Quantum Mott Transition and Multi-Furcating Criticality

Phenomenological theory of the Mott transition is presented. When the critical temperature of the Mott transition is much higher than the quantum degeneracy temperature, the transition is essentially described by the Ising universality class. Below the critical temperature, phase separation or first-order transition occurs. However, if the critical point is involved in the Fermi degeneracy region, a marginal quantum critical point appears at zero temperature. The originally single Mott critical point generates subsequent many unstable fixed points through various Fermi surface instabilities induced by the Mott criticality characterized by the diverging charge susceptibility or doublon susceptibility. This occurs in marginal quantum-critical region. Charge, magnetic and superconducting instabilitites compete severely under these critical charge fluctuations. The quantum Mott transition triggers multi-furcating criticality, which goes beyond the conventional concept of multicriticality in quantum phase transitions. Near the quantum Mott transition, the criticality generically drives growth of inhomogeneous structure in the momentum space with singular points of flat dispersion on the Fermi surface. The singular points determine the quantum dynamics of the Mott transition by the dynamical exponent $z=4$. We argue that many of filling-control Mott transitions are classified to this category. Recent numerical results as well as experimental results on strongly correlated systems including transition metal oxides, organic materials and $^3$He layer adsorbed on a substrate are consistently analyzed especially in two-dimensional systems.Comment: 28 pages including 2 figure

Gap symmetry and structure of Fe-based superconductors

The recently discovered Fe-pnictide and chalcogenide superconductors display low-temperature properties suggesting superconducting gap structures which appear to vary substantially from family to family, and even within families as a function of doping or pressure. We propose that this apparent nonuniversality can actually be understood by considering the predictions of spin fluctuation theory and accounting for the peculiar electronic structure of these systems, coupled with the likely 'sign-changing s-wave' (s\pm) symmetry. We review theoretical aspects, materials properties and experimental evidence relevant to this suggestion, and discuss which further measurements would be useful to settle these issues.Comment: 86 pages, revie

From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics

This review gives a rather general discussion of high temperature superconductors as an example of a strongly correlated material. The argument is made that in view of the many examples of unconventional superconductors discovered in the past twenty years, we should no longer be surprised that superconductivity emerges as a highly competitive ground state in systems where Coulomb repulsion plays a dominant role. The physics of the cuprates is discussed, emphasizing the unusual pseudogap phase in the underdoped region. It is argued that the resonating valence bond (RVB) picture, as formulated using gauge theory with fermionic and bosonic matter fields, gives an adequate physical understanding, even though many details are beyond the powers of current calculational tools. The recent discovery of quantum oscillations in a high magnetic field is discussed in this context. Meanwhile, the problem of the quantum spin liquid (a spin system with antiferromagnetic coupling which refuses to order even at zero temperature) is a somewhat simpler version of the high $T_c$ problem where significant progress has been made recently. It is understood that the existence of matter fields can lead to de-confinement of the U(1) gauge theory in 2+1 dimensions, and novel new particles (called fractionalized particles), such as fermionic spinons which carry spin ${1\over 2}$ and no charge, and gapless gauge bosons can emerge to create a new critical state at low energies. We even have a couple of real materials where such a scenario may be realized experimentally. The article ends with answers to questions such as: what limits $T_c$ if pairing is driven by an electronic energy scale? why is the high $T_c$ problem hard? why is there no consensus? and why is the high $T_c$ problem important?Comment: Submitted as "Key Issue" essay for Report of Progress in Physics; v2: References are added and typos correcte

Cooperative localization-delocalization in the high Tc cuprates

The intrinsic metastable crystal structure of the cuprates results in local dynamical lattice instabilities, strongly coupled to the density fluctuations of the charge carriers. They acquire in this way simultaneously both, delocalized and localized features. It is responsible for a partial fractioning of the Fermi surface, i.e., the Fermi surface gets hidden in a region around the anti-nodal points, because of the opening of a pseudogap in the normal state, arising from a partial charge localization. The high energy localized single-particle features are a result of a segregation of the homogeneous crystal structure into checker-board local nano-size structures, which breaks the local translational and rotational symmetry. The pairing in such a system is dynamical rather than static, whereby charge carriers get momentarily trapped into pairs in a deformable dynamically fluctuating ligand environment. We conclude that the intrinsically heterogeneous structure of the cuprates must play an important role in this type of superconductivity.Comment: 14 pages, 8 figures, Proceedings of the "International Conference on Condensed Matter Theories", Quito, 2009 Int. J. Mod. Phys. B 2010 (Accepted