Topological invariants for standard model: From semi-metal to topological insulator

Volovik, G. E.

doi:10.1134/s0021364010020013

Cited by 70 publications

(92 citation statements)

References 65 publications

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“…Indeed, the γ coefficient bears a qualitative resemblance to the quasiclassical expression (11) for the current. Calculating the integrated current that results from (15) using (14) and self-consistent values of η x (r), η y (r) from BdG calculations, the result is in qualitative agreement with numerical BdG for all lattice structures and gap anisotropies studied.…”

Section: Gradient Expansion Of the Bcs Action For A Chiral P-wavesupporting

confidence: 59%

“…Previous authors 12,14,15 have used such an expansion of the action with respect to gradients of the scalar A 0 (r) potential to understand the edge current. A vector potential A(r) is also included to generate an expression for the current from the action, taking it to be zero after this is done.…”

Section: Gradient Expansion Of the Bcs Action For A Chiral P-wavementioning

confidence: 99%

“…For lattice models, it depends not just on the chirality or winding of the order parameter, but also the topology of the Fermi surface, but always takes an integer value. One manifestation of a non-zero Chern number is a quantized value of the "static" Hall conductivity [12][13][14][15]25 :…”

Section: Topological Properties In the Continuum Limitmentioning

confidence: 99%

“…(We will refer to condition (ii) as the soft edge limit). Under these circumstances the gradient expansion gives [12][13][14][15] …”

Section: Introductionmentioning

confidence: 99%

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Nontopological nature of the edge current in a chiralp-wave superconductor

et al. 2015

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The edges of time reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are non-topological-and therefore sensitive to microscopic details-even if we neglect Meissner screening. We give insight into the non-topological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov-de Gennes equations, the quasiclassical approximation, and the gradient expansion, and describe those special cases where edge currents do have a topological character. While edge currents are not quantized, they are generically large, but can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr2RuO4.

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Section: Gradient Expansion Of the Bcs Action For A Chiral P-wavesupporting

confidence: 59%

Section: Gradient Expansion Of the Bcs Action For A Chiral P-wavementioning

confidence: 99%

Section: Topological Properties In the Continuum Limitmentioning

confidence: 99%

“…(We will refer to condition (ii) as the soft edge limit). Under these circumstances the gradient expansion gives [12][13][14][15] …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nontopological nature of the edge current in a chiralp-wave superconductor

et al. 2015

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“…Their effective action in the presence of an electromagnetic field has been studied with a focus on the electric-magnetic duality, 18 and analogies have been made with the topological invariants of the Standard Model of particle physics. 19 The surface states of topological insulators in strong magnetic fields have been investigated in Ref. 20.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional surface charge transport in topological insulators

et al. 2010

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We construct a theory of charge transport by the surface states of topological insulators in three dimensions. The focus is on the experimentally relevant case when the Fermi energy εF and transport scattering time τ satisfy εF τ / 1, but εF lies below the bottom of the conduction band. Our theory is based on the spin density matrix and takes the quantum Liouville equation as its starting point. The scattering term is determined to linear order in the impurity density ni and explicitly accounts for the absence of backscattering, while screening is included in the random phase approximation. The main contribution to the conductivity is ∝ n −1 i and has different carrier density dependencies for different forms of scattering, while an additional contribution is independent of ni. The dominant scattering angles can be inferred by studying the ratio of the transport time to the Bloch lifetime as a function of the Wigner-Seitz radius rs. The current generates a spin polarization that could provide a smoking-gun signature of surface state transport. We also discuss the effect on the surface states of adding metallic contacts.

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From the adiabatic theorem of quantum mechanics to topological states of matter

Budich

Trauzettel²

2013

Physica Rapid Research Ltrs

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Abstractmagnified imageOwing to the enormous interest the rapidly growing field of topological states of matter (TSM) has attracted in recent years, the main focus of this review is on the theoretical foundations of TSM. Starting from the adiabatic theorem of quantum mechanics which we present from a geometrical perspective, the concept of TSM is introduced to distinguish gapped many body ground states that have representatives within the class of non‐interacting systems and mean field superconductors, respectively, regarding their global geometrical features. These classifying features are topological invariants defined in terms of the adiabatic curvature of these bulk insulating systems. We review the general classification of TSM in all symmetry classes in the framework of K‐Theory. Furthermore, we outline how interactions and disorder can be included into the theoretical framework of TSM by reformulating the relevant topological invariants in terms of the single particle Green's function and by introducing twisted boundary conditions, respectively. We finally integrate the field of TSM into a broader context by distinguishing TSM from the concept of topological order which has been introduced to study fractional quantum Hall systems. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Topological invariants for standard model: From semi-metal to topological insulator

Abstract: We consider topological invariants describing semimetal (gapless) and insulating (gapped) states of the quantum vacuum of Standard Model and possible quantum phase transitions between these states. PACS:

Cited by 70 publications

References 65 publications

Nontopological nature of the edge current in a chiralp-wave superconductor

Nontopological nature of the edge current in a chiralp-wave superconductor

Two-dimensional surface charge transport in topological insulators

From the adiabatic theorem of quantum mechanics to topological states of matter

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