Doppler shift on local density of states and local impurity scattering in the vortex state

Abstract

The vortex state thermal and transport properties of the high T c copper oxides can be understood in a d-wave gap model and are dominated by the extended quasiparticle states that exist along the nodal directions in momentum space. The Doppler shift on these states due to the circulating supercurrents around the vortex core, introduces new van Hove ridges into the energy dependent local density of states (LDOS) as a function of distance in the region between cores. We emphasize the topology of these ridges and the effect on them of local static impurity scattering in Born and unitary limit. We treat possible orthorhombicity. Effective local scattering rates are also obtained. Typeset using REVT E X 1

Microscopic interpretation of the Dynes formula for the tunneling density of states

“…(1), in Fig. 1 we reproduce the recently measured low-temperature tunneling data on a series of MoC films with varying thickness [4], together with their fits to the Dynes formula. Similarly perfect agreement between experimental data for disordered superconductors and the Dynes formula has in fact been observed quite frequently, see e.g.…”

“…To answer this question, let us remember that, in a wide field range, type-II superconductors exhibit the vortex state. If the density of states is to be measured sufficiently far away from the vortex cores, as is assumed in this work, then the orbital effect of the magnetic field can be taken into account by the Doppler shift, which is proportional to the local momentum of the supercurrent flow q in the point where the density of states is being measured [4]. This changes the bare electron Green's function in presence of magnetic field tô…”

“…(3) applies even in a clean system, since arXiv:1606.02983v2 [cond-mat.supr-con] 16 Aug 2016 the electron-phonon scattering has also a pair-breaking component at finite temperatures T . However, the mechanism of Mikhailovsky et al predicts that Γ scales with T according to Γ ∝ T 3 , and therefore it is not of direct relevance to the experiments of [4,8,9] and the like, where the parameter Γ is only weakly T -dependent and does not vanish in the low-temperature limit.…”

“…1, which must have a truly intrinsic origin. [4], with fits to the thermally smeared Dynes formula. For further details see [7].…”

“…(3) should be therefore sought in presence of elastic pair-breaking processes, such as scattering on magnetic impurities [12] and/or fluctuating order parameter [13]. However, the latter possibility seems to be ruled out by the spatial homogeneity of the tunneling spectra observed in [4]. Moreover, a fluctuating order parameter is expected to produce appreciable change of N (ω) only for |ω| ≈∆ [13].…”