Fermionic Chern-Simons theory for the fractional quantum Hall effect in bilayers

López, Ana María; Fradkin, Eduardo

doi:10.1103/physrevb.51.4347

Cited by 67 publications

(110 citation statements)

References 35 publications

Supporting

Mentioning

102

Contrasting

Order By: Relevance

“…The results reveal large spin reversal energies that are due to residual quasiparticle interactions [26,27,28,29,30]. In conjunction with determinations of CM transitions the light scattering measurements of spin excitations represent unique experimental tests of composite fermion theory.…”

mentioning

confidence: 94%

See 1 more Smart Citation

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Dujovne¹,

Hirjibehedin²,

Pinczuk³

et al. 2003

Solid State Communications

View full text Add to dashboard Cite

Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5 ≥ ν ≥ 1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν 1/3 and at ν 2/5 identify a structure of lowest spin-split Landau levels of composite fermions that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν = 1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results. The fractional quantum Hall effect (FQHE) is an electron condensation phenomenon that occurs at low temperatures when two-dimensional electron systems of very low disorder are exposed to high magnetic fields. The FQH states are archetypes of quantum fluids that emerge in low dimensional electron systems due to the impact of fundamental interactions. In the FQHE the 2D electron system becomes incompressible at certain values of the Landau level filling factor ν = nhc/eB, where n is the electron density and B is the perpendicular magnetic field. In the filling factor range 1 ≥ ν ≥ 1/3 the major sequence of the FQHE occurs at 'magic' filling factors ν = p/(2p ± 1), where p is an integer. The composite fermion (CF) framework interprets the sequence by attaching two vortices of the many body wavefunction to each electron [1,2]. Chern-Simons gauge fields incorporate electron interactions so that CF's experience effective magnetic fields B * = B − B 1/2 = ±B/(2p ± 1), where B 1/2 is the perpendicular magnetic field at ν = 1/2 [3, 4, 5]. Composite fermion quasiparticles have spin-split energy levels characteristic of charged fermions with spin 1/2 moving in the effective magnetic field B * . The levels resemble spin-split Landau levels of electrons. The number p thus becomes the CF Landau level filling factor and in FQHE states at ν = p/(2p ± 1) there are p fully occupied levels of composite fermions.Structures of spin-split CF levels are shown schematically in Fig. 1 for ν 1/3 and ν 2/5. The spacing between sequential CF levels with same spin is represented as a cyclotron frequency [3,6,7,8,9,10,11,12], ω c = eB * /cm CF , where m CF is a CF effective mass. Figure 1 also presents the transitions of composite fermions near filling factors 1/3 and 2/5. The charge mode (CM) transitions are spin-conserving. The spin wave (SW) and spin flip (SF) transitions involve a spin-reversal. The CM transition energies, however, could be different from CF level spacings. The difference is due to the changes in self-interaction energies that may occur when quasiparticles and quasiholes are created [9].Neutral pair excitations of quasiparti...

show abstract

mentioning

confidence: 94%

“…where E ↑↓ represents the spin reversal energy due to interactions among quasiparticles [26,27,28,29,30]. The bare Zeeman energy is E Z = gµ B B T , where B T is the total magnetic field, µ B is the Bohr magneton and g ∼ 0.44 is the absolute value of the Lande factor of GaAs.…”

mentioning

confidence: 99%

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Dujovne¹,

Hirjibehedin²,

Pinczuk³

et al. 2003

Solid State Communications

View full text Add to dashboard Cite

show abstract

“…That such phases ( called in-and out-phases) arise from the inter-layer Coulomb interaction has been demonstrated in Ref. [6]. We find that the Bilayer Quantum Hall System is in general in a mixed phase, which is a superposition of the in-and out-phases.…”

Section: Introductionmentioning

confidence: 79%

“…[6]. Comparing the matrix κ in two above cases with the standard form of the Chern-Simons terms of Bilayer Quantum Hall systems [1,5] we have k = j 8πg 2 , where j is an integer.…”

Section: The Chern-simons Termsmentioning

confidence: 99%

See 1 more Smart Citation

Chern-Simons terms in noncommutative geometry and its application to bilayer quantum hall systems

1996

View full text Add to dashboard Cite

Considering bilayer systems as extensions of the planar ones by an internal space of two discrete points, we use the ideas of Noncommutative Geometry to construct the gauge theories for these systems. After integrating over the discrete space we find an effective 2 + 1 action involving an extra complex scalar field, which can be interpreted as arising from the tunneling between the layers. The gauge fields are found in different phases corresponding to the different correlations due to the Coulomb interaction between the layers. In a particular * On leave from High Energy Division, Centre

show abstract

Multicomponent Quantum Hall Systems: The Sum of Their Parts and More

Girvin

MacDonald

1996

Perspectives in Quantum Hall Effects

164

View full text Add to dashboard Cite

The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons have degrees of freedom in addition to the two-dimensional orbital degree of freedom. We will be primarily interested in the situation where a finite number of states, most-commonly two, are available for each orbital state within a degenerate Landau level and will refer to these systems as multicomponent systems. Physical realizations of the additional degree of freedom include the electron spin, the valley index in multi-valley semiconductors, and the layer index in multiple-quantum-well systems. The consideration of multi-component systems expands the taxonomy of incompressible states and fractionally charged excitations, and for example, leads to the appearance of fractions with even denominators. More interestingly, it also leads us to new physics, including novel spontaneously broken symmetries and in some cases, finite temperature phase transitions. We present an introduction to this rich subject.

show abstract

Fermionic Chern-Simons theory for the fractional quantum Hall effect in bilayers

Cited by 67 publications

References 35 publications

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Chern-Simons terms in noncommutative geometry and its application to bilayer quantum hall systems

Multicomponent Quantum Hall Systems: The Sum of Their Parts and More

Contact Info

Product

Resources

About