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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$\mathit{\nu }\mathbf{=}$5/2 which is believed to be a Bardeen-Cooper-Schrieffer-type, paired state of flux-particle composite fermions (CFs). Here, we report the observation of even-denominator FQHSs at$\mathit{\nu }\mathbf{=}$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.

 

Strong interactions and topology drive a wide variety of correlated ground states. Some of the most interesting of these ground states, such as fractional quantum Hall states and fractional Chern insulators, have fractionally charged quasiparticles. Correlations in these phases are captured by the binding of electrons and vortices into emergent particles called composite fermions. Composite fermion quasiparticles are randomly localized at high levels of disorder and may exhibit charge order when there is not too much disorder in the system. However, more complex correlations are predicted when composite fermion quasiparticles cluster into a bubble, and then these bubbles order on a lattice. Such a highly correlated ground state is termed the bubble phase of composite fermions. Here we report the observation of such a bubble phase of composite fermions, evidenced by the re-entrance of the fractional quantum Hall effect. We associate this re-entrance with a bubble phase with two composite fermion quasiparticles per bubble. Our results demonstrate the existence of a new class of strongly correlated topological phases driven by clustering and charge ordering of emergent quasiparticles. 

Abstract The interplay of strong Coulomb interactions and of topology is currently under intense scrutiny in various condensed matter and atomic systems. One example of this interplay is the phase competition of fractional quantum Hall states and the Wigner solid in the two-dimensional electron gas. Here we report a Wigner solid at ν  = 1.79 and its melting due to fractional correlations occurring at ν  = 9/5. This Wigner solid, that we call the reentrant integer quantum Hall Wigner solid, develops in a range of Landau level filling factors that is related by particle-hole symmetry to the so called reentrant Wigner solid. We thus find that the Wigner solid in the GaAs/AlGaAs system straddles the partial filling factor 1/5 not only at the lowest filling factors, but also near ν  = 9/5. Our results highlight the particle-hole symmetry as a fundamental symmetry of the extended family of Wigner solids and paint a complex picture of the competition of the Wigner solid with fractional quantum Hall states. 

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations^1–3. Here we investigate transport properties of hDWs in theν = 2/3 fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.

 

Topological insulators are a class of electronic materials exhibiting robust edge states immune to perturbations and disorder. This concept has been successfully adapted in photonics, where topologically nontrivial waveguides and topological lasers were developed. However, the exploration of topological properties in a given photonic system is limited to a fabricated sample, without the flexibility to reconfigure the structurein situ. Here, we demonstrate an all-optical realization of the orbital Su–Schrieffer–Heeger model in a microcavity exciton-polariton system, whereby a cavity photon is hybridized with an exciton in a GaAs quantum well. We induce a zigzag potential for exciton polaritons all-optically by shaping the nonresonant laser excitation, and measure directly the eigenspectrum and topological edge states of a polariton lattice in a nonlinear regime of bosonic condensation. Furthermore, taking advantage of the tunability of the optically induced lattice, we modify the intersite tunneling to realize a topological phase transition to a trivial state. Our results open the way to study topological phase transitions on-demand in fully reconfigurable hybrid photonic systems that do not require sophisticated sample engineering.