Anisotropic composite fermions and fractional quantum Hall effect

Mueed, M. A.; Kamburov, D.; Hasdemir, S.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Shayegan, M.

doi:10.1103/physrevb.93.195436

Cited by 13 publications

(11 citation statements)

References 41 publications

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“…With improvements in device quality, theories of reduced backscattering in anisotropic devices can be tested. [32][33][34] An interesting prospect in high quality single layer MX3 devices is the study of an anisotropic quantum hall 194 and anisotropic fractional quantum hall effect [195][196][197][198] . 24 The optical properties of the TMTCs offer many directions for future studies.…”

Section: Discussionmentioning

confidence: 99%

Electronics and optoelectronics of quasi-1D layered transition metal trichalcogenides

et al. 2017

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The isolation of graphene and transition metal dichalcongenides has opened a veritable world to a great number of layered materials which can be exfoliated, manipulated, and stacked or combined at will. With continued explorations expanding to include other layered materials with unique attributes, it is becoming clear that no one material will fill all the post-silicon era requirements. Here we review the properties and applications of layered, quasi-one dimensional transition metal trichalcogenides (TMTCs) as novel materials for next generation electronics and optoelectronics. The TMTCs present a unique chain-like structure which gives the materials their quasi-one dimensional properties such as high anisotropy ratios in conductivity and linear dichroism. The range of band gaps spanned by this class of materials (0.2 eV-2 eV) makes them suitable for a wide variety of applications including field-effect transistors, infrared, visible and ultraviolet photodetectors, and unique applications related to their anisotropic properties which opens another degree of freedom in the development of next generation electronics. In this review we survey the historical development of these remarkable materials with an emphasis on the recent activity generated by the isolation and characterization of atomically thin titanium trisulfide (TiS3).

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Section: Discussionmentioning

confidence: 99%

Electronics and optoelectronics of quasi-1D layered transition metal trichalcogenides

et al. 2017

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“…Very recent experiments by Mueed et al 5 have reported a study of the gap of the fully spin polarized 2/3 fractional Hall state as a function of the anisotropy parameter. They find that for up to γ = 0.80 there is essentially no change in the gap, as expected from theory.…”

Section: Excitations Gapsmentioning

confidence: 99%

“…Striking recent experiments from Princeton by Gokmen et al 1 , Kamburov et al 2,3 and Mueed et al 4,5 have investigated the role of electron mass anisotropy on the composite fermion (CF) Fermi sea, which was predicted in the early 1990s by Halperin, Lee and Read…”

Section: Introductionmentioning

confidence: 99%

“…Anisotropy in the mass for electrons (at zero magnetic field) can occur due to the band structure, e.g. in AlAs quantum wells 17 where the Fermi pockets are elliptical with the longitudinal and transverse electron band masses that differ by a factor of ∼5, or can be produced by application of an in-plane magnetic field in finite width GaAs quantum wells 5,[18][19][20] . Direct measurements of the CF Fermi wave vectors in perpendicular directions 2,3 demonstrate that the CF Fermi sea also becomes anisotropic.…”

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confidence: 99%

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Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

Balram

Jain

2016

Phys. Rev. B

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The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this article that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [Phys. Rev. Lett. 107, 116801 (2011)], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.

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“…For 2D electrons occupying AlAs conduction-band valleys with an anisotropic effective mass, a pronounced transport anisotropy was reported for CFs, but the anisotropy of the CF Fermi contour could not be measured because of the insufficient sample quality [5]. More recently, experiments probed the Fermi contour anisotropy of low-field carriers (both electrons and holes), and of CFs in GaAs quantum wells by subjecting them to an additional parallel magnetic field (B ) [12][13][14][15][16]. However, the B -induced anisotropy is primarily caused by the coupling between the in-plane and out-of-plane motions of the carriers, rendering a theoretical understanding of the data challeng- ing.…”

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confidence: 99%

Transference of Fermi Contour Anisotropy to Composite Fermions

Rosales

Mueed

et al. 2017

Phys. Rev. Lett.

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There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying in situ in-plane strain and measuring their Fermi wavevector anisotropy through commensurability oscillations. For strains on the order of 10 −4 we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field (αCF) is less than the anisotropy of their low-field hole (fermion) counterparts (αF), and closely follows the relation: αCF = √ αF.The energy gap measured for the ν = 2/3 FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to αF ∼ 3.3, the highest anisotropy achieved in our experiments.High-mobility, two-dimensional (2D), charged carriers at high perpendicular magnetic fields B and low temperatures exhibit rich many-body physics driven by Coulomb interaction. Examples include the fractional quantum Hall state (FQHS), Wigner crystal, and stripe phase [1,2]. Recently, the role of anisotropy has become a focus of new studies . This interest has been amplified by the recognition that, although the FQHSs at fillings 1/q (q = odd integer) are well described by Laughlin's wave function with a rotational symmetry [24], there is a geometric degree of freedom associated with the anisotropy of the 2D carrier system [8].The fundamental issue we address here is how the anisotropy of the energy-band structure of the low-field carriers transfers to the interacting particles at high B and, in particular, to the FQHSs and composite fermions (CFs). The latter are electron-flux quasi-particles that form a Fermi sea at a half-filled Landau level [2,25], and provide a simple explanation for the nearby FQHSs [26].

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Anisotropic composite fermions and fractional quantum Hall effect

Cited by 13 publications

References 41 publications

Electronics and optoelectronics of quasi-1D layered transition metal trichalcogenides

Electronics and optoelectronics of quasi-1D layered transition metal trichalcogenides

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

Transference of Fermi Contour Anisotropy to Composite Fermions

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