2-D electron liquid solidifies in a magnetic field

ScienceDaily (Nov. 5, 2011) — 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, Florida State and Purdue universities.

The research appears in the Oct. 27 edition of the journal 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 two-dimensional 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," said 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 two-dimensional 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 added.

Indeed, formation of a hexagonally ordered two-dimensional 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 added.

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," said Landman.

This work was supported by the Office of Basic Energy Sciences of the US Department of Energy.

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Journal Reference:

Constantine Yannouleas, Uzi Landman. Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of the lowest Landau-level states in the neighborhood of ?=1/3. Physical Review B, 2011; 84 (16) DOI: 10.1103/PhysRevB.84.165327

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Electron accelerator scientists report breakthroughs

ScienceDaily (Oct. 25, 2011) — Cornell scientists have surpassed two major scientific milestones toward proving the technology of a novel, exceedingly powerful X-ray source.

For more than a decade, Cornell scientists have been conducting research and development for an Energy Recovery Linac (ERL) electron accelerator that would produce X-ray beams 1,000 times brighter than any in existence.

The university ultimately hopes to use ERL technology to upgrade the Cornell High Energy Synchrotron Source (CHESS), one of five U.S. national facilities for hard X-ray synchrotron radiation research.

The National Science Foundation provided $50 million for 2006-14 to build instrumentation for prototyping and testing ERL concepts proposed by the Cornell team of faculty, students and collaborators. Specifically, the program goals are to prove that electron beams of unmatched quality could be created and accelerated to continuously produce X-ray beams with the laserlike property of coherence. No such X-ray source presently exists.

Cornell's ERL team is now reporting that its prototype electron injector is producing beams with a so-called emittance of 0.8 micrometers -- the smallest ever recorded from an electron source of this type. The injector is the key component needed to make an ERL work by creating electron beams that are tightly packed and traveling at nearly the speed of light. The emittance is a measure of how tightly packed the electron beams are.

This small emittance, say the scientists, proves that the ERL could produce X-ray beams focused down to exceedingly small volumes, allowing investigation of materials with unprecedented precision and speed.

In another breakthrough for the ERL project, the scientists have built and tested a prototype seven-cell superconducting radio frequency (SRF) cavity. SRF cavities are needed to accelerate the electrons from the injector to very high energies in order to produce the X-rays. The SRF cavities are operated at -456 F (-271 C), just 2 degrees above absolute zero temperature.

The Cornell researchers' SRF cavity has met the first performance specifications necessary to continuously power a high intensity ERL. It has been tested in a vertical cryostat at the required temperature and electric field gradients -- a significant milestone because it proves the cavities can perform at high power while within the scientific and cost parameters of the project.

The team must now demonstrate the efficacy of their cavities in horizontal tests, which will take place in 2012.

"These developments go a long way toward proving that an ERL X-ray source will work as predicted by simulations and theory," said Sol Gruner, director of CHESS.

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Electron accelerator scientists report breakthroughs

ScienceDaily (Oct. 25, 2011) — Cornell scientists have surpassed two major scientific milestones toward proving the technology of a novel, exceedingly powerful X-ray source.

For more than a decade, Cornell scientists have been conducting research and development for an Energy Recovery Linac (ERL) electron accelerator that would produce X-ray beams 1,000 times brighter than any in existence.

The university ultimately hopes to use ERL technology to upgrade the Cornell High Energy Synchrotron Source (CHESS), one of five U.S. national facilities for hard X-ray synchrotron radiation research.

The National Science Foundation provided $50 million for 2006-14 to build instrumentation for prototyping and testing ERL concepts proposed by the Cornell team of faculty, students and collaborators. Specifically, the program goals are to prove that electron beams of unmatched quality could be created and accelerated to continuously produce X-ray beams with the laserlike property of coherence. No such X-ray source presently exists.

Cornell's ERL team is now reporting that its prototype electron injector is producing beams with a so-called emittance of 0.8 micrometers -- the smallest ever recorded from an electron source of this type. The injector is the key component needed to make an ERL work by creating electron beams that are tightly packed and traveling at nearly the speed of light. The emittance is a measure of how tightly packed the electron beams are.

This small emittance, say the scientists, proves that the ERL could produce X-ray beams focused down to exceedingly small volumes, allowing investigation of materials with unprecedented precision and speed.

In another breakthrough for the ERL project, the scientists have built and tested a prototype seven-cell superconducting radio frequency (SRF) cavity. SRF cavities are needed to accelerate the electrons from the injector to very high energies in order to produce the X-rays. The SRF cavities are operated at -456 F (-271 C), just 2 degrees above absolute zero temperature.

The Cornell researchers' SRF cavity has met the first performance specifications necessary to continuously power a high intensity ERL. It has been tested in a vertical cryostat at the required temperature and electric field gradients -- a significant milestone because it proves the cavities can perform at high power while within the scientific and cost parameters of the project.

The team must now demonstrate the efficacy of their cavities in horizontal tests, which will take place in 2012.

"These developments go a long way toward proving that an ERL X-ray source will work as predicted by simulations and theory," said Sol Gruner, director of CHESS.

Recommend this story on Facebook, Twitter,
and Google +1:

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Story Source:

The above story is reprinted from materials provided by Cornell University. The original article was written by Anne Ju.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here