FFLO and vortex states in superconductors with strong paramagnetic effect

摘要: In type-II superconductors (Fetter & Hohenberg, 1969), magnetic fields penetrate into as quantized flux lines with quanta φ0 = hc/2e, where h is Planck constant, c velocity of light, e electron’s charge. Around a line, pair potential ∆(r) Cooper has vortex structure, phase winding 2π reflecting screening super-current around line. At the core, amplitude |∆(r)| suppressed, and low energy excitations appear within superconducting gap electronic states. Vortex physics makes important roles in study unconventional superconductors, because characters hidden uniform state at zero field vortices. For example, anisotropic on Fermi surface momentum space, states show real-space anisotropy local density (LDOS) N(E, r) core. The core image observed by scanning tunneling microscopy (STM) (Hess et al., 1990; Nishimori 2004). cores, zero-energy level are seen star shape tails extending toward node or weak-gap directions (Hayashi 1996; 1997; Ichioka Schopohl Maki, 1995). From spatial average states, we can estimate (DOS) N(E 0), which determines temperature (T) behaviors physical quantities. Due to differences 0) shows different (H) dependences. These H-dependences studied identify pairing symmetry experiments for such as, specific heat (Moler 1994; Nohara 1999), thermal conductivity, paramagnetic susceptibility (Zheng 2002). H-dependence C(H) often used distinguish presence nodes potential. As Sommerfeld coefficient γ(H) ≡ limT→0 C(H)/T, ∝ H s-wave full gap, √ Volovik effect d-wave line (Ichioka 1999a;b; Miranovic 2003; Nakai 2004; Volovik, 1993). curves expected smoothly recover normal value towards upper critical Hc2. However, some heavy fermion deviates from these curves. CeCoIn5, convex curves, i.e., Hα (α > 1) higher fields(Ikeda 2001). This behavior not understood only effects symmetry. A similar also UBe13 (Ramirez 1999). experimental data magnetization curve Mtotal(H) CeCoIn5 fields, instead conventional concave (Tayama an 10