Glide reflection symmetry, Brillouin zone folding and superconducting pairing for the P4/nmmP4/nmm space group

Motivated by the studies of the superconducting pairing states in the iron-based superconductors, we analyze the effects of Brillouin zone folding procedure from a space group symmetry perspective for a general class of materials with the $P4/nmm$ space group. The Brillouin zone folding amounts to working with an effective one-Fe unit cell, instead of the crystallographic two-Fe unit cell. We show that the folding procedure can be justified by the validity of a glide reflection symmetry throughout the crystallographic Brillouin zone and by the existence of a minimal double degeneracy along the edges of the latter. We also demonstrate how the folding procedure fails when a local spin-orbit coupling is included although the latter does not break any of the space group symmetries of the bare Hamiltonian. In light of these general symmetry considerations, we further discuss the implications of the glide reflection symmetry for the superconducting pairing in an effective multi-orbital $t-J_{1}-J_{2}$ model. We find that the $P4/nmm$ space group symmetry allows only pairing states with even parity under the glide reflection and zero total momentum

Kondo effect due to a hydrogen impurity in graphene: A multichannel Kondo problem with diverging hybridization

We consider the Kondo effect, arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the C3 rotation symmetry, and we retain only the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) ∝1/[|ω|ln2(Λ/|ω|)] near the Dirac point ω→0 even though the bulk density of states vanishes linearly. We study the resulting three-impurity multichannel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-1/2 doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity

Reputation formation and reinforcement of biases in a post-truth world

A potentially biased expert transmits information about a binary state to a decision maker over two periods. The expert is imperfectly informed and is concerned about her reputation for unbiasedness. The decision maker wants his action to match the state in every period, but the true state is never observed. So, he updates his belief about the state by considering both the expert's report and her reputation. The expert now faces two competing incentives - to improve her reputation by disavowing potential bias, and to shift the decision maker's future belief about the state. The game has several novel equilibria. I show that a biased expert may never be disciplined to be honest, while both unbiased and biased experts may lie to signal unbiasedness. A report that disavows a bias is typically seen as conforming to norms, but here it could also arise from reputational incentives to be contrarian