Flux flow resistivity in the two-gap superconductivity

We investigate flux flow state in the two-gap superconductor in which two s-wave gaps with different amplitudes exist on two separated Fermi surfaces. The flux flow resistivity is obtained based on the Bardeen-Stephen relation and the result agrees well with anomalous field dependence of the flow resistivity recently observed in the two-gap superconductor MgB2. Some typical properties of the vortex in this system are also discussed. key words: MgB2, two-gap structure, flux flow, extension of the Bardeen-Stephen relation The vortex lines in type II superconductors catch the Lorentz force under an external current and begin to flow perpendicular to the current and magnetic field when the Lorentz force exeeds the pinning force. This is the flux flow state and the finite resistivity arises[1]. The essence of the flux flow resistivity is the presence of the bound states inside the vortex core. The energy gap of these states are so small that the conductivity in the core is practically normal. Such states were found by Caroli, de Gennes and Matricon by using the microscopic methods[2]. In both of the dirty and moderately clean s-wave superconductors, the flux flow resistivity ρf is proportional to the magnetic field H[1], namely, ρf = H Hc2 ρn, (1) where Hc2 is the upper critical field and ρn the normal-state resistivity. This is the so-called BardeenStephen relation[3]. In the low temperature region, this relation holds well almost all of the field range in the vortex state. [4] The superconductivity of MgB2 has been investigated with keen interest since it has the highest transition temperature (Tc ≃ 39K) in the metalic compounds at present and the great amount of investigations has been done[5]. One of the most characteristic features in this superconductor is that two s-wave gaps with different amplitudes exist on the two separated Fermi surfaces having roughly equal density of states (DOS). The two-gap model was proposed by first-principle calculations[6, 7], and experimental results obtained by point contact spectroscopy,[8] specific heat measurements[9] and angle-resolved photoemission spectroscopy[10] support the model. Recently, the measurement of the flux flow resistivity in MgB2 was reported by Matsuda’s group[11]. Large deviations from the H-linear dependence for the flux flow resistivity has been found, in spite of the s-wave pairing symmetry of MgB2[12, 13, 14]. Such anomalous behavior is expected to be related to the two-gap structure, but a clear explanation has not been given so far. In this paper, we investigate the flux flow state in the two-gap system and propose new scenario for the anomalous flux flow resistivity. We investigate at first the vortex in two-gap system before discussing the flux flow state. Let ΨL and ΨS stand for the order parameter for the large energy gap and that for the small energy gap, respectively. We use a Ginzburg-Landau(GL) free energy for the two-gap system in weak coupling approach with a Josephson-type interaction[15],