Developing fractional quantum Hall states at $\nu$ = $\frac{1}{7}$ and $\frac{2}{11}$ in the presence of significant Landau level mixing

Abstract

Termination of the fractional quantum Hall states (FQHSs) and the emergence of Wigner crystal phases at very small Landau level filling factors ($\nu$) have been of continued interest for decades. Recently, in ultra-high-quality, dilute GaAs 2D electron systems (2DESs), strong evidence was reported for FQHSs at $\nu =1/7,2/13$ and 2/11 which fall in the $\nu =p/(6p\pm 1)$ Jain series of FQHSs, interpreted as integer ($p=1$, 2) QHSs of 6-flux composite fermions (${}^6$CFs). These states are surrounded by strongly-insulating phases which are generally believed to be Wigner crystals. Here, we study an ultra-high-quality 2DES confined to an AlAs quantum well where the 2D electrons have a much larger effective mass ($m^{\ast }\simeq 0.45m_e$) and a smaller dielectric constant ($\epsilon \simeq 10{\epsilon }_0$) compared to GaAs 2D electrons ($m^{\ast }\simeq 0.067m_e$ and $\epsilon \simeq 13{\epsilon }_0$). This combination of $m^{\ast }$ and $\epsilon$ renders the Landau level mixing parameter $\kappa$, defined as the ratio of the Coulomb and cyclotron energies, $\simeq 9$ times larger in AlAs 2DESs ($\kappa \propto m^{\ast }/\epsilon$). Qualitatively similar to the GaAs 2DESs, we observe an insulating behavior reentrant around a strong $\nu =1/5$ FQHS, and extending to $\nu <1/5$. Additionally, we observe a clear minimum in magnetoresistance at $\nu =2/11$, and an inflection point at $\nu =1/7$ which is very reminiscent of the first report of an emerging FQHS at $\nu =1/7$ in GaAs 2DESs. The data provide evidence for developing QHSs of ${}^6$CFs at very small fillings. This is very surprising because $\kappa$ near $\nu \simeq 1/6$ in our sample is very large ($\simeq 4$), and larger $\kappa$ has the tendency to favor Wigner crystal states over FQHSs at small fillings. Our data should inspire calculations that accurately incorporate $\kappa$ in competing many-body phases of ${}^6$CFs at extremely small fillings near $\nu =1/6$.

arXiv comment7 pages, 4 figures, journal

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• Competing Many-Body Phases at Small Fillings in Ultrahigh-Quality GaAs 2D Hole Systems: Role of Landau Level Mixing
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Cascade of fractional quantum Hall states in 2D system