Effective field theories for topological insulators by functional bosonization

Chan, AtMa P. O.; Hughes, Taylor L.; Ryu, Shinsei; Fradkin, Eduardo

doi:10.1103/physrevb.87.085132

Cited by 60 publications

(92 citation statements)

References 122 publications

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“…Based on both low energy effective theory approach and numerical results in a microscopic model of doped topological insulators, we propose two physical consequences of the anomaly, the chiral modes in magnetic vortices, and the magnon-plasmon coupling. An open question is whether it is possible to write down a topological effective field theory to characterize the transport properties of the Weyl semimetals, as in the topological insulators 5,16,37 . Since there are gapless fermions in Weyl semimetals, it is not clear whether a local bosonic effective field theory can be obtained.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Chiral gauge field and axial anomaly in a Weyl semimetal

2013

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Weyl fermions are two-component chiral fermions in (3 + 1)-dimensions. When coupled to a gauge field, the Weyl fermion is known to have an axial anomaly, which means the current conservation of the left-handed and right-handed Weyl fermions cannot be preserved separately. Recently, Weyl fermions have been proposed in condensed matter systems named as "Weyl semi-metals". In this paper we propose a Weyl semi-metal phase in magnetically doped topological insulators, and study the axial anomaly in this system. We propose that the magnetic fluctuation in this system plays the role of a "chiral gauge field" which minimally couples to the Weyl fermions with opposite charges for two chiralities. We study the anomaly equation of this sytem and discuss its physical consequences, including one-dimensional chiral modes in a ferromagnetic vortex line, and a novel plasmon-magnon coupling.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Chiral gauge field and axial anomaly in a Weyl semimetal

2013

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“…This is just the electric-magnetic duality in (2 + 1) dimensions: it plays a role in the bosonization of (2 + 1)-dimensional fermions through the tomographic representation [12,[58][59][60][61] and other approaches [30,31]. In our setting, this duality is just the first-order Hamiltonian description of the relativistic wave equation, that is inherited from the first-order bulk theory.…”

Section: Jhep05(2017)135mentioning

confidence: 93%

“…• That of bosonic theories, also called hydrodynamic approach, dealing with topological gauge theories and their description of braiding relations and boundary excitations [12,[26][27][28][29][30][31].…”

Section: Jhep05(2017)135mentioning

confidence: 99%

Three-dimensional topological insulators and bosonization

Cappelli

Randellini

Sisti

2017

J. High Energ. Phys.

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Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

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“…We have 19) where U in S W Z [U ] is the continuum field U (t, x, y). It remains to evaluate ∂ y S W Z [U ].…”

Section: B Edge Theory Of the Bosonic Integer Quantum Hall Systemmentioning

confidence: 99%

Bosonic analog of a topological Dirac semimetal: Effective theory, neighboring phases, and wire construction

2016

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We construct a bosonic analog of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions ±k0 in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry Z T I 2 , where T is timereversal and I is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic version by replacing each Dirac cone with a copy of the O(4) Nonlinear Sigma Model (NLSM) with topological theta term and theta angle θ = ±π. One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case matching what one might expect from, for example, a bosonic Chern insulator. We also investigate the stability of the BSM model and find that the composite Z T I 2 symmetry again plays an important role. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges and statistics of vortex excitations, and the stability to symmetry-allowed perturbations. We briefly comment on the relation between the various descriptions of the O(4) NLSM with θ = π used in this paper (a dual vortex description and a description in terms of four massless fermions) and the recently proposed dual description of the BTI surface in terms of 2 + 1 dimensional Quantum Electrodynamics with two flavors of fermion (N = 2 QED3). In a set of four Appendixes we review some of the tools used in the paper, and also derive some of the more technical results.

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Effective field theories for topological insulators by functional bosonization

Cited by 60 publications

References 122 publications

Chiral gauge field and axial anomaly in a Weyl semimetal

Chiral gauge field and axial anomaly in a Weyl semimetal

Three-dimensional topological insulators and bosonization

Bosonic analog of a topological Dirac semimetal: Effective theory, neighboring phases, and wire construction

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