The Chern-Simons Fermi Liquid Description of Fractional Quantum Hall States

Simon, Steven H.

doi:10.1142/9789812815989_0002

Cited by 23 publications

(42 citation statements)

References 64 publications

(184 reference statements)

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“…Typically, it is argued that weak localization effects cannot be observed in the presence of Chern-Simon field fluctuations. This conclusion derives from the infrared divergence in the density of states of low frequency excitations at small wave vectors q [8]. In our sample, however, there is a rather high infrared cutoff due to small geometrical size and low carrier density.…”

Section: −1 *mentioning

confidence: 51%

“…Fluctuations in the gauge field were soon realized to have strong influence on the quantum correction of the composite fermion conductivity [6]. Subsequently, a Fermi liquid type of theory was proposed for half-filled Landau level [7] where various observables in the low-temperature limit are described in terms of Fermi liquid parameters [8], involving most notably the effective mass m * for composite fermions, which is expected to have a strong enhancement near half filling.There is extensive experimental evidence in favor of weakly interacting Fermi sea of composite fermions effectively in a zero magnetic field at ν = 1/2. Transport anomalies in the lowest Landau level of two-dimensional electrons at half filling were observed by Jiang et al [9].…”

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confidence: 99%

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confidence: 99%

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Weak antilocalization of composite fermions in graphene

2018

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Composite fermions in fractional quantum Hall (FQH) systems are believed to form a Fermi sea of weakly interacting particles at half filling ν = 1/2. Recently, it was proposed (D. T. Son, Phys. Rev. X 5, 031027 (2015)) that these composite fermions are Dirac particles. In our work, we demonstrate experimentally that composite fermions found in monolayer graphene are Dirac particles at half filling. Our experiments have addressed FQH states in high-mobility, suspended graphene Corbino disks in the vicinity of ν = 1/2. We find strong temperature dependence of conductivity σ away from half filling, which is consistent with the expected electron-electron interaction induced gaps in the FQH state. At half filling, however, the temperature dependence of conductivity σ(T ) becomes quite weak as expected for a Fermi sea of composite fermions and we find only logarithmic dependence of σ on T . The sign of this quantum correction coincides with weak antilocalization of composite fermions, which reveals the relativistic Dirac nature of composite fermions in graphene.The fractional quantum Hall (FQH) state is a many body phenomenon where fractionally charged elementary excitations lead to quantization of the Hall conductance at fractional filling factor ν = hn/(eB) at carrier density n and magnetic field B [1]. The generation of these incompressible liquid states requires a large Coulomb interaction energy compared with the disorder potential, putting strict requirements on temperature, the quality of the two-dimensional electron gas (2-DEG) and the strength of the magnetic field. Owing to reduced screening in atomically thin graphene, the electrons in graphene interact with larger Coulomb interaction energy than electrons in semiconductor heterostructures, providing an extraordinary setting for studies of FQH states and their description in terms of composite fermions [2][3][4].The composite fermion theory [2] and Composite Fermion Chern-Simon (CFCS) theory have been very successful in outlining a unified picture of fractional quantum Hall effect. Lopez and Fradkin [5] showed that the problem of interacting electrons moving in 2D in the presence of an external magnetic field is equivalent to a fermion system, described by a Chern-Simon gauge field, where electrons are bound to even number of vortex lines. Fluctuations in the gauge field were soon realized to have strong influence on the quantum correction of the composite fermion conductivity [6]. Subsequently, a Fermi liquid type of theory was proposed for half-filled Landau level [7] where various observables in the low-temperature limit are described in terms of Fermi liquid parameters [8], involving most notably the effective mass m * for composite fermions, which is expected to have a strong enhancement near half filling.There is extensive experimental evidence in favor of weakly interacting Fermi sea of composite fermions effectively in a zero magnetic field at ν = 1/2. Transport anomalies in the lowest Landau level of two-dimensional electrons at half filling were ...

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Section: −1 *mentioning

confidence: 51%

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confidence: 99%

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confidence: 99%

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Weak antilocalization of composite fermions in graphene

2018

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“…(Here we follow the notation of Ref. 27.) Ignoring the contribution from the different spin-components for the moment, a current density j of flux-carrying CFs gives rise to a gauge electric field e( j) that is perpendicular to the current.…”

Section: Preliminaries and Semi-quantitative Discussionmentioning

confidence: 99%

“…[σ CF ] xy = [σ CF ] yx = 0). In our analysis below we use the usual assumption that α 2 [σ CF ] xx [σ CF ] yy 1 [27]. The validity of this inequality is discussed in detail in the Appendix.…”

Section: Preliminaries and Semi-quantitative Discussionmentioning

confidence: 99%

Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

2018

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Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid. * These two authors contributed equally. arXiv:1712.02357v2 [cond-mat.str-el]

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Twenty Years Since the Discovery of the Fractional Quantum Hall Effect

Dyakonov

2003

Recent Trends in Theory of Physical Phenomena in High Magnetic Fields

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The Chern-Simons Fermi Liquid Description of Fractional Quantum Hall States

Cited by 23 publications

References 64 publications

Weak antilocalization of composite fermions in graphene

Weak antilocalization of composite fermions in graphene

Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

Twenty Years Since the Discovery of the Fractional Quantum Hall Effect

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