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Fermi Surfaces of Composite Fermions

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Abstract

The fractional quantum Hall (FQH) effect was discovered in two-dimensional electron systems subject to a large perpendicular magnetic field nearly four decades ago. It helped launch the field of topological phases, and in addition, because of the quenching of the kinetic energy, gave new meaning to the phrase “correlated matter.” Most FQH phases are gapped like insulators and superconductors; however, a small subset with even denominator fractional fillings \(\nu \) of the Landau level, typified by \(\nu =1/2\), is found to be gapless, with a Fermi surface akin to metals. We discuss our results, obtained numerically using the infinite density matrix renormalization group scheme, on the effect of non-isotropic distortions with discrete N-fold rotational symmetry of the Fermi surface at zero magnetic field on the Fermi surface of the correlated \(\nu = 1/2\) state. We find that while the response for \(N = 2\) (elliptical) distortions is significant (and in agreement with experimental observations with no adjustable parameters), it decreases very rapidly as N is increased. Other anomalies, like resilience to breaking the Fermi surface into disjoint pieces, are also found. This highlights the difference between Fermi surfaces formed from the kinetic energy, and those formed of purely potential energy terms in the Hamiltonian.

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Notes

  1. \(\delta \) may be 0 or 1/2 depending on the boundary conditions (periodic or antiperiodic) of CFs, which are emergent.

  2. This is partly explained by the absence of a quadratic term (\(c_2=0\) by symmetry), but also due to the (unexplained, as far as we know) smallness of the symmetry-allowed cubic term \(c_3\).

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Acknowledgements

We acknowledge support from DOE BES Grant DE-SC0002140. RNB acknowledges the hospitality of the Aspen Center for Physics during the writing of this manuscript. The work presented was done in collaboration with Scott Geraedts. The infinite DMRG libraries used in this work were created by Michael Zaletel, Roger Mong and the TenPy collaboration. We thank Mansour Shayegan for useful discussions.

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  1. Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544, USA

    R. N. Bhatt

  2. Department of Physics, Princeton University, Princeton, NJ, 08544, USA

    Matteo Ippoliti

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Bhatt, R.N., Ippoliti, M. Fermi Surfaces of Composite Fermions. J Low Temp Phys 201, 25–40 (2020). https://doi.org/10.1007/s10909-020-02389-3

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