Formation of an edge striped phase in the &nu=1/3 fractional quantum
Hall system
E.V. Tsiper and V.J. Goldman
Department of Physics, SUNY at Stony Brook, Stony Brook, NY 11794.
We have performed an exact diagonalization study of up to N = 12
interacting electrons on a disk at filling&\nu = 1/3 for both Coulomb
and V1 short-range interaction for which Laughlin wave
function is the exact solution. For Coulomb interaction and N >= 10 we
find persistent radial oscillations in electron density, which are not
captured by the Laughlin wave function. Our results strongly suggest
formation of a chiral edge striped phase in quantum Hall systems. The
amplitude of the charge density oscillations decays slowly, perhaps as
a square root of the distance from the edge; thus the spectrum of edge
excitations is likely to be affected.
Identifying the ν = 5/2 Topological Order through Charge Transport Measurements.
Physical review letters, 128(1), p.016401, 2022.
Hu, Y., Ge, Y., Zhang, J.X. and Jain, J.K.,
Crystalline solutions of the Kohn-Sham equations in the fractional quantum Hall regime.
Physical Review B, 104(3), p.035122, 2021.
Hu, Y.,
Applications of Kohn-Sham Density Functional Theory to Topological Particles.
Doctoral dissertation, The Pennsylvania State University, 2021.
Jain, J.K.,
Thirty years of composite fermions and beyond.
In Fractional Quantum Hall Effects: New Developments, ed by B.I. Halperin and J.K. Jain (pp. 1-78). ISBN: 978-981-121-748-7, 2020.
Kohn-Sham theory of the fractional quantum Hall effect.
Physical review letters, 123(17), p.176802, 2019.
Bentalha, Z.E.A.,
Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F2.
Mathematical Physics, Analysis and Geometry, 21(2), p.10, 2018.
Grivnin, A., Inoue, H., Ronen, Y., Baum, Y., Heiblum, M., Umansky, V. and Mahalu, D.,
Nonequilibrated counterpropagating edge modes in the fractional quantum Hall regime.
Physical Review Letters, 113(26), p.266803, 2014.
Soulé, P., Jolicoeur, T. and Lecheminant, P.,
Many-body study of a quantum point contact in the fractional quantum Hall regime at ν = 5/2.
Physical Review B, 88(23), p.235107, 2013.
Soule, P. and Jolicoeur, T.,
Edge properties of principal fractional quantum Hall states in the cylinder geometry.
Physical Review B, 86(11), p.115214, 2012.
Yannouleas, C. and Landman, U.,
Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of the lowest Landau-level states in the neighborhood of ν = 1/3.
Physical Review B, 84(16), p.165327, 2011.
Sreejith, G.J., Jolad, S., Sen, D. and Jain, J.K.,
Microscopic study of the 2/5 fractional quantum Hall edge.
Physical Review B, 84(24), p.245104, 2011.
Shrivastava, K.N.,
Laughlin's Wave Function and Angular Momentum.
InternationalJournal of Modern Physics B, 25(10), pp.1301-1357, 2011.
Tölö, E. and Harju, A.,
Reduced density-matrix functional theory in quantum Hall systems.
Physical Review B, 81(7), p.075321, 2010.
Tölö, E.,
Nanostructures in the quantum Hall regime.
Doctoral dissertation, Aalto University, 2010.
Bonderson, P., Shtengel, K. and Slingerland, J.K.,
Interferometry of non-Abelian anyons.
Annals of Physics, 323(11), pp.2709-2755, 2008.
Orgad, D. and Agam, O.,
Correlated tunneling and the instability of the fractional quantum Hall edge.
Physical review letters, 100(15), p.156802, 2008.
Horsdal, M.,
Effects of interaction-induced second Landau level mixing in the ν = 1 quantum Hall effect.
Physical Review B, 77(19), p.195312, 2008.
Yannouleas, C. and Landman, U.,
Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods.
Reports on Progress in Physics, 70(12), p.2067, 2007.
Jeon, G.S., Chang, C.C. and Jain, J.K.,
Semiconductor quantum dots in high magnetic fields.
The European Physical Journal B, 55(3), pp.271-282, 2007.
Merlo, M., Braggio, A., Magnoli, N. and Sassetti, M.,
Transport of fractional Hall quasiparticles through an antidot.
Physical Review B, 75(19), p.195332, 2007.
Cabo, A., Claro, F., Pérez, A. and Maze, J.,
Holelike analytic mean-field solutions in the fractional quantum Hall regime.
Physical Review B, 76(7), p.075308, 2007.
Camino, F.E., Zhou, W. and Goldman, V.J.,
Transport in the Laughlin quasiparticle interferometer: Evidence for topological protection in an anyonic qubit.
Physical Review B, 74(11), p.115301, 2006.
Grayson, M.,
Electron correlations at the fractional quantum Hall edge.
Solid state communications, 140(2), pp.66-71, 2006.
Tsiper, E.V.,
Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.
Physical review letters, 97(7), p.076802, 2006.
Khlebnikov, S.,
Piezoelectric coupling, phonons, and tunneling into a quantum Hall edge.
Physical Review B, 73(4), p.045331, 2006.
Basu, B. and Bandyopadhyay, P.,
Fractional quantum Hall edge electrons and Berry's phase.
Physica Scripta, 73(4), p.332, 2006.
Kailasvuori, J.,
Quasiparticles in the Quantum Hall Effect.
Doctoral dissertation, Stockholm University, 2006.
Patton, K.R. and Geller, M.R.,
Infrared catastrophe and tunneling into strongly correlated electron systems: Exact x-ray edge limit for the one-dimensional electron gas and two-dimensional Hall fluid.
Physical Review B, 73(24), p.245306, 2006.
Basu, B., Bandyopadhyay, P. and Dhar, S.,
Charge and statistics of quasiparticles in fractional quantum Hall effect.
International Journal of Modern Physics B, 20(32), pp.5405-5416, 2006.
Patton, K.R.,
Tunneling in low-dimensional and strongly correlated electron systems.
Doctoral dissertation, University of Georgia, 2006.
Tsiper, E.V.,
Computer simulation of resonant tunneling through quantum antidot in the fractional quantum Hall regime: evidence of fractional quantization of electric charge.
Nanostructures: physics and technology, p.127, 2006.
Wan, X., Evers, F. and Rezayi, E.H.,
Universality of the edge-tunneling exponent of fractional quantum Hall liquids.
Physical review letters, 94(16), p.166804, 2005.
Emperador, A., Lipparini, E. and Pederiva, F.,
Many-electron quantum dots in the fractional quantum Hall regime.
Physical Review B, 72(3), p.033306, 2005.
Patton, K.R. and Geller, M.R.,
Infrared catastrophe and tunneling into strongly correlated electron systems: Perturbative x-ray edge limit.
Physical Review B, 72(12), p.125108, 2005.
Hansson, T.H., Kailasvuori, J., Karlhede, A. and von Unge, R.,
Solitons and quasielectrons in the quantum Hall matrix model.
Physical Review B, 72(20), p.205317, 2005.
Jeon, G.S. and Jain, J.K.,
Density profile of a hole at the fractional Hall edge.
Physical Review B, 71(4), p.045337, 2005.
Patton, K.R. and Geller, M.R.,
Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid.
arXiv preprint cond-mat/0510601, 2005.
Boyarsky, A., Cheianov, V.V. and Ruchayskiy, O.,
Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge.
Physical Review B, 70(23), p.235309, 2004.
Hwang, N.Y., Yang, S.R.E., Sim, H.S. and Yi, H.,
Maximum density hole droplets of an antidot in strong magnetic fields.
Physical Review B, 70(8), p.085322, 2004.
Basu, B. and Bandyopadhyay, P.,
Fractional Quantum Hall Edge Electrons, Chiral Anomaly and the Berry Phase.
arXiv preprint cond-mat/0401418, 2004.
Grayson, M.,
Electronic correlations at the edge of a quantum Hall liquid.
In The Electron Liquid Paradigm in Condensed Matter Physics, ed by G. F. Giuliani, G.F. and Vignale G. (pp. 515-526). IOS Press. ISBN: 978-1-58603-446-7, 2004.
Hwang, N.Y., Yang, S.R.E., Sim, H.S. and Yi, H.,
Hole maximum density droplets of an antidot in strong magnetic fields.
arXiv preprint cond-mat/0404525, 2004.
Jain, J.K.,
Composite fermions: Edge states and fractional statistics.
In The Electron Liquid Paradigm in Condensed Matter Physics, ed by G.F. Giuliani, G.F. and Vignale G. (pp. 499-513). IOS Press. ISBN: 978-1-58603-446-7, 2004.
Yang, K.,
Field theoretical description of quantum Hall edge reconstruction.
Physical review letters, 91(3), p.036802, 2003.
Yannouleas, C. and Landman, U.,
Two-dimensional quantum dots in high magnetic fields: rotating-electron-molecule versus composite-fermion approach.
Physical Review B, 68(3), p.035326, 2003.
Yang, K.,
Field theoretical description of quantum Hall edge reconstruction.
Physical review letters, 91(3), p.036802, 2003.
Wan, X., Rezayi, E.H. and Yang, K.,
Edge reconstruction in the fractional quantum Hall regime.
Physical Review B, 68(12), p.125307, 2003.
More about the Laughlin droplet.
arXiv preprint cond-mat/0310015, 2003.
Wan, X., Yang, K. and Rezayi, E.H.,
Reconstruction of fractional quantum Hall edges.
Physical review letters, 88(5), p.056802, 2002.
Yannouleas, C. and Landman, U.,
Trial wave functions with long-range Coulomb correlations for two-dimensional N-electron systems in high magnetic fields.
Physical Review B, 66(11), p.115315, 2002.
Saxena, A. and Dandoloff, R.,
Stabilization of half-skyrmions: Heisenberg spins on a non-simply connected manifold.
Physical Review B, 66(10), p.104414, 2002.
Tsiper, E.V.,
Analytic Coulomb matrix elements in the lowest Landau level in disk geometry.
Journal of Mathematical Physics, 43(3), pp.1664-1667, 2002.