**"Quantum critical metals in d=3+1 dimensions"**

R. Mahajan: D. M. Ramirez, S. Kachru, and S. Raghu; Phys. Rev. B, 09/10/13.

**Abstract**:

We study the problem of disorder-free metals in the vicinity of a quantum critical point in *d*=3+1 dimensions. We begin with perturbation theory in the Yukawa coupling between the electrons and undamped bosons (order-parameter fluctuations) and show that the perturbation expansion breaks down below energy scales where the bosons get substantially Landau damped. Above this scale, however, we find a regime in which low-energy fermions obtain an imaginary self-energy that varies linearly with frequency, realizing the “marginal Fermi liquid” phenomenology [Varma *et al.*, Phys. Rev. Lett. **63**, 1996 (1989)]. We discuss a large-*N* theory in which the marginal Fermi liquid behavior is enhanced while the role of Landau damping is suppressed, and show that quasiparticles obtain a decay rate parametrically larger than their energy.