No Arabic abstract
The fractional quantum Hall state (FQHS) observed at a half-filled Landau level in an interacting two-dimensional electron system (2DES) is among the most exotic states of matter as its quasiparticles are expected to be Majoranas with non-Abelian statistics. We demonstrate here the unexpected presence of such a state in a novel 2DES with a strong band-mass anisotropy. The FQHS we observe has unusual characteristics. While its Hall resistance is well-quantized at low temperatures, it exhibits highly-anisotropic in-plane transport resembling compressible stripe/nematic charge-density-wave phases. More striking, the anisotropy sets in suddenly below a critical temperature, suggesting a finite-temperature phase transition. Our observations highlight how anisotropy modifies the many-body phases of a 2DES, and should further fuel the discussion surrounding the enigmatic even-denominator FQHS.
The multi-component nature of bilayer graphene (BLG), together with the ability to controllably tune between the various ground state orders, makes it a rich system in which to explore interaction driven phenomena. In the fractional quantum Hall effect (FQHE) regime, the unique Landau level spectrum of BLG is anticipated to support a non-Abelian even-denominator state that is tunable by both electric and magnetic fields. However, observation of this state, which is anticipated to be stronger than in conventional systems, has been conspicuously difficult. Here we report transport measurements of a robust even denominator FQHE in high-mobility, dual gated BLG devices. We confirm that the stability of the energy gap can be sensitively tuned and map the phase diagram. Our results establish BLG as a dynamic new platform to study topological ground states with possible non-Abelian excitations.
Monolayer (ML) semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure -- just like graphene -- facilitates gate-tunability, while the sizable band gap and strong spin-orbit coupling hold promise for properties beyond graphene. Measurements under large magnetic fields have revealed an unusual LL structure, distinct from other 2D electron systems. However, owing to limited sample quality and poor electrical contact, probing the lowest Landau levels (LLs) has been challenging, and observation of electron correlations within the fractionally filled LLs regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of ML WSe$_2$ in the extreme quantum limit, and observe fractional quantum Hall (FQH) states in the lowest three LLs. The odd-denominator FQH sequences demonstrate a systematic evolution with the LL orbital index, which has not been observed in any other system but is consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime.
Proposed even-denominator fractional quantum Hall effect (FQHE) states suggest the possibility of excitations with non-Abelian braid statistics. Recent experiments on wide square quantum wells observe even-denominator FQHE even under electrostatic tilt. We theoretically analyze these structures and develop a procedure to accurately test proposed quantum Hall wavefunctions. We find that tilted wells favor partial subband polarization to yield Abelian even-denominator states. Our results show that tilting quantum wells effectively engineers different interaction potentials allowing exploration of a wide variety of even-denominator states.
We report the observation of developing fractional quantum Hall states at Landau level filling factors $ u = 1/2$ and 1/4 in electron systems confined to wide GaAs quantum wells with significantly $asymmetric$ charge distributions. The very large electric subband separation and the highly asymmetric charge distribution at which we observe these quantum Hall states, together with the fact that they disappear when the charge distribution is made symmetric, suggest that these are one-component states, possibly described by the Moore-Read Pfaffian wavefunction.
It was recently pointed out that topological liquid phases arising in the fractional quantum Hall effect (FQHE) are not required to be rotationally invariant, as most variational wavefunctions proposed to date have been. Instead, they possess a geometric degree of freedom corresponding to a shear deformation that acts like an intrinsic metric. We apply this idea to a system with an anisotropic band mass, as is intrinsically the case in many-valley semiconductors such as AlAs and Si, or in isotropic systems like GaAs in the presence of a tilted magnetic field, which breaks the rotational invariance. We perform exact diagonalization calculations with periodic boundary conditions (torus geometry) for various filling fractions in the lowest, first and second Landau levels. In the lowest Landau level, we demonstrate that FQHE states generally survive the breakdown of rotational invariance by moderate values of the band mass anisotropy. At 1/3 filling, we generate a variational family of Laughlin wavefunctions parametrized by the metric degree of freedom. We show that the intrinsic metric of the Laughlin state adjusts as the band mass anisotropy or the dielectric tensor are varied, while the phase remains robust. In the n=1 Landau level, mass anisotropy drives transitions between incompressible liquids and compressible states with charge density wave ordering. In n>=2 Landau levels, mass anisotropy selects and enhances stripe ordering with compatible wave vectors at partial 1/3 and 1/2 fillings.