Research & Development World

  • R&D World Home
  • Topics
    • Aerospace
    • Automotive
    • Biotech
    • Careers
    • Chemistry
    • Environment
    • Energy
    • Life Science
    • Material Science
    • R&D Management
    • Physics
  • Technology
    • 3D Printing
    • A.I./Robotics
    • Software
    • Battery Technology
    • Controlled Environments
      • Cleanrooms
      • Graphene
      • Lasers
      • Regulations/Standards
      • Sensors
    • Imaging
    • Nanotechnology
    • Scientific Computing
      • Big Data
      • HPC/Supercomputing
      • Informatics
      • Security
    • Semiconductors
  • R&D Market Pulse
  • R&D 100
    • Call for Nominations: The 2025 R&D 100 Awards
    • R&D 100 Awards Event
    • R&D 100 Submissions
    • Winner Archive
    • Explore the 2024 R&D 100 award winners and finalists
  • Resources
    • Research Reports
    • Digital Issues
    • R&D Index
    • Subscribe
    • Video
    • Webinars
  • Global Funding Forecast
  • Top Labs
  • Advertise
  • SUBSCRIBE

2D electron liquid solidifies in a magnetic field

By R&D Editors | November 7, 2011

/sites/rdmag.com/files/legacyimages/RD/News/2011/11/GTphysicsx500.jpg

click to enlarge

Electron densities for the ground state of N=7 electrons in a magntic field, at: (a) fractional filling ? =1/3, corresponding to the angular momentum L2 = 63, shown in red on the left hand side (? = 0, ? = 1). The total wave function is ?= ?63 whose density is seen to exhibit a uniform circular amplitude characteristic of a liquid state, and (b) a mixed state in the neighborhood of ? =1/3, obtained by disorder-induced coupling between the ground state ?63 and the adjacent excited state with L1 = 57. The density of the broken-symmetry mixed state ?= ? ?57 + ? ?63 (with ? = 1/ 2, ? =1/ 2) , shown in blue on the right, exhibits a non-uniform crystalline pattern, portraying formation of a disorder-pinned wigner crystallite. The results were obtained through exact diagonalization of the hamiltonian, with the parameters corresponding to GaAs, i.e. a dielectric constant ? = 13.1 and an effective mass m* =0.0067 me, and a confining potential of 3.6 meV. Lengths are given in units of the magnetic length lB, and the units of the vertical axes are 10?2lB-2. The electron density is normalized to the number
of particles, N. Source: Georgia Institute of Technology

Physicists from the Georgia Institute of Technology have developed a theory
that describes, in a unified manner, the coexistence of liquid and pinned solid
phases of electrons in two dimensions under the influence of a magnetic field.
The theory also describes the transition between these phases as the field is
varied. The theoretical predictions by Constantine Yannouleas and Uzi Landman,
from Georgia Tech’s School of Physics, aim to explain and provide insights into the
origins of experimental findings published last year by a team of researchers
from Princeton University, Florida
State University, and Purdue
University. The research
appears in Physical Review B.

The experimental discovery in 1982 of a new Hall conductance step at a fraction
?=1/m with m=3, that is at (1/3)e2/h (with more conductance steps,
at other m, found later)—where h is the Planck constant and e is the electron
charge—was made for 2D electrons at low temperatures and strong magnetic fields
and was greeted with great surprise. The theoretical explanation of this
finding a year later by Robert Laughlin in terms of a new form of a quantum
fluid, earned him and the experimentalists Horst Störmer and Daniel Tsui the
1998 Nobel Prize with the citation “for the discovery of a new form of quantum
fluid with fractionally charged excitations.” These discoveries represent
conceptual breakthroughs in the understanding of matter, and the fractional
quantum Hall effect (FQHE) liquid states, originating from the highly
correlated nature of the electrons in these systems, have been termed as new
states of matter.

“The quantum fluid state at the 1/3 primary fraction is the hallmark of the
FQHE, whose theoretical understanding has been formulated around the antithesis
between a new form of quantum fluid and the pinned Wigner crystal,” says
Landman, Regents’ and Institute Professor in the School of Physics, F.E.
Callaway Chair and director of the Center for Computational Materials Science
(CCMS) at Georgia Tech. “Therefore, the discovery of pinned crystalline
signatures in the neighborhood of the 1/3 FQHE fraction, measured as resonances
in the microwave spectrum of the 2D electron gas and reported in the Physical Review Letters in September
2010 by a group of researchers headed by Daniel Tsui, was rather surprising,”
he adds.

Indeed, formation of a hexagonally ordered 2D electron solid phase, a so
called Wigner crystal (WC) named after the Nobel laureate physicist Eugene
Wigner who predicted its existence in 1934, has been anticipated for smaller
quantum Hall fractional fillings, ?, of the lowest Landau level populated by
the electrons at high magnetic fields, for example ? = 1/9, 1/7, and even 1/5.
However, the electrons in the ?=1/3 fraction were believed to resist crystallization
and remain liquid.

The Georgia Tech physicists developed a theoretical formalism that, in
conjunction with exact numerical solutions, provides a unified microscopic
approach to the interplay between FQHE liquid and Wigner solid states in the
neighborhood of the 1/3 fractional filling. A major advantage of their approach
is the use of a single class of variational wave functions for description of
both the quantum liquid and solid phases.

“Liquid characteristics of the fractional quantum Hall effect states are
associated with symmetry-conserving vibrations and rotations of the strongly
interacting electrons and they coexist with intrinsic correlations that are
crystalline in nature,” Senior Research Scientist Yannouleas and Landman wrote
in the opening section of their paper. “While the electron densities of the
fractional quantum Hall effect liquid state do not exhibit crystalline
patterns, the intrinsic crystalline correlations which they possess are
reflected in the emergence of a sequence of liquid states of enhanced
stability, called cusp states, that correspond in the thermodynamic limit to
the fractional quantum Hall effect filling fractions observed in Hall conductance
measurements,” they add.

The key to their explanation of the recent experimental observations
pertaining to the appearance of solid characteristics for magnetic fields in
the neighborhood of the 1/3 filling fraction is their finding that “away from
the exact fractional fillings, for example near ?=1/3, weak pinning
perturbations, due to weak disorder, may overcome the energy gaps between
adjacent good angular momentum symmetry-conserving states. The coupling between
these states generates broken-symmetry ground states whose densities exhibit spatial
crystalline patterns. At the same time, however, the energy gap between the
ground state at ?=1/3 and adjacent states is found to be sufficiently large to
prevent disorder-induced mixing, thus preserving its quantum fluid nature.”

Furthermore, the work shows that the emergence of the crystalline features,
via the pinning perturbations, is a consequence of the aforementioned presence
of crystalline correlations in the symmetry-conserving states. Consequently,
mixing rules that govern the nature of the disorder-pinned crystalline states have
been formulated and tested. Extrapolation of the calculated results to the
thermodynamic limit shows development of a hexagonal Wigner crystal with
enhanced stability due to quantum correlations.

“In closing, the nature of electrons in the fractional quantum Hall regime
continues now for close to three decades to be a subject of great fascination,
a research field that raises questions whose investigations can lead to deeper
conceptual understanding of matter and many-body phenomena, and a rich source of
surprise and discovery,” says Landman.

SOURCE

Related Articles Read More >

KIST carbon nanotube supercapacitor holds capacity after 100,000 cycles
A new wave of metalworking lets semiconductor crystals bend and stretch
LLNL deposits quantum dots on corrugated IR chips in a single step
KATRIN inauguration photo form 2018
Neutrinos pinned below 0.45 eV; KATRIN halves the particle’s mass ceiling
rd newsletter
EXPAND YOUR KNOWLEDGE AND STAY CONNECTED
Get the latest info on technologies, trends, and strategies in Research & Development.
RD 25 Power Index

R&D World Digital Issues

Fall 2024 issue

Browse the most current issue of R&D World and back issues in an easy to use high quality format. Clip, share and download with the leading R&D magazine today.

Research & Development World
  • Subscribe to R&D World Magazine
  • Enews Sign Up
  • Contact Us
  • About Us
  • Drug Discovery & Development
  • Pharmaceutical Processing
  • Global Funding Forecast

Copyright © 2025 WTWH Media LLC. All Rights Reserved. The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of WTWH Media
Privacy Policy | Advertising | About Us

Search R&D World

  • R&D World Home
  • Topics
    • Aerospace
    • Automotive
    • Biotech
    • Careers
    • Chemistry
    • Environment
    • Energy
    • Life Science
    • Material Science
    • R&D Management
    • Physics
  • Technology
    • 3D Printing
    • A.I./Robotics
    • Software
    • Battery Technology
    • Controlled Environments
      • Cleanrooms
      • Graphene
      • Lasers
      • Regulations/Standards
      • Sensors
    • Imaging
    • Nanotechnology
    • Scientific Computing
      • Big Data
      • HPC/Supercomputing
      • Informatics
      • Security
    • Semiconductors
  • R&D Market Pulse
  • R&D 100
    • Call for Nominations: The 2025 R&D 100 Awards
    • R&D 100 Awards Event
    • R&D 100 Submissions
    • Winner Archive
    • Explore the 2024 R&D 100 award winners and finalists
  • Resources
    • Research Reports
    • Digital Issues
    • R&D Index
    • Subscribe
    • Video
    • Webinars
  • Global Funding Forecast
  • Top Labs
  • Advertise
  • SUBSCRIBE