Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System.

Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν=1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the ν=1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν=1/2 FQHS depend strongly on valley occupancy.

[1]  Kenji Watanabe,et al.  Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene , 2021, Physical Review X.

[2]  Ajit C. Balram,et al.  Origin of the ν=1/2 fractional quantum Hall effect in wide quantum wells , 2020, 2010.08911.

[3]  B. Halperin.  The Half-Full Landau Level , 2020, 2012.14478.

[4]  B. Halperin,et al.  Thirty Years of Composite Fermions and Beyond , 2020, Fractional Quantum Hall Effects.

[5]  California,et al.  Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding , 2019, 1905.10248.

[6]  Ajit C. Balram,et al.  Prediction of a Non-Abelian Fractional Quantum Hall State with f-Wave Pairing of Composite Fermions in Wide Quantum Wells. , 2019, Physical review letters.

[7]  K. West,et al.  Unconventional Anisotropic Even-Denominator Fractional Quantum Hall State in a System with Mass Anisotropy. , 2018, Physical Review Letters.

[8]  A. Young,et al.  Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene , 2018, Nature Physics.

[9]  K. West,et al.  Multivalley two-dimensional electron system in an AlAs quantum well with mobility exceeding 2×106cm2V−1s−1 , 2018, Physical Review Materials.

[10]  K. West,et al.  Direct Observation of Composite Fermions and Their Fully-Spin-Polarized Fermi Sea near ν=5/2. , 2018, Physical review letters.

[11]  T. Taniguchi,et al.  Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene , 2017, Nature Physics.

[12]  Y. Oreg,et al.  Observation of half-integer thermal Hall conductance , 2017, Nature.

[13]  R. Bhatt,et al.  Connection between Fermi contours of zero-field electrons and ν = 1 2 composite fermions in two-dimensional systems , 2017, 1704.06265.

[14]  M. Shayegan,et al.  Transference of Fermi Contour Anisotropy to Composite Fermions. , 2017, Physical review letters.

[15]  K. West,et al.  Quantum Hall Spin Diode. , 2017, Physical review letters.

[16]  K. West,et al.  Microwave spectroscopic observation of a Wigner solid within the ν = 1 / 2 fractional quantum Hall effect , 2015, 1504.08182.

[17]  K. West,et al.  Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States. , 2016, Physical review letters.

[18]  W. Zhu,et al.  Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase , 2016, 1608.07761.

[19]  Ajit C. Balram,et al.  Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect , 2015, 1512.01894.

[20]  K. West,et al.  Geometric Resonance of Composite Fermions Near the ν=1/2 Fractional Quantum Hall State. , 2015, Physical review letters.

[21]  R. Winkler,et al.  Splitting of the Fermi Contour of Quasi-2D Electrons in Parallel Magnetic Fields. , 2015, Physical review letters.

[22]  N. Regnault,et al.  Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels , 2015, 1503.09132.

[23]  M. Kawasaki,et al.  Even-denominator fractional quantum Hall physics in ZnO , 2015, Nature Physics.

[24]  R. Winkler,et al.  Even-denominator fractional quantum Hall effect at a Landau level crossing , 2014, 1401.7742.

[25]  R. Winkler,et al.  Fractional quantum Hall effect at ν=1/2 in hole systems confined to GaAs quantum wells. , 2014, Physical review letters.

[26]  R. Winkler,et al.  Fermi contour anisotropy of GaAs electron-flux composite fermions in parallel magnetic fields , 2013, 1308.1728.

[27]  K. West,et al.  Phase diagrams for the stability of theν=12fractional quantum Hall effect in electron systems confined to symmetric, wide GaAs quantum wells , 2013, 1306.5290.

[28]  R. Willett,et al.  The quantum Hall effect at 5/2 filling factor , 2013, Reports on progress in physics. Physical Society.

[29]  B. Halperin,et al.  Fractional quantum Hall phase transitions and four-flux states in graphene. , 2013, Physical review letters.

[30]  Fu-Chun Zhang,et al.  Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions , 2012, 1203.1982.

[31]  Amir Yacoby,et al.  Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene , 2012, Science.

[32]  N. Kumada,et al.  Unraveling the Spin Polarization of the ν = 5/2 Fractional Quantum Hall State , 2012, Science.

[33]  D. Maude,et al.  NMR probing of the spin polarization of the ν=5/2 quantum Hall state. , 2012, Physical review letters.

[34]  T. Gokmen,et al.  Transference of transport anisotropy to composite fermions , 2010, 1009.5732.

[35]  M. R. Peterson,et al.  Quantum Hall phase diagram of half-filled bilayers in the lowest and the second orbital Landau levels: Abelian versus non-Abelian incompressible fractional quantum Hall states , 2010, 1002.4359.

[36]  O. Gunawan,et al.  Parallel magnetic-field tuning of valley splitting in AlAs two-dimensional electrons , 2008, 0811.3194.

[37]  S. Simon,et al.  Non-Abelian Anyons and Topological Quantum Computation , 2007, 0707.1889.

[38]  O. Gunawan,et al.  Two‐dimensional electrons occupying multiple valleys in AlAs , 2006, cond-mat/0606158.

[39]  D. Tsui,et al.  Two-flux composite fermion series of the fractional quantum Hall states in strained Si. , 2004, Physical review letters.

[40]  M. Shayegan,et al.  Low-temperature, in situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator , 2003, cond-mat/0411740.

[41]  M. Shayegan,et al.  Enhanced electron mobility and high order fractional quantum Hall states in AlAs quantum wells , 2002 .

[42]  K. West,et al.  Experimental evidence for a spin-polarized ground state in the ν = 5/2 fractional quantum Hall effect , 2001, cond-mat/0103144.

[43]  Santos,et al.  Evidence for a Bilayer Quantum Wigner Solid. , 1996, Physical review letters.

[44]  K. Hirakawa,et al.  High‐quality two‐dimensional electron system confined in an AlAs quantum well , 1993 .

[45]  Lee,et al.  Theory of the half-filled Landau level. , 1993, Physical review. B, Condensed matter.

[46]  Xie,et al.  Quantized Hall effect and quantum phase transitions in coupled two-layer electron systems. , 1993, Physical review. B, Condensed matter.

[47]  Santos,et al.  Correlated states of an electron system in a wide quantum well. , 1992, Physical review letters.

[48]  Hu,et al.  Electronic structure of parallel two-dimensional electron systems in tilted magnetic fields. , 1992, Physical review. B, Condensed matter.

[49]  Wilczek,et al.  Paired Hall states in double-layer electron systems. , 1992, Physical review. B, Condensed matter.

[50]  West,et al.  New fractional quantum Hall state in double-layer two-dimensional electron systems. , 1992, Physical review letters.

[51]  Santos,et al.  Observation of a nu =1/2 fractional quantum Hall state in a double-layer electron system. , 1992, Physical review letters.

[52]  Gregory W. Moore,et al.  Nonabelions in the fractional quantum Hall effect , 1991 .

[53]  A. Macdonald.  The fractional hall effect in multi-component systems , 1990 .

[54]  Macdonald,et al.  Fractional quantum Hall effect in two-layered systems. , 1989, Physical review. B, Condensed matter.

[55]  Chakraborty,et al.  Fractional quantum Hall effect at half-filled Landau level in a multiple-layer electron system. , 1987, Physical review letters.

[56]  Kunze.  Effective-mass change of electrons in Si inversion layers under parallel magnetic fields. , 1987, Physical review. B, Condensed matter.

[57]  Tu,et al.  Effective mass of a space-charge layer on GaAs in a parallel magnetic field. , 1986, Physical review. B, Condensed matter.

[58]  S. J. PERRY,et al.  Low Temperature , 1881, Nature.