Ubiquitous V-shape density of states in mixed state of clean limit type II superconductors; STM experiment and theory

Much attention has been focused on exotic super- conductors, ranging from high Tc cuprates, Ce and U based heavy Fermion materials, filled skutterdites such as PrOs4Sb12 to cobaltites NaxCoO2� yH2O(1, 2). The identification of the Cooper-pair symmetry consists of two parts; its parity and the gap structure. The former is responsible for the spin structure of a pair which is either singlet or triplet. This can be probed by directly measuring the spin susceptibility through NMR Knight shift experiment under an applied field. The latter gap structure is related to the orbital symmetry of a Cooper pair. This can be probed by thermodynamic measure- ments via a variety of experimental methods, such as temperature (T) dependence of specific heat C(T), ther- mal conductivity �(T) or nuclear relaxation time T1(T) in NMR-NQR experiments. The basic principle of this identification for the gap structure is based on the fact that the energy (E) de- pendence of the density of states (DOS) N(E) near the Fermi level, which characterizes low-lying excitations of a given gap structure. This N(E) gives rise to a specific power law temperature dependence(2). For example, the line (point) node gap yields a C(T)/T ∼ T(T 2) behavior in specific heat, �(T) ∼ T 2 (T 3) for thermal conduc- tivity and T −1 1 ∼ T 3 (T 5) in nuclear relaxation time at lower T region. This comes from the fact that the den- sity of states is described by a specific functional form; N(E) ∝ |E| for line node and N(E) ∝ E2 for point node, through which a simple power counting rule yields spe- cific power law indices in various quantities. Therefore it is decisive to precisely understand the DOS form N(E) in order to identify the gap structure. We have attained a lot of information of the pairing symmetry in various superconductors by this way(2).