Relativistic corrections in magnetic systems

Crépieux, Adeline; Bruno, P.

doi:10.1103/physrevb.64.094434

Cited by 138 publications

(245 citation statements)

References 25 publications

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“…Later on, Streda's separation of the offdiagonal conductivity in two parts has been rederived by using the Kubo formalism. 22 As we see from Eq. ͑20͒, the contribution yx …”

Section: Discussionsupporting

confidence: 58%

Anomalous Hall effect in a two-dimensional electron gas

et al. 2007

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The anomalous Hall effect in a magnetic two-dimensional electron gas with Rashba spin-orbit coupling is studied within the Kubo-Streda formalism in the presence of pointlike potential impurities. We find that all contributions to the anomalous Hall conductivity vanish to leading order in disorder strength when both chiral subbands are occupied. In the situation that only the majority subband is occupied, all terms are finite in the weak scattering limit and the total anomalous Hall conductivity is dominated by skew scattering. We compare our results to previous treatments and resolve some of the discrepancies present in the literature.

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“…Later on, Streda's separation of the offdiagonal conductivity in two parts has been rederived by using the Kubo formalism. 22 As we see from Eq. ͑20͒, the contribution yx …”

Section: Discussionsupporting

confidence: 58%

Anomalous Hall effect in a two-dimensional electron gas

et al. 2007

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“…There are, however, other contributions to the Hall effect that are ignored in such a theory including anomalous velocity 12,17,18,26,27 and the side-jump 6,[28][29][30][31][32][33] effects. The presence of these additional contributions is directly linked to induced nonzero interband elements of the density matrix, in other words, the interband coherence, as recognized since the work of Luttinger and Kohn.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach

et al. 2007

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The anomalous Hall effect ͑AHE͒ is a consequence of spin-orbit coupling in a ferromagnetic metal and related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder contributions to the AHE are difficult to treat systematically using a semiclassical Boltzmann equation approach, even when weak localization corrections are disregarded. In this article we explicitly demonstrate the equivalence of an appropriately modified semiclassical transport theory which includes anomalous velocity and side-jump contributions and microscopic Kubo-Streda perturbation theory, with particular unconventional contributions in the semiclassical theory identified with particular Feynman diagrams when calculations are carried out in a band-eigenstate representation. The equivalence we establish is verified by explicit calculations for the case of the two-dimensional Dirac model Hamiltonian relevant to graphene.

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“…However, it has not been used often in numerical calculations because of the complications of dealing with an integration in energy. Instead, it is possible to perform analytical integrations by parts [26] to obtain a more treatable expression for the static conductivity at zero temperature, which became known as the Kubo-Streda formula [27]. For the diagonal elements of the conductivity tensor (α = β), the integration leads to the Kubo-Greenwood formula [15].…”

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confidence: 99%

“…The expression above was first obtained by Bastin and collaborators in 1971 [1] and later generalized for any independent electron approximation [26]. However, it has not been used often in numerical calculations because of the complications of dealing with an integration in energy.…”

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confidence: 99%

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

2015

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We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation [1]. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.PACS numbers: 71.23. An,72.15.Rn,71.30.+h One of the most important experimental probes in condensed matter physics is the electrical response to an external electrical field. In addition to the longitudinal conductivity, in specific circumstances, a system can present a transverse conductivity under an electrical perturbation. The Hall effect [2] and the anomalous Hall effect in magnetic materials [3] are two examples of this type of response. Paramagnetic materials with spin-orbit interaction can also present transverse spin currents [4]. There are also the quantized versions of the three phenomena: while the quantum Hall effect (QHE) was observed more than 30 years ago [5], the quantum spin Hall effect (QSHE) and the quantum anomalous Hall effect (QAHE) could only be observed [6, 7] with the recent discovery of topological insulators, a new class of quantum matter [8].In the linear response regime, the conductivity tensor can be calculated using the Kubo formalism [9]. The Hall conductivity can be easily obtained in momentum space in terms of the Berry curvature associated with the bands [10]. The downside of working in momentum space, however, is that the robustness of a topological state in the presence of disorder can only be calculated perturbatively [11]. Real-space implementations of the Kubo formalism for the Hall conductivity, on the other hand, allow the incorporation of different types of disorder in varying degrees, while providing flexibility to treat different geometries. Real-space techniques, however, normally require a large computational effort. This has generally restricted their use to either small systems at any temperature [12,13], or large systems at zero temperature [14].In this Letter, we propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula [1] and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method [16]. There are few numerical methods that use Chebyshev expansions to calculate the longitudinal DC conductivity [17][18][19][20] and transverse conductivity [14,21] at zero temperature. An advantage of our approach is the possibility of obtaining both conductivities for large systems in a single calculation step, independe...

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Relativistic corrections in magnetic systems

Cited by 138 publications

References 25 publications

Anomalous Hall effect in a two-dimensional electron gas

Anomalous Hall effect in a two-dimensional electron gas

Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter

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