Connection between Fermi contours of zero-field electrons and 
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 composite fermions in two-dimensional systems

Ippoliti, Matteo; Geraedts, Scott D.; Bhatt, R. N.

doi:10.1103/physrevb.96.045145

Cited by 13 publications

(5 citation statements)

References 32 publications

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“…This has allowed the measurement of the CFL's response to different kinds of anisotropy, including strain-induced quadrupolar distortions 21 , higher-moment warping of hole bands 22 , and splitting of hole bands into separated Fermi pockets 23 . In all three cases, measurements are found to agree with numerical simulations 17,24,25 .…”

Section: Introductionsupporting

confidence: 65%

Geometry of flux attachment in anisotropic fractional quantum Hall states

2018

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Fractional quantum Hall (FQH) states are known to possess an internal metric degree of freedom that allows them to minimize their energy when contrasting geometries are present in the problem (e.g., electron band mass and dielectric tensor). We investigate the internal metric of several incompressible FQH states by probing its response to band mass anisotropy using infinite DMRG simulations on a cylinder geometry. We test and apply a method to extract the internal metric of a FQH state from its guiding center structure factor. We find that the response to band mass anisotropy is approximately the same for states in the same Jain sequence, but changes substantially between different sequences. We provide a theoretical explanation of the observed behavior of primary states at filling ν = 1/m in terms of a minimal microscopic model of flux attachment.

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Section: Introductionsupporting

confidence: 65%

Geometry of flux attachment in anisotropic fractional quantum Hall states

2018

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“…This is true whether the ground state at ν = 1/2 is compressible [67], or is an incompressible FQHS [22]. In the case of an compressible, CF, ground state at ν = 1/2, the experimental finding of the connectivity of the CF Fermi sea has in fact been corroborated qualitatively by numerical, many-body calculations [68]. This connectivity, as well as the presence of numerous one-component (odd-numerator) FQHSs such as ν = 3/5, 5/9, 3/7, and 5/11 on the nearby flanks of the ν = 1/2 FQHS provide strong evidence that the 1/2 FQHS is likely also a one-component state, presumably a Pfaffian state as recent theories conclude [32][33][34].…”

Section: Insets)mentioning

confidence: 88%

Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system

Hossain,

Ma,

Chung

et al. 2023

Preprint

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Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν = 1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conductionband valleys with an anisotropic effective mass. The anisotropy and multi-valley degree of freedom offer an unprecedented tunability of the ν = 1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short-and longrange Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν = 1/2 FQHS depend strongly on valley occupancy.

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“…It is straightforward to find values of the parameter C and Fermi energy F where the system has an annular Fermi sea at zero field and the N = 0 Landau level is the one with lowest energy, giving a CFL with a circular Fermi sea. Breaking up the zero-field Fermi sea into multiple annular pieces [27] also yields a single, circular Fermi sea of CFs. In short, the CFL Fermi sea is completely insensitive to such isotropic distortions of the electron spectrum.…”

Section: Isotropic Distortionsmentioning

confidence: 99%

“…We now take a brief departure from anisotropic deformations to consider the effect of circularly symmetric, but otherwise arbitrary, deformations of the electron dispersion [27]. We note in passing that non-parabolic dispersions could occur in any strongly interacting fermionic system with continuous translational and full rotational symmetry (i.e.…”

Section: Isotropic Distortionsmentioning

confidence: 99%

Fermi Surfaces of Composite Fermions

Bhatt

Ippoliti

2020

J Low Temp Phys

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The fractional quantum Hall (FQH) effect was discovered in twodimensional electron systems subject to a large perpendicular magnetic field nearly four decades ago. It helped launch the field of topological phases, and in addition, because of the quenching of the kinetic energy, gave new meaning to the phrase "correlated matter". Most FQH phases are gapped like insulators and superconductors; however, a small subset with even denominator fractional fillings ν of the Landau level, typified by ν = 1/2, are found to be gapless, with a Fermi surface akin to metals. We discuss our results, obtained numerically using the infinite-Density Matrix Renormalization Group (iDMRG) scheme, on the effect of non-isotropic distortions with discrete Nfold rotational symmetry of the Fermi surface at zero magnetic field on the Fermi surface of the correlated ν = 1/2 state. We find that while the response for N = 2 (elliptical) distortions is significant (and in agreement with experimental observations with no adjustable parameters), it decreases very rapidly as N is increased. Other anomalies, like resilience to breaking the Fermi surface into disjoint pieces, are also found. This highlights the difference between Fermi surfaces formed from the kinetic energy, and those formed of purely potential energy terms in the Hamiltonian.Keywords fractional quantum Hall effect · two dimensional electron gas · Fermi surface

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Connection between Fermi contours of zero-field electrons and ν=12 composite fermions in two-dimensional systems

Cited by 13 publications

References 32 publications

Geometry of flux attachment in anisotropic fractional quantum Hall states

Geometry of flux attachment in anisotropic fractional quantum Hall states

Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system

Fermi Surfaces of Composite Fermions

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