Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


A standard measurement of resistance, the quantum Hall effect, changes dramatically at the edge of a sample

A standard measurement of resistance, the quantum Hall effect, changes dramatically at the edge of a sample

When a conductor carrying electrical current is placed in a magnetic field, the flowing electrons experience a force perpendicular to both the magnetic field and the current. The production of voltage, or potential difference, by this (Lorentz) force is known as the Hall effect. It is exploited in several electronic devices such as flow sensors, joysticks, car ignitions and even spacecraft propulsion.

At very low temperatures, the classical Hall effect breaks up and displays some striking quantum characteristics. In fact, this so-called integer quantum Hall effect reveals quantizations that are so precise they have been used to accurately determine some important numbers in quantum mechanics, including the fine-structure constant that characterizes the strength of electromagnetic forces.

Now, Akira Furusaki at the RIKEN Advanced Science Institute in Wako and co-workers in Japan and the USA have shown that the quantum Hall effect is strongly affected by boundaries at the edge of a material1. Their findings could alter the underlying quantum theories of condensed matter.

Quantum quirkiness in the Hall effect

During the classical Hall effect, the electrons moving under the influence of the Lorentz force experience resistance to their flow. This ‘Hall resistance’ increases linearly with the strength of the magnetic field.

The quantum version of the Hall effect was discovered in 1980 when researchers measured the properties of electrons confined to just two dimensions at very low temperatures near absolute zero. Here, the Hall resistance looks very different—it jumps up in quantized steps as the magnetic field strength increases, producing a series of plateaus.

The size of each step is determined by two fundamental constants, the electron charge e and Planck’s constant h, regardless of the material being studied. This quantum Hall effect is so precisely quantized that it is now used as a standard of resistance measurement.

Many theories have been proposed to explain exactly how electrons move between the resistance plateaus in the quantum Hall effect.

At such low temperatures the electrons experience a phenomenon called Anderson localization—they are scattered so much that they cannot propagate over any distance, and effectively stay in one place. This means that their wavefunctions are very narrow, and the sample effectively acts as an insulator against the Hall effect.

The main theoretical challenge is to work out what happens to delocalize the wavefunctions, allowing the system to jump between adjacent plateaus.

Finding fractals

Previous research completed by Furusaki and co-workers has helped them to explain the Anderson localization. In one study2, they examined the electron wavefunctions in materials that can undergo transitions from metallic (electrically conducting) to insulating behavior.

They found that the electron distribution obeys so-called multifractal statistics, meaning that they follow similar patterns on both small and large scales. However, the electrons at the sample’s boundary edges showed quite different distributions from those in the bulk of the sample.

The researchers realized that the boundary differences will influence the quantum Hall effect. Previous calculations have missed this subtlety by using bulk physical quantities that are valid only in the center of a sample.

“We showed that boundary multifractal properties are different from bulk multifractal properties,” explains Furusaki. “It was a very natural next step for us to study boundary multifractality in the integer quantum Hall effect.”

Examining the edge

The quantum Hall effect depends on impurities or defects in the sample, which can be thought of as hills that the electrons must climb over or skirt around. At the sample edges, there are limits to the directions the electrons can travel to overcome these obstacles, so their dynamics are different. However, it turns out that these restrictions at the edges are crucial in producing the quantum Hall effect.

“In a sample showing the quantum Hall effect, electron wavefunctions in the bulk are all localized and cannot carry electric current. Instead, there are ‘edge wavefunctions’ extended along the edge of the sample which can carry current,” explains Furusaki.

“When the electrons undergo a transition between two successive resistance plateaus, the number of edge states changes by 1. At the transition point the wave functions, both at bulk and at boundary, are neither extended nor localized; they are called critical.”

Furusaki and colleagues recalculated these critical wavefunctions for electrons undergoing a transition between plateaus near the edge of a sample. They found that the transitions do not follow the same multifractal statistics that have been assumed in previous studies.

Edging towards a new future

Any new theories for the quantum Hall effect will have to take these constraints into account. Furusaki looks forward to unraveling the final details of this remarkable example of quantum physics in action.

“Some recent experiments are using scanning tunneling microscopy to observe electrons in a quantum Hall sample, but they are still at a primitive stage and resolution is not high,” he says. “I suspect that the edge states in the quantum Hall effect should indirectly affect the electron distribution at boundaries, but it will take more work to get a good understanding of it.”

In the future, the quantum Hall effect could become important in the world of electronics. In a different study3, Furusaki and his collaborators have already explained an unusual quantum Hall effect caused by the relativistic nature of electrons in graphene, which could eventually replace silicon in integrated circuits.

1. Obuse, H., Subramaniam, A.R., Furusaki, A., Gruzberg, I.A. & Ludwig, A.W.W. Boundary multifractality at the integer quantum Hall plateau transition: Implications for the critical theory. Physical Review Letters 101, 116802 (2008).

2. Obuse, H., Subramaniam, A. R., Furusaki, A., Gruzberg, I. A. & Ludwig, A. W. W. Multifractality and conformal invariance at 2D metal-insulator transition in the spin-orbit symmetry class. Physical Review Letters 98, 156802 (2007).

3. Nomura, K., Ryu, S., Koshino, M., Mudry, C. & Furusaki, A. Quantum Hall effect of massless Dirac fermions in a vanishing magnetic field. Physical Review Letters 100, 246806 (2008).

The corresponding author for this highlight is based at the RIKEN Condensed Matter Theory Laboratory

Akira Furusaki

Akira Furusaki was born in Saitama, Japan, in 1966. He graduated from Faculty of Science, the University of Tokyo in 1988 and obtained his PhD in physics in 1993 from the same university. He became a research associate at Department of Applied Physics, the University of Tokyo in 1991, and worked as a postdoctoral associate for two years at Department of Physics, Massachusetts Institute of Technology in USA, before being appointed as an associate professor at Yukawa Institute for Theoretical Physics, Kyoto University in 1996. Since October 2002 he has been a chief scientist of Condensed Matter Theory Laboratory at RIKEN. His research focuses on developing theories of quantum electronic transport, superconductivity and magnetism in solids. He received Nishinomiya Yukawa Commemoration Prize in Theoretical Physics (2004).

Saeko Okada | ResearchSEA
Further information:

More articles from Physics and Astronomy:

nachricht Light-driven atomic rotations excite magnetic waves
24.10.2016 | Max-Planck-Institut für Struktur und Dynamik der Materie

nachricht Move over, lasers: Scientists can now create holograms from neutrons, too
21.10.2016 | National Institute of Standards and Technology (NIST)

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Light-driven atomic rotations excite magnetic waves

Terahertz excitation of selected crystal vibrations leads to an effective magnetic field that drives coherent spin motion

Controlling functional properties by light is one of the grand goals in modern condensed matter physics and materials science. A new study now demonstrates how...

Im Focus: New 3-D wiring technique brings scalable quantum computers closer to reality

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

Im Focus: Scientists develop a semiconductor nanocomposite material that moves in response to light

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

Im Focus: Diamonds aren't forever: Sandia, Harvard team create first quantum computer bridge

By forcefully embedding two silicon atoms in a diamond matrix, Sandia researchers have demonstrated for the first time on a single chip all the components needed to create a quantum bridge to link quantum computers together.

"People have already built small quantum computers," says Sandia researcher Ryan Camacho. "Maybe the first useful one won't be a single giant quantum computer...

Im Focus: New Products - Highlights of COMPAMED 2016

COMPAMED has become the leading international marketplace for suppliers of medical manufacturing. The trade fair, which takes place every November and is co-located to MEDICA in Dusseldorf, has been steadily growing over the past years and shows that medical technology remains a rapidly growing market.

In 2016, the joint pavilion by the IVAM Microtechnology Network, the Product Market “High-tech for Medical Devices”, will be located in Hall 8a again and will...

All Focus news of the innovation-report >>>



Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Oasis of life in the ice-covered central Arctic

24.10.2016 | Earth Sciences

‘Farming’ bacteria to boost growth in the oceans

24.10.2016 | Life Sciences

Light-driven atomic rotations excite magnetic waves

24.10.2016 | Physics and Astronomy

More VideoLinks >>>