We argue that in order to study the magneto-transport in a relativistic Weyl fluid, it is needed to take into account the associated quantum corrections, namely the side-jump effect, at least to second order. To this end, we impose Lorentz invariance to a system of free Weyl fermions in the presence of the magnetic field and find the second order correction to the energy dispersion. By developing a scheme to compute the integrals in the phase space, we show that the mentioned correction has non-trivial effects on the thermodynamics of the system. Specifically, we compute the expression of the negative magnetoresistivity in the system from the enthalpy density in equilibrium. Then in analogy with Weyl semimetal, in the framework of the chiral kinetic theory and under the relaxation time approximation, we explicitly compute the magneto-conductivities, at low temperature limit (T ≪ µ). We show that the conductivities obey a set of Ward identities which follow from the generating functional including the Chern-Simons part. * abbasi@ipm.ir † ftaghinavaz@ipm.ir ‡ omid.

We consider a fluid with weakly broken time and translation symmetries. We assume the fluid also possesses a U (1) symmetry which is not only weakly broken, but is anomalous. We use the second order chiral quasi-hydrodynamics to compute the magneto conductivities of this fluid in the presence of a weak magnetic field. Analogous to the electrical and thermoelectric conductivities, it turns out that the thermal conductivity depends on the coefficient of mixed gauge-gravitational anomaly. Our results can be applied to the hydrodynamic regime of every arbitrary system, once the thermodynamics of that system is known. By applying them to a free system of Weyl fermions at low temperature limit T ≪ µ, we find that our fluid is Onsager reciprocal if the relaxation in all energy, momentum and charge channels occurs at the same rate. In the high temperature limit T ≫ µ, we consider a strongly coupled SU (N c ) gauge theory with N c ≫ 1. Its holographic dual in thermal equilibrium is a magnetized charged brane from which, we compute the thermodynamic quantities and subsequently evaluate the conductivities in gauge theory. On the way, we show that analogous to the weak regime in the system of Weyl fermions, an energy cutoff emerges to regulate the thermodynamic quantities in the strong regime of boundary gauge theory. From this gravity background we also find the coefficients of chiral magnetic effect in agreement with the well-known result of Son-Surowka. * abbasi@ipm.ir † armin.ghazi@physics.

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In the electron dynamics in quantum matter, the Berry curvature of the electronic wave function provides the artificial magnetic field (AMF) in momentum space, which leads to non-trivial contributions to transport coefficients. It is known that in the presence of electron-electron and/or electron-phonon interactions, there is an extra contribution to the electron dynamics due to the artificial electric field (AEF) in momentum space. In this work, we construct hydrodynamic equations for the electrons in time-reversal invariant but inversion-breaking systems and find the novel hydrodynamic coefficients related to the AEF. Furthermore, we investigate the novel linear and non-linear transport coefficients in presence of the AEF.

Shift current and second harmonic generation (SHG) are nonlinear optical responses that are often used for photovoltaic effect and the detection of subtle symmetry breaking patterns in materials. It has been recently shown that topological semimetals such as Weyl semimetals with broken inversion symmetry can generate large nonlinear optical responses. In this paper, we investigate both shift current and SHG in a class of topological nodal line semimetal (NLSM) systems with broken inversion symmetry, which may arise intrinsically or via an applied electric field. It is shown that certain classes of NLSM systems offer more singular shift current and SHG in comparison to the well-known Weyl semimetal systems.