*Harvard* *Condensed Matter Theory Seminars*

**Type-IV Superconductivity and Dimensional Crossovers in a Magnetic Field**

- My talk consists of two parts. In the first part, type-IV superconductivity phenomenon is suggested, where type-IV superconductor is defined as d(s)-wave singlet superconductor at H=0 and in Meissner phase, which demonstrates singlet-triplet mixed order parameter in vortex phase. This phenomenon is shown to be general and based on careful account for spin-splitting paramagnetic effects and related symmetry properties of superconducting order parameter and, therefore, does not depend on microscopic mechanism of superconductivity. It is shown that singlet-triplet mixing effects are expected to be of the order of unity in such modern superconductors as high-Tc, organic, and MgB2 materials.

In the second part, the unified theory of magnetic phenomena in low-dimensional organic conductors and superconductors, which is based on an idea about different types of 3D ->2D and 3D ->1D->2D dimensional crossovers for some many-body and one-body effects, is suggested. This theory explains such unique experimentally observed phenomena as field-induced spin- and charge-density-wave phase diagrams and related 3D QHE, superconductivity surviving at ultra-high magnetic fields, H >> Hc2, Magic Angles effects, Interference Commensurate, Danner-Chaikin, and other magnetic and angular oscillations.

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