How disorder affects the Berry-phase anomalous Hall conductivity: A reciprocal-space analysis

Bianco, Raffaello; Resta, Raffaele; Souza, Ivo

doi:10.1103/physrevb.90.125153

Cited by 26 publications

(26 citation statements)

References 38 publications

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“…Following the arguments of Ref. [5] we argue here that Eq. (8) may yield the sum of the intrinsic and side-jump contributions to the AHC, while instead it may not include the skew scattering [2].…”

Section: Arxiv:170208885v1 [Cond-matmes-hall] 28 Feb 2017mentioning

confidence: 99%

“…We pause at this point to make contact with Ref. [5], where a supercell approach to dirty metals was actually proposed: in retrospective, the approach of Ref. defined for the clean metal-to some extrinsic contributions of geometrical nature.…”

Section: Arxiv:170208885v1 [Cond-matmes-hall] 28 Feb 2017mentioning

confidence: 99%

“…The standard approach requires an unbounded crystalline sample where the orbitals have the Bloch form; this was extended in Ref. [5] to "dirty" metals in a supercell framework, where the geometric contribution includes some extrinsic effects.Recent work has demonstrated the locality of AHC, although in the insulating case only [6]. One does not require lattice periodicity and reciprocal-space paraphernalia: the AHC can be defined and computed for bounded samples and/or for macroscopically inhomogeneous systems (e.g.…”

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confidence: 99%

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confidence: 99%

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Locality of the anomalous Hall conductivity

Marrazzo

Resta

2017

Phys. Rev. B

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The geometrical intrinsic contribution to the anomalous Hall conductivity (AHC) of a metal is commonly expressed as a reciprocal-space integral: as such, it only addresses unbounded and macroscopically homogeneous samples. Here we show that the geometrical AHC has an equivalent expression as a local property. We define a "geometrical marker" which actually probes the AHC in inhomogeneous systems (e.g. heterojunctions), as well as in bounded samples. The marker may even include extrinsic contributions of geometrical nature.PACS numbers: 72.15.Eb,72.20.My The Hall conductivity is "anomalous" whenever it is nonzero in absence of an applied magnetic field. The phenomenon requires the absence of time-reversal symmetry: it was discovered by Hall himself in 1881 in ferromagnetic metals. The possibility of observing anomalous Hall conductivity (AHC) in insulators was pointed out in 1988 by Haldane, who proposed a model Hamiltonian where the AHC is nonzero and quantized [1]; the AHC value is determined by the topology of the electronic ground state. In metals extrinsic mechanisms are essential to make the longitudinal dc conductivity finite. In absence of timereversal symmetry extrinsic mechanisms contribute to the AHC as well: these go under the name of side-jump and skew-scattering [2]. Since the early 2000s [3,4] it became clear that an intrinsic effect, only dependent on the ground wavefunction of the pristine crystal, provides an important additional contribution to the AHC. The latter contribution is geometrical in nature; its expression is the nonquantized version of the corresponding formula for insulators. In this work we only address the geometrical/topological AHC in metals/insulators, which is customarily expressed as the Fermi-volume integral of the Berry curvature, Eq. (4) below. The standard approach requires an unbounded crystalline sample where the orbitals have the Bloch form; this was extended in Ref. [5] to "dirty" metals in a supercell framework, where the geometric contribution includes some extrinsic effects.Recent work has demonstrated the locality of AHC, although in the insulating case only [6]. One does not require lattice periodicity and reciprocal-space paraphernalia: the AHC can be defined and computed for bounded samples and/or for macroscopically inhomogeneous systems (e.g. heterojunctions). The extension to the metallic case is not obvious, since one of the reasons for the locality of the (quantized) AHC is the r-space exponential decay of the one-body density matrix in insulators ("nearsightedness" [7]). In metals instead such decay is only power-law, which hints to a possibly different behavior. Furthermore the Hall current in insulators may only flow in the edge region, while in metals the current flows through the bulk of the sample as well. Our major result is that even in metals the AHC is a local property: for a bounded sample it can be expressed in terms of the one-body density matrix, evaluated in the sample bulk. We show this by means of simulations on model two-dimensional b...

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Section: Arxiv:170208885v1 [Cond-matmes-hall] 28 Feb 2017mentioning

confidence: 99%

Section: Arxiv:170208885v1 [Cond-matmes-hall] 28 Feb 2017mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Locality of the anomalous Hall conductivity

Marrazzo

Resta

2017

Phys. Rev. B

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“…The gauge of the alloy Hamiltonians is guaranteed to be smooth due to the single set of HDWFs used in the generalized interpolation. If one simply mixes the MLWFs for x = 0 and x = 1, such a smooth gauge is more difficult to achieve [42].…”

Section: A Virtual Crystal Approximation (Vca)mentioning

confidence: 99%

Higher-dimensional Wannier functions of multiparameter Hamiltonians

et al. 2015

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When using Wannier functions to study the electronic structure of multi-parameter Hamiltonians H (k,λ) carrying a dependence on crystal momentum k and an additional periodic parameter λ, one usually constructs several sets of Wannier functions for a set of values of λ. We present the concept of higher dimensional Wannier functions (HDWFs), which provide a minimal and accurate description of the electronic structure of multi-parameter Hamiltonians based on a single set of HDWFs. The obstacle of non-orthogonality of Bloch functions at different λ is overcome by introducing an auxiliary real space, which is reciprocal to the parameter λ. We derive a generalized interpolation scheme and emphasize the essential conceptual and computational simplifications in using the formalism, for instance, in the evaluation of linear response coefficients. We further implement the necessary machinery to construct HDWFs from ab initio within the full-potential linearized augmented plane-wave method (FLAPW). We apply our implementation to accurately interpolate the Hamiltonian of a one-dimensional magnetic chain of Mn atoms in two important cases of λ: (i) the spin-spiral vector q, and (ii) the direction of the ferromagnetic magnetizationm. Using the generalized interpolation of the energy, we extract the corresponding values of magneto-crystalline anisotropy energy, Heisenberg exchange constants, and spin stiffness, which compare very well with the values obtained from direct first principles calculations. For toy models we demonstrate that the method of HDWFs can also be used in applications such as the virtual crystal approximation, ferroelectric polarization and spin torques.

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Berry‐Phase Effect in Single‐Molecule Magnets: Analytical and Numerical Results

Anaya-García

Salgado-Blanco

González

2022

Physica Status Solidi (b)

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Herein, transport signatures of quantum interference on the current through a single‐molecule magnet transistor tunnel coupled to oppositely polarized leads in the presence of a local transverse and longitudinal magnetic field are theoretically and numerically investigated. These calculations are based on a density matrix approach where the ground‐state energy splitting induced by tunneling of the spin between different paths is treated with the aid of perturbation theory. Using this approach, it is shown that it is possible to use an effective Hamiltonian, which describes the Berry‐phase interference as a function of the transverse magnetic field, which completely blocks the current flow when the single‐molecule magnet is placed between oppositely polarized leads. Finally, this effective Hamiltonian is used in an open‐source Python software (QmeQ) that allows us to calculate the current through the single‐molecule magnet with oppositely polarized leads tunnel coupled to the single‐molecule magnet. The analytical results are well reproduced by numerical simulations.

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How disorder affects the Berry-phase anomalous Hall conductivity: A reciprocal-space analysis

Cited by 26 publications

References 38 publications

Locality of the anomalous Hall conductivity

Locality of the anomalous Hall conductivity

Higher-dimensional Wannier functions of multiparameter Hamiltonians

Berry‐Phase Effect in Single‐Molecule Magnets: Analytical and Numerical Results

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