Two-Dimensional Mott-Hubbard Electrons in an Artificial Honeycomb Lattice

A collective electron excitation displays an unusual dependence on an applied magnetic field. Artificial crystal lattices can be used to tune repulsive Coulomb interactions between electrons. We trapped electrons, confined as a two-dimensional gas in a gallium arsenide quantum well, in a nanofabricated lattice with honeycomb geometry. We probed the excitation spectrum in a magnetic field, identifying collective modes that emerged from the Coulomb interaction in the artificial lattice, as predicted by the Mott-Hubbard model. These observations allow us to determine the Hubbard gap and suggest the existence of a Coulomb-driven ground state.

[1]  Gabriel Kotliar,et al.  Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory , 2004 .

[2]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[3]  A molecular state of correlated electrons in a quantum dot , 2008, 0902.2130.

[4]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[5]  N. Ong,et al.  Zero-energy state in graphene in a high magnetic field. , 2007, Physical review letters.

[6]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[7]  Z. Meng,et al.  Quantum spin liquid emerging in two-dimensional correlated Dirac fermions , 2010, Nature.

[8]  J. Dalibard,et al.  Many-Body Physics with Ultracold Gases , 2007, 0704.3011.

[9]  K. West,et al.  Delocalized-localized transition in a semiconductor two-dimensional honeycomb lattice , 2010, 1007.3168.

[10]  K. Haller.  Quantum Electrodynamics , 1979, Nature.

[11]  West,et al.  Spectroscopic measurement of large exchange enhancement of a spin-polarized 2D electron gas. , 1992, Physical review letters.

[12]  Tapash Chakraborty,et al.  Properties of graphene: a theoretical perspective , 2010, 1003.0391.

[13]  M. Polini,et al.  Engineering artificial graphene in a two-dimensional electron gas , 2009, 0904.4191.

[14]  C. Marianetti,et al.  Electronic structure calculations with dynamical mean-field theory , 2005, cond-mat/0511085.

[15]  Kentaro Nomura,et al.  Quantum Hall ferromagnetism in graphene. , 2006, Physical review letters.

[16]  Andrew G. Glen,et al.  APPL , 2001 .

[17]  D. Vollhardt.  Dynamical Mean‐Field Theory of Electronic Correlations in Models and Materials , 2010, 1004.5069.

[18]  L. Levitov,et al.  Spin-filtered edge states and quantum Hall effect in graphene. , 2006, Physical Review Letters.

[19]  K. Novoselov,et al.  Gap opening in the zeroth Landau level of graphene , 2009, 0904.0948.

[20]  Tim Byrnes,et al.  Quantum simulation of Fermi-Hubbard models in semiconductor quantum-dot arrays , 2007, 0711.2841.

[21]  S. Louie,et al.  Making massless Dirac fermions from a patterned two-dimensional electron gas. , 2008, Nano letters.

[22]  M. Katsnelson,et al.  Modeling electronic structure and transport properties of graphene with resonant scattering centers , 2010, 1007.3930.

[23]  Albrecht,et al.  Evidence of Hofstadter's Fractal Energy Spectrum in the Quantized Hall Conductance. , 2001, Physical review letters.

[24]  M. Katsnelson,et al.  Theory of optically forbidden d–d transitions in strongly correlated crystals , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[25]  Xiao-Liang Qi,et al.  Topological Mott insulators. , 2007, Physical review letters.

[26]  M. Fisher,et al.  Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes , 2006, cond-mat/0604601.

[27]  Landau-level splitting in graphene in high magnetic fields. , 2006, Physical review letters.