Dissipative and nonequilibrium effects near a superconductor-metal quantum critical point
Dissipative and nonequilibrium effects near a superconductor-metal quantum critical point
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超导体-金属量子临界点附近的耗散效应和非平衡效应
DOI：
10.1103/physrevb.78.214512
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发表时间：
2008
影响因子：
3.7
通讯作者：
A. Mitra
中科院分区：
文献类型：
--
作者：
A. Mitra
我们提出了一个微观推导的影响，在超导体-金属量子临界点附近的系统上的电流。研究的模型是一个二维巡回电子系统，其中的电子通过相互吸引的相互作用，并耦合到一个底层正常的金属基板，提供了一个源的耗散，也提供了一个源的非弹性散射，允许非平衡稳态达到。导出了正常侧超导涨落的非平衡Keldysh作用量。电流流动，除了它的最小耦合的序参量被发现引起两个新的效果。一个是噪声源，它充当有效温度$T_{eff} = e E v_F \tau_{sc}$，其中$E$是外部电场，$v_F$是费米速度，$\tau_{sc}$是逃逸到正常金属衬底的时间。其次，电流也会引起序参量的漂移。导出了超导能隙和电流的标度方程，并发现只要包括温度T \sim T_{eff}$，则与以前的唯象处理是一致的。电流引起的漂移被发现产生额外的修正的缩放是由一个小的因素${\cal O}（\frac{1}{E_F \tau_{sc}}）$，$E_F$是费米能量。
We present a microscopic derivation of the effect of current flow on a system near a superconductor-metal quantum critical point. The model studied is a 2d itinerant electron system where the electrons interact via an attractive interaction and are coupled to an underlying normal metal substrate which provides a source of dissipation, and also provides a source of inelastic scattering that allows a nonequilibrium steady state to reach. A nonequilibrium Keldysh action for the superconducting fluctuations on the normal side is derived. Current flow, besides its minimal coupling to the order parameter is found to give rise to two new effects. One is a source of noise that acts as an effective temperature $T_{eff} = e E v_F \tau_{sc}$ where $E$ is the external electric field, $v_F$ the Fermi velocity, and $\tau_{sc}$ is the escape time into the normal metal substrate. Secondly current flow also produces a drift of the order-parameter. Scaling equations for the superconducting gap and the current are derived and are found to be consistent with previous phenomenological treatments as long as a temperature $T \sim T_{eff}$ is included. The current induced drift is found to produce additional corrections to the scaling which are smaller by a factor of ${\cal O}(\frac{1}{E_F \tau_{sc}})$, $E_F$ being the Fermi energy.