The electron-nuclear hyperfine interaction shows up in a variety of phenomena including e.g. NMR studies of correlated states and spin decoherence effects in quantum dots. Here we focus on the hyperfine coupling and the NMR spin relaxation time, T1 in Weyl semimetals. Since the density of states in Weyl semimetals varies with the square of the energy around the Weyl point, a naive power counting predicts a 1/T1T ∼ E 4 scaling with E the maximum of temperature (T ) and chemical potential. By carefully investigating the hyperfine interaction between nuclear spins and Weyl fermions, we find that while its spin part behaves conventionally, its orbital part diverges unusually with the inverse of energy around the Weyl point. Consequently, the nuclear spin relaxation rate scales in a graphene like manner as 1/T1T ∼ E 2 ln(E/ω0) with ω0 the nuclear Larmor frequency. This allows us to identify an effective hyperfine coupling constant, which is tunable by gating or doping, which is relevant for decoherence effect in spintronics devices and double quantum dots where hyperfine coupling is the dominant source of spin-blockade lifting.
We first analyze the recent experimental data on the nuclear spin-lattice relaxation rate of the Weyl semimetal TaP. We argue that its non-monotonic temperature dependence is explained by the temperature dependent chemical potential of Weyl fermions. We also develop the theory of the Knight shift in Weyl semimetals, which contains two counteracting terms. The diamagnetic term follows − ln[W/ max(|µ|, kBT )] with W , µ and T being the high energy cutoff, chemical potential and temperature, respectively, and is always negative. The paramagnetic term scales with µ and changes sign depending on the doping level. Altogether, the Knight shift is predicted to vanish or even change sign upon changing the doping or the temperature, making it a sensitive tool to identify Weyl points. We also calculate the Korringa relation for Weyl semimetals which shows an unusual energy dependence rather than being constant as expected for a non-interacting Fermi system.
Close to the Fermi energy, nodal loop semimetals have a torus-shaped, strongly anisotropic Fermi surface which affects their transport properties. Here we investigate the non-equilibrium dynamics of nodal loop semimetals by going beyond linear response and determine the time evolution of the current after switching on a homogeneous electric field. The current grows monotonically with time for electric fields perpendicular to the nodal loop plane however it exhibits non-monotonical behavior for field orientations aligned within the plane. After an initial non-universal growth ∼ Et, the current first reaches a plateau ∼ E. Then, for perpendicular directions, it increases while for in-plane directions it decreases with time to another plateau, still ∼ E. These features arise from interband processes. For long times or strong electric fields, the current grows as ∼ E 3/2 t or ∼ E 3 t 2 for perpendicular or parallel electric fields, respectively. This non-linear response represents an intraband effect where the large number of excited quasiparticles respond to the electric field. Our analytical results are benchmarked by the numerical evaluation of the current from continuum and tight-binding models of nodal loop semimetals.
A detailed derivation of the off‐diagonal spin–spin correlation functions of 3D Weyl semimetals in the static ω = 0 limit for small wavevectors at zero temperature is presented. The real part of the spin correlation function is evaluated analytically and follows ln(W/|μ|) behavior, with W and μ being the high‐energy cutoff and chemical potential, respectively. Its imaginary part grows linearly with μ. These quantities are also evaluated using brute force numerical integration, and the numerical data agree convincingly with the analytical result. This work provides the starting point to determine the Knight shift of Weyl semimetals from the hyperfine coupling through the wavevector‐dependent susceptibility.
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