Quantum-Critical Resistivity of Strange Metals in a Magnetic Field

Resistivity in the quantum-critical fluctuation region of several metallic compounds such as the cuprates, the heavy fermions, Fe chalogenides and pnictides, Moiré bilayer graphene, and WSe_{2} is linear in temperature T as well as in the magnetic field H_{z} perpendicular to the planes. Scattering of fermions by the fluctuations of a time-reversal odd polar vector field Ω has been shown to give a linear in T resistivity and other marginal Fermi-liquid properties. An extension of this theory to an applied magnetic field is presented. A magnetic field is shown to generate a density of vortices in the field Ω proportional to H_{z}. The elastic scattering of fermions from the vortices gives a resistivity linear in H_{z} with the coefficient varying as the marginal Fermi-liquid susceptibility ln(ω_{c}/T). Quantitative comparison with experiments is presented for cuprates and Moiré bilayer graphene.