Effective theories of the fractional quantum Hall effect at generic filling fractions

Blok, B.; Wen, Xiao-Gang

doi:10.1103/physrevb.42.8133

Cited by 187 publications

(200 citation statements)

References 25 publications

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“…One such route is the fractionalization of electrons due to strong correlations. We will implement this through the parton construction a la Blok and Wen,33,34 to find effective topological field theories. We start with a construction of time-reversal breaking fractional states in D = 2 + 1 dimensions by com-bining functional bosonization and the parton construction.…”

Section: Dimensional Reductionmentioning

confidence: 99%

“…V, we explore possibility of topological phases that arise because of strong interactions, e.g., "frac-tional" topological insulators. Starting from the BF theories for non-interacting topological insulators, and, following the parton approach pioneered by Blok and Wen 33,34 in the FQHE by implementing strong correlations as a constraint among fields, we give a derivation of topological field theories which describe strongly interacting topological phases. Finally, we present our conclusions in Sec.…”

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confidence: 99%

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Effective field theories for topological insulators by functional bosonization

et al. 2013

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Effective field theories that describes the dynamics of a conserved U(1) current in terms of "hydrodynamic" degrees of freedom of topological phases in condensed matter are discussed in general dimension D = d+1 using the functional bosonization technique. For non-interacting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII) and in the "primary series" of topological insulators in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ-term (when D is even). For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative "fractional" topological insulators and their possible effective field theories, and use them to determine the physical properties of these non-trivial quantum phases.

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Section: Dimensional Reductionmentioning

confidence: 99%

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confidence: 99%

Effective field theories for topological insulators by functional bosonization

et al. 2013

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“…8 These approaches were later reconciled, and unified by the effective description of the FQHE in terms of multicomponent Chern-Simons theories in (2 + 1)-dimensional space and time. [9][10][11][12][13][14][15] These topological effective theories for the hierarchy of FQHE deliver a correspondence between the physics in the two-dimensional bulk and the physics along one-dimensional boundaries at which the two-dimensional sample terminates. [16][17][18][19][20][21] It is possible to double the Chern-Simons effective theory representing the universal properties of the FQHE at some filling fraction ν = 1/(2m + 1), m ∈ Z so as to obtain a time-reversal symmetric theory.…”

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confidence: 99%

Time-reversal symmetric hierarchy of fractional incompressible liquids

et al. 2011

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We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described by the bulk theory.

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“…This situation is similar to the FQHE in two-dimensional electron systems (2DES) induced by strong external magnetic fields. In the latter case the FQHE must be described in terms of the effective Chern-Simons theory (12)(13)(14)(15), which is in addition to the simple vector potential associated with the external magnetic field that can only account for the IQHE. However, we note that to date there have not been self-consistent theoretical calculations for strain-induced FQHE.…”

Section: Cvd-grown Graphene On Cumentioning

confidence: 99%

Nano-Scale Strain-Induced Giant Pseudo-Magnetic Fields and Charging Effects in CVD-Grown Graphene on Copper

Yeh

Teague

et al. 2011

ECS Trans.

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Scanning tunneling microscopic and spectroscopic (STM/STS) studies of graphene grown by chemical vapor deposition (CVD) on copper reveal that the monolayer carbon structures remaining on copper are strongly strained and rippled, with different regions exhibiting different lattice structures and local electronic density of states (LDOS). The large and non-uniform strain induces pseudo-magnetic field up to ∼ 50 Tesla, as manifested by the integer and fractional pseudo-magnetic field quantum Hall effects (IQHE and FQHE) in the LDOS of graphene. Additionally, ridges appear along the boundaries of different lattice structures, which exhibit excess charging effects. For graphene transferred from copper to SiO2 substrates after the CVD growth, the average strain and the corresponding charging effects and pseudo-magnetic fields become much reduced. These findings suggest the feasibility of strain-engineering of graphene-based nano-electronics.

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Effective theories of the fractional quantum Hall effect at generic filling fractions

Cited by 187 publications

References 25 publications

Effective field theories for topological insulators by functional bosonization

Effective field theories for topological insulators by functional bosonization

Time-reversal symmetric hierarchy of fractional incompressible liquids

Nano-Scale Strain-Induced Giant Pseudo-Magnetic Fields and Charging Effects in CVD-Grown Graphene on Copper

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