We introduce the concept of the {em odd-frequency} Bose Einstein Condensate (BEC), characterized by the odd frequency/time two-boson expectation value. To illustrate the concept of odd frequency BEC we present simple classification of pair boson cond
ensates that explicitly permits this state. We point qualitative differences of odd-frequency BEC with conventional BEC and introduce the order parameter and wave function for the odd-frequency BEC.
A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger
Hamiltonian. This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call Dirac materials. In order to establish this class of materials, we illustrate how Dirac fermions emerge in multiple entirely different condensed matter systems and we discuss how Dirac fermions have been identified experimentally using electron spectroscopy techniques (angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy). As a consequence of their common low-energy excitations, this diverse set of materials shares a significant number of universal properties in the low-energy (infrared) limit. We review these common properties including nodal points in the excitation spectrum, density of states, specific heat, transport, thermodynamic properties, impurity resonances, and magnetic field responses, as well as discuss many-body interaction effects. We further review how the emergence of Dirac excitations is controlled by specific symmetries of the material, such as time-reversal, gauge, and spin-orbit symmetries, and how by breaking these symmetries a finite Dirac mass is generated. We give examples of how the interaction of Dirac fermions with their distinct real material background leads to rich novel physics with common fingerprints such as the suppression of back scattering and impurity-induced resonant states.
We consider the theory of Kondo effect and Fano factor energy dependence for magnetic impurity (Co) on graphene. We have performed a first principles calculation and find that the two dimensional $E_1$ representation made of $d_{xz},d_{yz}$ orbitals
is likely to be responsible for the hybridization and ultimately Kondo screening for cobalt on graphene. There are few high symmetry sites where magnetic impurity atom can be adsorbed. For the case of Co atom in the middle of hexagon of carbon lattice we find anomalously large Fano $q$-factor, $qapprox 80$ and strongly suppressed coupling to conduction band. This anomaly is a striking example of quantum mechanical interference related to the Berry phase inherent to graphene band structure.
We focus on inelastic neutron scattering in $URu_2Si_2$ and argue that observed gap in the fermion spectrum naturally leads to the spin feature observed at energies $omega_{res} = 4-6 meV$ at momenta at $bQ^* = (1pm 0.4, 0,0)$. We discuss how spin fe
atures seen in $URu_2Si_2$ can indeed be thought of in terms of {em spin resonance} that develops in HO state and is {em not related} to superconducting transition at 1.5K. In our analysis we assume that the HO gap is due to a particle-hole condensate that connects nested parts of the Fermi surface with nesting vector $bf{Q}^* $. Within this approach we can predicted the behavior of the spin susceptibility at $bQ^*$ and find it to be is strikingly similar to the phenomenology of resonance peaks in high-T$_c$ and heavy fermion superconductors. The energy of the resonance peak scales with $T_{HO}$ $omega_{res} simeq 4 k_BT_{HO}$. We discuss observable consequences spin resonance will have on neutron scattering and local density of states.
Superconducting excitations -- Bogoliubov quasiparticles -- are the quantum mechanical mixture of negatively charged electron (-e) and positively charged hole (+e). We propose a new observable for Angular Resolved Photoemission Spectroscopy (ARPES) s
tudies that is the manifestation of the particle-hole entanglement of the superconducting quasiparticles. We call this observable a {em Bogoliubov angle}. This angle measures the relative weight of particle and hole amplitude in the superconducting (Bogoliubov) quasiparticle. We show how this quantity can be measured by comparing the ratio of spectral intensities at positive and negative energies.
Recent observation of proximity effect cite{Morpurgo:2007} has ignited interest in superconductivity in graphene and its derivatives. We consider Ca-intercalated graphene bilayer and argue that it is a superconductor, and likely with a sizeable $T_{c
}$. We find substantial and suggestive similarities between Ca-intercalated bilayer (C$_{6}$CaC$_{6}$), and CaC$_{6} $, an established superconductor with $T_{c}$ = 11.5 K. In particular, the nearly free electron band, proven to be instrumental for superconductivity in intercalated graphites, does cross the chemical potential in (C$_{6}$CaC$% _{6}$), despite the twice smaller doping level, satisfying the so-called textquotedblleft Cambridge criteriontextquotedblright . Calculated properties of zone-center phonons are very similar to those of CaC$%_{6}.$ This suggests that the critical temperature would probably be on the same scale as in CaC$_{6}$.
