Anomalous Hall effect in a two-dimensional electron gas

Nunner, Tamara S.; Sinitsyn, Nikolai A.; Borunda, Mario F.; Dugaev, V. K.; Kovalev, Alexey A.; Abanov, Ar.; Timm, Carsten; Jungwirth, T.; Inoue, Jun; MacDonald, Allan H.; Sinova, Jairo

doi:10.1103/physrevb.76.235312

Cited by 83 publications

(101 citation statements)

References 24 publications

(63 reference statements)

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“…In the super clean limit (τ → ∞), the above value agrees with the previous result 11 . In this paper, we are considering the effect of inhomogeneous longitudinal electric field, i.e., q E q on the Anomalous Hall conductivity.…”

Section: Resultssupporting

confidence: 92%

“…A number of studies on AHC have been performed within the model of two-dimensional ferromagneticRashba gas, using the Kubo formalism 6,[8][9][10][11][12][13][14] ,the Keldysh technique 6,15,16 , and the semiclassical treatment of Boltzmann transport equation 17,18 . According to the studies in Kubo formalism, the magnitude of AHC is sensitive to whether only one or both the subbands are occupied by the electrons, i.e., whether or not the Fermi level is situated below the band-gap created by exchange energy, ∆ ex .…”

Section: Introductionmentioning

confidence: 99%

“…On the contrary, all these terms are finite for ǫ F < ∆ ex . A comprehensive analysis of these works can be found in the detailed study of Nunner et al 11 . Using the Keldysh technique in a T-matrix approximation, Onoda et al 15,19 , however, find a strong SS contribution that leads to non-zero AHC even when ǫ F > ∆ ex .…”

Section: Introductionmentioning

confidence: 99%

“…There is no controversy, however, in the metallic weakscattering regime (ǫ F τ > 1), where τ is the mean scattering time of an electron. When the Fermi level goes far above the band gap (ǫ F > ∆ ex ), i.e., when both the chiral subbands are occupied, the AHC vanishes 5,7,11,20 , making this regime a somewhat uninteresting one. We however note that AHE is intimately related to spin hall effect 21,22 and there are instances of enhancement of spinHall conductivity 23 and occurrence of a induced transverse force 24 due to inhomogeneity of the applied electric field.…”

Section: Introductionmentioning

confidence: 99%

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Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

Sensharma

Mandal

2012

Phys. Rev. B

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It is known that the anomalous Hall conductivity (AHC) in a disordered two dimensional electron system with Rashba spin-orbit interaction and finite ferromagnetic spin-exchange energy is zero in the metallic weak-scattering regime because of the exact cancellation of the bare-bubble contribution by the vertex correction. We study the effect of inhomogeneous longitudinal electric field on the AHC in such a system. We predict that AHC increases from zero (at zero wavenumber), forms a peak, and then decreases as the wavenumber for the variation of electric field increases. The peakvalue of AHC is as high as the bare-buble contribution. We find that the wave number, q, at which the peaks occur is the inverse of the geometric mean of the mean free path of an electron and the spin-exchange length scale. Although the Rashba energy is responsible for the peak-value of AHC, the peak position is independent of it.

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Section: Resultssupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

Sensharma

Mandal

2012

Phys. Rev. B

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“…Bending of the spectrum due to quadratic terms removes the nontrivial total Berry phase but doubles the Fermi surface. This significantly complicates the calculation of the Hall conductivity [21] as compared to the massive Dirac model considered here. Nevertheless, the X and Ψ diagrams must be also included in σ xy within these general models.…”

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confidence: 98%

Anomalous Hall effect with massive Dirac fermions

Ado¹,

Дмитриев²,

Ostrovsky³

et al. 2015

EPL

122

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-Anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization. Generally, there are three mechanisms contributing to anomalous Hall conductivity: intrinsic, side jump, and skew scattering. The standard diagrammatic approach to the anomalous Hall effect is limited to computation of ladder diagrams. We demonstrate that this approach is insufficient. An important additional contribution comes from diagrams with a single pair of intersecting disorder lines. This contribution constitutes an inherent part of skew scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity. We argue that this statement is general and applies to all models of anomalous Hall effect. We illustrate it by an explicit calculation for two-dimensional massive Dirac fermions with weak disorder. In this case, inclusion of the diagrams with crossed impurity lines reverses the sign of the skew scattering term and strongly suppresses the total Hall conductivity at high electron concentrations.Many ferromagnetic materials exhibit a finite Hall effect, i.e. transverse voltage in response to a current, without applying external magnetic field. This phenomenon is commonly referred to as the anomalous Hall effect (AHE) [1]. Two important ingredients of AHE are magnetization and spin-orbit interaction. The former breaks timereversal symmetry and exerts a force acting on electron spins while the latter couples the spins to orbital degrees of freedom thus giving rise to the transport effect.AHE can also occur as a result of valley or isospin polarization rather than ordinary ferromagnetism [2]. The spin-orbit coupling can also be of a more general form as it is, e.g. in graphene [3,4] where the role of spin is played by the sublattice index. An important part of the anomalous Hall signal originates in the Berry curvature thus being of a topological origin [5]. It is, therefore, natural that the discovery of materials like graphene and topological insulators [6,7], which are characterized by non-trivial Berry phase of quasiparticles, has considerably broadened the interest to AHE from both theory and experiment [8][9][10][11][12][13][14].Despite the long history [15][16][17] and high experimental relevance of AHE, its theoretical description is a challenging task often leading to confusions. In modern literature, two common approaches based on the Boltzmann kinetic equation and Kubo-Středa diagrammatic formalism are discussed. Boltzmann equation provides an intuitive quasiclassical approach to the effect [1,18] but requires an accurate account of several mechanisms of Hall conductivity: intrinsic, side-jump, and skew-scattering. Intrinsic AHE is attributed to topological properties of the band [19] and is thus independent of disorder. Skew scattering is due to the asymmetry in the impurity scattering crosssection and side jump refers to the transverse displacement of an electron being scattered. An alternative microscopic Kubo-Středa formalism is more...

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Hydrodynamic approach to two-dimensional electron systems

Narozhny

2022

Riv. Nuovo Cim.

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The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. One such material, graphene, is not only an excellent platform for the experimental realization of the hydrodynamic flow of electrons, but also allows for a controlled derivation of the hydrodynamic equations on the basis of kinetic theory. The resulting hydrodynamic theory of electronic transport in graphene yields quantitative predictions for experimentally relevant quantities, e.g., viscosity, electrical conductivity, etc. Here I review recent theoretical advances in the field, compare the hydrodynamic theory of charge carriers in graphene with relativistic hydrodynamics and recent experiments, and discuss applications of hydrodynamic approach to novel materials beyond graphene.

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Anomalous Hall effect in a two-dimensional electron gas

Cited by 83 publications

References 24 publications

Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

Inhomogeneous longitudinal electric field-induced anomalous Hall conductivity in a ferromagnetic two-dimensional electron gas

Anomalous Hall effect with massive Dirac fermions

Hydrodynamic approach to two-dimensional electron systems

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