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Register a new userSensitivity of anomalous Hall effect to disorder correlations
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Both longitudinal and anomalous Hall conductivity are computed in the model of two-dimensional Dirac fermions with a mass in the presence of arbitrary correlated weak disorder. The anomalous Hall conductivity is shown to be highly sensitive to the correlation properties of the random potential, such as the correlation length, while it remains independent of the integral disorder strength. This property extends beyond the Dirac model making the anomalous Hall effect an interesting tool to probe disorder correlations.
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We consider the Anomalous Hall Effect (AHE) in thin disordered ferromagnetic films. Using a microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling, we develop a general formulation for strong, finite range impurity scattering. Explicit calculations are done within a short range but strong impurity scattering to obtain AH conductivities for both the skew scattering and side jump mechanisms. We also evaluate quantum corrections due to interactions and weak localization effects. We show that for arbitrary strength of the impurity scattering, the electron-electron interaction correction to the AH conductivity vanishes exactly due to general symmetry reasons. On the other hand, we find that our explicit evaluation of the weak localization corrections within the strong, short range impurity scattering model can explain the experimentally observed logarithmic temperature dependences in disordered ferromagnetic Fe films.
The anomalous Hall effect in disordered band ferromagnets is considered in the framework of quantum transport theory. A microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling is used. The Hall conductivity is calculated from the Kubo formula for both, the skew scattering and the side-jump mechanisms. The recently discussed Berry phase induced Hall current is also evaluated within the model. The effect of strong impurity scattering is analyzed and it is found to affect the ratio of the non-diagonal (Hall) and diagonal components of the conductivity as well as the relative importance of different mechanisms.
A short review paper for the quantum anomalous Hall effect. A substantially extended one is published as Adv. Phys. 64, 227 (2015).
We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation and calculate all the correlators needed for the localization length expression. We compare our results with numerical results for the special case, where the autocorrelation decays quadratically with distance. We look at disorder ranging from weak to strong disorder, which shows excellent agreement. For the numerical simulation, we introduce a generic method to obtain a random potential with an arbitrary autocorrelation function. The correlated potential is obtained in terms of the convolution between a Wiener stochastic potential and a function of the correlation.
We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering two suitable models of disorder, we explicitly show that disorder correlations can lead to a nonmonotonic behavior of the localization length versus energy. Numerical calculations performed within the transfer-matrix approach and analytical calculations performed within the phase formalism up to order three show excellent agreement and demonstrate the effect. We finally show how the nonmonotonic behavior of the localization length with energy can be observed using expanding ultracold-atom gases.
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