Effective field theory of a topological insulator and the Foldy–Wouthuysen transformation

Dayi, Omer Faruk; Elbistan, Mahmut; Yunt, Elif

doi:10.1016/j.aop.2011.11.013

Cited by 8 publications

(18 citation statements)

References 37 publications

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“…In the µ ≫ m limit it yields the topological spin Chern number [26,27] as it was discussed in Ref. [28]. This limit actually is equivalent to consider massless case given in Refs.…”

Section: Introductionmentioning

confidence: 93%

Spin currents of charged Dirac particles in rotating coordinates

Dayi

Yunt

2018

Annals of Physics

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The semiclassical Boltzmann transport equation of charged, massive fermions in a rotating frame of reference, in the presence of external electromagnetic fields is solved in the relaxation time approach to establish the distribution function up to linear order in the electric field in rotating coordinates, centrifugal force and the derivatives. The spin and spin current densities are calculated by means of this distribution function at zero temperature up to the first order. It is shown that the nonequilibrium part of the distribution function yields the spin Hall effect for fermions constrained to move in a plane perpendicular to the angular velocity and magnetic field. Moreover it yields an analogue of Ohm's law for spin currents whose resistivity depends on the external magnetic field and the angular velocity of the rotating frame. Spin current densities in three-dimensional systems are also established.

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“…In the µ ≫ m limit it yields the topological spin Chern number [26,27] as it was discussed in Ref. [28]. This limit actually is equivalent to consider massless case given in Refs.…”

Section: Introductionmentioning

confidence: 93%

Spin currents of charged Dirac particles in rotating coordinates

Dayi

Yunt

2018

Annals of Physics

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“…We can express (45) in terms of the Berry curvature G αβ M N (5) and enclose the monopole with the compact surface S d−1…”

Section: + 1 Dimensional Weyl Hamiltonian and Monopolesmentioning

confidence: 99%

Weyl semimetal and topological numbers

Elbistan

2017

Int. J. Mod. Phys. B

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Generalized Dirac monopoles in momentum space are constructed in even d + 1 dimensions from the Weyl Hamiltonian in terms of Green's functions. In 3 + 1 dimensions, the (unit) charge of the monopole is equal to both the winding number and the Chern number, expressed as the integral of the Berry curvature. Based on the equivalence of the Chern and winding numbers, a chirally coupled and Lorentz invariant field theory action is studied for the Weyl semimetal phase. At the one loop order, the effective action yields both the chiral magnetic effect and the anomalous Hall effect. The Chern number appears as a coefficient in the conductivity, thus emphasizes the role of topology. The anomalous contribution of chiral fermions to transport phenomena is reflected as the gauge anomaly with the Pfaffian invariant (E · B). Relevance of monopoles and Chern numbers for the semiclassical chiral kinetic theory is also discussed.1 Recently, a fascinating condensed matter realization of chiral fermions has been proposed. This new topological phase is called the Weyl semimetal [1][2][3]. Its band structure has linear crossings at the so-called Weyl points where the system is effectively represented by the 2 × 2 Weyl Hamiltonian. It is possible to derive a Berry potential [4] by considering the eigenstates of the Weyl Hamiltonian. The nontrivial topological properties of this novel phase [1,3,5] is reflected by the flux of the Berry potential which is itself written as a Chern number (see [6,7] as a recent application to chiral fermions).There are both theoretical [1-3, 8-15] and experimental [16-21] studies on Weyl semimetals. In their specific model Zyuzin and Burkov [10] showed that the topological transport properties of the Weyl semimetal, e.g., the chiral magnetic effect (CME) (see [22] and the references therein) and the anomalous Hall effect (AHE) [23], are related to the chiral anomaly [24][25][26].Field theory models of Weyl semimetal [10][11][12]14] are constructed by means of Dirac spinors coupled to a Lorentz symmetry breaking b µ vector [27,28]. Axial coupling γ 5 b µ is necessary to prevent the Weyl nodes to annihilate each other. However, these studies did not refer to the Chern number and its function, therefore the role of topology is not explicit. 2In this study we first investigate the relations between topological numbers associated with the 3 + 1 dimensional Weyl Hamiltonian. We construct a Dirac monopole of unit charge in momentum space in terms of the Green's function of the Weyl Hamiltonian. On the 2-dimensional boundary, the charge itself can be expressed as the Chern character of the Berry potential. It is also equal to the winding number of the Green's function.Then, focusing on a single isolated node, we consider a chirally coupled, Lorentz invariant field theory model for the type-I Weyl semimetal where the dispersion relation and quasiparticles respect the emergent Lorentz symmetry [29][30][31]. By integrating out the fermionic degrees of freedom via Feynman path integration, we relate the winding numb...

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“…For example, it has been a useful tool to describe fundamental and excited states of atomic nuclei [3], some interactions with gravitational and torsion fields [4][5][6][7][8]. Also, it was considered in scenarios with Lorentz symmetry violation [9][10][11][12], accelerated frames [13,14], topological defects [15,16] and topological insulators [17,18].…”

Section: Introductionmentioning

confidence: 99%

Effective theories and non-minimal couplings in low-dimensional systems

Campos,

Ospedal

2020

Preprint

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Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy-Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields.Next, we establish some comparisons and analyse particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell-Chern-Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.

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Effective field theory of a topological insulator and the Foldy–Wouthuysen transformation

Cited by 8 publications

References 37 publications

Spin currents of charged Dirac particles in rotating coordinates

Spin currents of charged Dirac particles in rotating coordinates

Weyl semimetal and topological numbers

Effective theories and non-minimal couplings in low-dimensional systems

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