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We study the effects of Landau level mixing in the limit of weak electron interaction. We use a numerical method to obtain the two- and three-body corrections to quantum Hall pseudopotentials, which are exact to lowest order in the Landau level mixing parameter. Our results are in general agreement with certain analytic results (some derived here, some derived by other authors) in the thermodynamic limit. We find that the convergence to this thermodynamic limit can be slow. This suggests that errors could occur if one tries to use pseudopotentials derived in a thermodynamic limit for numerical work on finite systems.
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We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low energy excitations following a recently developed approach [Pu, Wu and Jain, Phys. Rev. B 96, 195302 (2018)] and demonstrate them to be very accurate representations of the Coulomb eigenstates. We further ask how the Berry phase associated with a closed loop around the Fermi circle, predicted to be $pi$ in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)], is affected by Landau level mixing. For this purpose, we consider a simple model wherein we determine the variational ground state as a function of Landau level mixing within the space spanned by two basis functions: the lowest-Landau-level projected and the unprojected composite-fermion Fermi sea wave functions. We evaluate Berry phase for a path around the Fermi circle within this model following a recent prescription, and find that it rotates rapidly as a function of Landau level mixing. We also consider the effect of a particle-hole symmetry breaking three-body interaction on the Berry phase while confining the Hilbert space to the lowest Landau level. Our study deepens the connection between the $pi$ Berry phase and the exact particle-hole symmetry in the lowest Landau level.
We compute the effect of Landau-level-mixing on the effective two-body and three-body pseudopotentials for electrons in the lowest and second Landau levels. We find that the resulting effective three-body interaction is attractive in the lowest relative angular momentum channel. The renormalization of the two-body pseudopotentials also shows interesting structure. We comment on the implications for the $ u=5/2$ fractional quantum Hall state.
For weakly disordered fractional quantum Hall phases, the non linear photoconductivity is related to the charge susceptibility of the clean system by a Floquet boost. Thus, it may be possible to probe collective charge modes at finite wavevectors by electrical transport. Incompressible phases, irradiated at slightly above the magneto-roton gap, are predicted to exhibit negative photoconductivity and zero resistance states with spontaneous internal electric fields. Non linear conductivity can probe composite fermions charge excitations in compressible filling factors.
We show here that an extension of the Hamiltonian theory developed by us over the years furnishes a composite fermion (CF) description of the $ u =frac{1}{2}$ state that is particle-hole (PH) symmetric, has a charge density that obeys the magnetic translation algebra of the lowest Landau level (LLL), and exhibits cherished ideas from highly successful wave functions, such as a neutral quasi-particle with a certain dipole moment related to its momentum. We also a provide an extension away from $ u=frac{1}{2}$ which has the features from $ u=frac{1}{2}$ and implements the the PH transformation on the LLL as an anti-unitary operator ${cal T}$ with ${cal T}^2=-1$. This extension of our past work was inspired by Son, who showed that the CF may be viewed as a Dirac fermion on which the particle-hole transformation of LLL electrons is realized as time-reversal, and Wang and Senthil who provided a very attractive interpretation of the CF as the bound state of a semion and anti-semion of charge $pm {eover 2}$. Along the way we also found a representation with all the features listed above except that now ${cal T}^2=+1$. We suspect it corresponds to an emergent charge-conjugation symmetry of the $ u =1$ boson problem analyzed by Read.
We present in this Letter the results from two high quality, low density GaAs quantum wells. In sample A of electron density n=5.0x10^10 cm^-2, anisotropic electronic transport behavior was observed at u=7/2 in the second Landau level. We believe that the anisotropy is due to the large Landau level mixing effect in this sample. In sample B of density 4.1x10^10 cm^-2, strong 8/3, 5/2, and 7/3 fractional quantum Hall states were observed. Furthermore, our energy gap data suggest that, similar to the 8/3 state, the 5/2 state may also be spin unpolarized in the low density limit. The results from both samples show that the strong electron-electron interactions and a large Landau level mixing effect play an import role in the competing ground states in the second landau level.
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