been previously studied in the local response function, appears also in the nonlocal response. In the clean case, there is a large discrepancy between the excitation energy of the amplitude mode and the energy of the gap edge where the coupling b…
