An official website of the United States government
The discovery of the fractional quantum Hall state (FQHS) in 1982 ushered a new era of research in many-body condensed matter physics. Among the numerous FQHSs, those observed at even-denominator Landau level filling factors are of particular interest as they may host quasiparticles obeying non-Abelian statistics and be of potential use in topological quantum computing. The even-denominator FQHSs, however, are scarce and have been observed predominantly in low-disorder two-dimensional (2D) systems when an excited electron Landau level is half filled. An example is the well-studied FQHS at filling factor 5/2 which is believed to be a Bardeen-Cooper-Schrieffer-type, paired state of flux-particle composite fermions (CFs). Here, we report the observation of even-denominator FQHSs at 3/10, 3/8, and 3/4 in the lowest Landau level of an ultrahigh-quality GaAs 2D hole system, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaus. Quite remarkably, these states can be interpreted as even-denominator FQHSs of CFs, emerging from pairing of higher-order CFs when a CF Landau level, rather than an electron or a hole Landau level, is half-filled. Our results affirm enhanced interaction between CFs in a hole system with significant Landau level mixing and, more generally, the pairing of CFs as a valid mechanism for even-denominator FQHSs, and suggest the realization of FQHSs with non-Abelian anyons.
more »
« less
Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene
Motivated by the observation of even denominator fractional quantum Hall effect in the n= 3 Landau level of monolayer graphene [Kim et al., Nat. Phys. 15, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n= 2 graphene Landau level, whereas no pairing instability is found at half filling in the n= 0 and n= 1 graphene Landau levels. The relevance of these results to experiments is discussed.
more »
« less
- Award ID(s):
- 2037990
- PAR ID:
- 10480461
- Publisher / Repository:
- Physical Review Letters
- Date Published:
- Journal Name:
- Physical Review Letters
- Volume:
- 130
- Issue:
- 12
- ISSN:
- 0031-9007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
While a parent Hamiltonian for Laughlin wave function has been long known in terms of the Haldane pseudopotentials, no parent Hamiltonians are known for the lowest-Landau-level projected wave functions of the composite fermion theory at with . If one takes the two lowest Landau levels to be degenerate, the Trugman-Kivelson interaction produces the unprojected 2/5 wave function as the unique zero energy solution. If the lowest three Landau levels are assumed to be degenerate, the Trugman-Kivelson interaction produces a large number of zero energy states at Landau level filling of 3/7. We propose that adding an appropriately constructed three-body interaction yields the unprojected wave function as the unique zero energy solution, and report extensive exact diagonalization studies that provide strong support to this proposal.more » « less
-
Abstract Motivated by measurements of compressibility and STM spectra in twisted bilayer graphene, we analyze the pattern of symmetry breaking for itinerant fermions near a van Hove singularity. Making use of an approximate SU(4) symmetry of the Landau functional, we show that the structure of the spin/isospin order parameter changes with increasing filling via a cascade of transitions. We compute the feedback from different spin/isospin orders on fermions and argue that each order splits the initially 4-fold degenerate van Hove peak in a particular fashion, consistent with the STM data and compressibility measurements, providing a unified interpretation of the cascade of transitions in twisted bilayer graphene. Our results follow from a generic analysis of an SU(4)-symmetric Landau functional and are valid beyond a specific underlying fermionic model. We argue that an analogous van Hove scenario explains the cascade of phase transitions in non-twisted Bernal bilayer and rhombohedral trilayer graphene.more » « less
-
We study novel itinerant phases that can be accessed by doping a fractional quantum anomalous Hall (FQAH) insulator, with a focus on the experimentally observed Jain states at lattice filling 𝜈 =𝑝/(2𝑝 +1). Unlike in the lowest Landau level, where charge motion is confined into cyclotron orbits, the charged excitations in the FQAH occupy Bloch states with well-defined crystal momenta. At a nonzero doping density, this feature enables the formation of itinerant states of the doped anyons just beyond the FQAH plateau region. Focusing on the vicinity of 𝜈 =2/3, we describe a few possible itinerant states, including a topological superconductor with chiral neutral fermion edge modes as well as a more exotic pair density wave (PDW) superconductor with non-Abelian topological order. A Fermi liquid metal with a doping-induced period-3 charge density wave also occurs naturally in our analysis. This Fermi liquid (as well as the PDW) arises from pairing instabilities of a composite Fermi liquid metal that can emerge near filling 2/3. Though inspired by the theory of anyon superconductivity, we explain how our construction is qualitatively different. At a general Jain filling 𝜈 =𝑝/(2𝑝 +1), the same analytical framework leads to a wider variety of phases, including higher-charge superconductors and generalized composite Fermi liquids. We predict unusual physical signatures associated with each phase and analyze the crossover between different temperature regimes. These results provide a proof-of-principle that exotic itinerant phases can be stabilized by correlations intrinsic to the FQAH setup.more » « less
-
Crystalline graphene heterostructures, namely, Bernal bilayer graphene (BBLG) and rhombohedral trilayer graphene (RTLG), for example, subject to perpendicular electric displacement fields, display a rich confluence of competing orders, resulting in a valley-degenerate, spin-polarized half-metal at moderate doping, and a spin- and valley-polarized (nondegenerate) quarter-metal at lower doping. Here we show that such a quarter-metal can be susceptible toward the nucleation of a unique spin- and valley-polarized superconducting ground state, accommodating odd-parity (dominantly 𝑝 wave in BBLG and 𝑓 wave in RTLG) interlayer Cooper pairs that break the translational symmetry, giving rise to a Kekule (in BBLG) or columnar (in RTLG) pair density wave. Due to the trigonal warping in the normal state, the superconducting ground state produces threefold rotationally symmetric isolated Fermi rings of normal fermions, which can manifest via linear in temperature scaling of the specific heat. We present scaling of the zero-temperature pairing amplitude and the transition temperature of such pair density wave in the presence of trigonally warped disconnected, annular, and simply connected Fermi rings in the normal state, subject to an effective attractive interaction within a mean-field approximation.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevLett.130.126201
