TITOLO: Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
BREVE ABSTRACT: 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.
TESTO: In order to study quantum phenomena difficult to be directly investigated, scientists
use artificially-designed systems - called quantum simulators - that can be controlled and
manipulated in the laboratory. Quantum simulators have been developed quite recently and
are based on different technologies (cold atoms, photonic crystals, trapped ions, single
molecules on a clean metal surface, etc). This new-developed device is the first quantum
simulators based on a semiconductor material and permits to observe the quantum behavior
of electrons.
The most interesting phenomena occurring in condensed matter systems, such as
ferromagnetism and high-temperature superconductivity, originate from mutual interactions
among many degrees of freedom represented by electrons, lattice vibrations, spins, etc. These
unique breakthroughs in scientific knowledge, which have led to silent revolutions in everyday life, pose a great challenge to humans since exact calculations of the behavior of the
underlying complex systems are an impossible task, even for the more sophisticated and
powerful computers. Quantum simulators help bypassing the problem, by replacing the
“uncomputable” quantum system with a controllable artificial one, which is able to emulate
the dynamics of the original system.
The simulator developed by Singha et al. [1] consists of a honeycomb lattice realized on the
surface of a Gallium Arsenide (GaAs) heterostructure by advanced nanofabrication methods.
The artificial honeycomb lattice structure replicates that of graphene, a material in which
electrons behave in a peculiar way because of the crystal lattice geometry [2]. Moreover, one
can get the best out of the simulator as it is possible to modify some key parameters such as
the lattice constant of the artificial lattice, at will. This makes it possible to explore strong
electron-electron interactions in graphene-like systems.
The prototype has been tested with a “first run” that generated within the crystal a peculiar
state of the matter with intriguing low-energy collective excitations. This is the first step
towards the realization of an innovative class of solid-state quantum simulators, which may
soon help us understand some of the most complex quantum behaviors in the physics of the
matter.
References
[1] A. Singha, M. Gibertini, B. Karmakar, S. Yuan, M. Polini, G. Vignale, M.I. Katsnelson, A.
Pinczuk, L.N. Pfeiffer, K.W. West, and V. Pellegrini, Science 332, 1176 (2011).
[2] M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G. Vignale, A. Pinczuk, L.N. Pfeiffer, and K.W.
West, Phys. Rev. B 79, 241406(R) (2009).
IMMAGINI con DIDASCALIE:
Fig. 1: a) Scanning electron microscopy (SEM) image of the semiconductor artificial lattice. An
expanded view of the SEM image showing a single honeycomb cell (2r ~ 60 nm, a ~ 130 nm).
The two-dimensional electron gas is positioned ~ 170 nm below the surface with a lowtemperature mobility of 2.7 × 106 cm2/(V s). We also sketch a cartoon of the two-dimensional
potential trap for electrons induced by the nanofabricated pillar at the surface. b) Geometry of
the light scattering experiment: ωL,S labels the incident (scattered) photon energy and θ = 5˚ is
the tilt angle. c) Resonant inelastic light scattering spectra showing the cyclotron mode and
the new low-lying collective mode at B = 5.48 T and T = 1.7 K. d) Evolution of the energies of
the cyclotron mode (black filled circles) and of the new collective mode at frequencies ωHB
(red filled squares) at T = 1.7 K. The black dashed line is a linear fit to the data using ωc =
eB/(mb c). We find mb = 0.067 me with me the bare electron mass, in agreement with the bulk
GaAs value. The red dashed line is a fit with ωHB = α B1/2.
Fig. 2: a) A cartoon of the spectral function A(ω) of the patterned/unpatterned 2DEG
(red/black). The Landau level peaks at ω = ωc(n + 1/2) are split by on-site Coulomb
interactions into Hubbard lower and upper peaks, which are separated by U~e2/lB, where lB
is the magnetic length. b) The relevant electronic process which contributes to the Raman
scattering cross section. The initial state is labeled by |1>, the final state by |2>, while the
intermediate state with one hole and an extra electron is labeled by |n>. The final excited state
is separated from the ground state by the Hubbard charge gap U, i.e. by the energy cost of
having two antiparallel spin electrons on the same site. In the intermediate state we have also
depicted the absorbed (at frequency ωL) and emitted (at frequency ωS) photons. The square
wells denote two neighboring minima of the artificial-lattice potential. The core levels are not
shown. The green areas denote valence-band electrons, which are assumed to be unaffected
by the periodic modulation.
AUTORI, AUTORE DI RIFERIMENTO (CON CONTATTO) E PERSONE COINVOLTE:
Autori: A. Singha, M. Gibertini, B. Karmakar, S. Yuan, M. Polini, G. Vignale, M.I. Katsnelson, A.
Pinczuk, L.N. Pfeiffer, K.W. West, and V. Pellegrini
Autori di riferimento: Marco Polini, e-mail: m.polini@sns.it, skype id: mp_sns; Vittorio
Pellegrini, e-mail: vp@sns.it, skype id: vpellegrini69.
Personale CNR-NANO coinvolto: A. Singha (now at the Department of Physics, Bose
Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata 700009, India), M. Gibertini, B.
Karmakar, M. Polini, and V. Pellegrini.