Transference of Fermi Contour Anisotropy to Composite Fermions

Abstract

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].

Fermi Surfaces of Composite Fermions

“…In particular, we investigated the effect of having a discrete N -fold symmetry in the zero-field kinetic energy, which could arise as a result of lattice symmetry, on the shape of the Fermi surface at high magnetic field at ν = 1/2. Surprisingly, while we found the Fermi surface distorts easily from a circular to an elliptical shape (in a manner that was quantitatively in agreement with experiments on strained GaAs quantum wells [16], see Fig. 2), other types of distortions elicited a much more subtle response.…”

“…Dots represent results obtained from experimentally measured oscillations in the resistivity as a result of commensuration effects. From Ref [16]…”

Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions

“…The various numerical and analytical approaches all confirm that the long-range Coulomb potential gives a universal square-root supression of the bare anisotropy for interacting Dirac fermions, reminiscent of the experimental finding at the half-filled Landau level in Ref. (1). A natural interesting question is whether this is a mere coincidence or is an indicator for the predicted emergent Dirac fermion nature of the half-filled Landau level.…”

2kF density wave instability of composite Fermi liquid

“…Moreover, the mixed form factor could be realized and tunable in bilayer graphene by an interlayer electric bias and magnetic field [39][40][41][42], then breaking the rotational symmetry may potentially probe the density wave instability of CFL. The mass anisotropy exists in AlAs quantum wells [74,75] in nature or could be introduced by applying an in-plane field [76] or uniaxial strain [77,78], so then realizing a density wave instability on top of an anisotropic CFL is also a promising direction to pursue experimentally.…”