### セミナー概要

日時：2013年1月18日（金）16:00~
講師：Shunji Tsuchiya (Tokyo University of Science)

タイトル：Collective modes of attractive Dirac fermions: Higgs mode, Cooperons, and excitons

Motivated by recent developments of graphene physics and cold atom experiments in optical lattices, we study collective modes of attractive fermions on the two-dimensional honeycomb lattice. The attractive Hubbard model on the honeycomb lattice was found to exhibit a quantum phase transition at half-filling between a semimetal with massless Dirac fermion excitations and a simple s-wave superfluid (superconducting) phase. We calculate collective modes in superfluid phase as well as in normal phase in the vicinity of the quantum critical point within the generalized random phase approximation. We find evidence for an undamped Higgs amplitude mode below the two-particle continuum, together with a gapless Anderson-Bogoliubov (AB) mode in the superfluid phase. As approaching the quantum critical point from the superfluid phase, the energy gap of the Higgs mode decreases and eventually the Higgs mode and AB mode become degenerate at the quantum critical point. In the normal phase, we find that these collective modes split into Cooperon and exciton excitations that are particle-particle and particle-hole bound states, respectively. We discuss possibilities of observing these collective modes in cold atom experiments.