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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, twisted bi-layer graphene and WSe$_2$, is linear in temperature $T$ as well as in a magnetic field $H$. Scattering of fermions by the excitations of a time-reversal odd polar vector field ${\bf Ω}$ characterizing loop-current fluctuations has been shown to give a linear in T resistivity and other anomalous properties in the cuprates. An extension of this theory to an applied magnetic field is presented. Magnetic field is shown to generate vortices in the field ${\bf Ω}$ proportional to $H_z$, the component orthogonal to the conducting planes. The elastic scattering of fermions from the vortices gives a resistivity linear in $H_z$. The coefficient of the linear in $H_z$ resistivity is predicted to vary as the marginal fermi-liquid susceptibility $\propto \ln(\frac{ω_c}{T})$ at criticality. Quantitative comparison with experiments is presented.