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ScienceWeek
CONDENSED MATTER: ON TWO-DIMENSIONAL ELECTRON GASES
The following points are made by A.C. Durst and S.M. Girvin (Science 2004 304:1752):
1) A two-dimensional electron gas (2DEG) is a type of metal in which electrons are confined to move only within a two-dimensional plane formed at the interface between two semiconductors. At high magnetic fields, this system exhibits the quantum Hall effects, phenomena in which the transverse (Hall) component of the electrical resistance is quantized in integer or fractional units of a fundamental quantum of resistance. These effects have been studied exhaustively over the past two decades and were the subject of two Nobel Prizes.
2) In newer experiments which were conducted at much lower magnetic fields, experimenters subjected the system to microwave radiation and found that in the presence of microwaves of the right frequencies, the electrical resistance of the 2DEG would decrease (1). This is very surprising because one would expect that the absorption of microwaves would cause the system to heat up (just as food in a microwave oven does), exciting vibrational modes that scatter electrons and thereby increase the electrical resistance. More surprising still, it was found that for a high enough radiation intensity, the resistance could be reduced nearly all the way to zero (2,3). Researchers became very curious very quickly(4).
3) States of matter characterized by zero resistance hold a special place in the heart of a condensed matter physicist because zero resistance is often an indication that some interesting physics is afoot. Most materials exhibit some electrical resistance because the flow of electrons is inhibited by scattering from impurities, defects, and excited modes of the system. For a material in equilibrium to exhibit zero resistance, it must organize itself into some sort of collective state in which all of the electrons work together to make the state robust against these scattering mechanisms that degrade the electrical current.
4) So one possibility is that this new microwave-induced zero-resistance state corresponds to a new collective state induced by the presence of the microwaves. This idea is appealing because in the absence of microwaves, and at much higher magnetic fields, this very system exhibits the quantum Hall effects, which are indeed characterized by collective states of matter. Note, however, that in quantum Hall systems, zeros in the longitudinal (dissipative) resistance are accompanied by plateaus in the transverse (Hall) resistance, which are crucial to the physics of the quantum Hall effects. Yet in the present case, no such plateaus are observed. Nonetheless, some other collective effect could be at work here, and ideas along these lines have been discussed (2).
5) However, there is another possibility. Because the system is pumped with microwaves, it is continuously supplied with energy from an outside source, and therefore is not in equilibrium. A pumped system can exhibit zero resistance, or even negative resistance, without forming a collective state, as long as the pump is able to overwhelm the effect of the probe used to measure the resistance (5). The probe in this case is the applied dc current. Without microwaves, a dc voltage builds up in response to the applied current as prescribed by the dark (no- microwaves) resistance. If the effect of the microwaves is to induce an additional dc voltage in the opposite direction, the measured resistance will decrease. If this voltage matches the dark voltage, the resistance will be zero. If it exceeds it, the resistance will be negative.
References (abridged):
1. M. A. Zudov et al., Phys. Rev. B 64, 201311 (2001)
2. R. G. Mani et al., Nature 420, 646 (2002)
3. M. A. Zudov et al., Phys. Rev. Lett. 90, 46807 (2003)
4. B. J. Keay et al., Phys. Rev. Lett. 75, 4102 (1995)
5. A. C. Durst et al., Phys. Rev. Lett. 91, 86803 (2003)
Science http://www.sciencemag.org
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Notes by ScienceWeek:
The story of the Hall effect begins with a mistake made by James Clerk Maxwell (1831-1879). In the first edition of his /Treatise on Electricity and Magnetism/, which appeared in 1873, Maxwell discussed the deflection of a current by a magnetic field. He then said (in error): "It must be carefully remembered that the mechanical force which urges a conductor... acts, not on the electric current, but on the conductor which carries it."
In 1878, Edwin Hall (1855-1938), a student at Johns Hopkins University, was reading Maxwell for a class taught by Henry Rowland (1848-1901). Hall asked Rowland about Maxwell's remark, and Rowland replied that he "doubted the truth of Maxwell's statement and had some time before made a hasty experiment... though without success."
Hall made a fresh start and designed a different experiment, aimed at measuring, instead, the magneto-resistance -- that is, the change of the electrical resistance due to the magnetic field. As we now know, that is a much harder experiment, and it too failed. Maxwell appeared to be safe. Hall then decided to repeat Rowland's experiment. Following his mentor's suggestion, Hall replaced the original metal conducting bar with a thin gold leaf to compensate for the weakness of the available magnetic field. That did the trick. He found that -- Maxwell to the contrary notwithstanding -- the magnetic field permanently altered the charge distribution, thereby deflecting the galvanometer connected to the lateral edges of the conductor. The transverse potential difference between the edges is called the "Hall voltage". The "Hall conductance" is essentially the longitudinal current divided by this transverse voltage.
The discovery earned Hall a position at Harvard University. His paper came out in 1879, the year of Maxwell's death at age 48. In the second edition of Maxwell's book, which appeared in 1881, a polite footnote by the editor says: "Mr. Hall has discovered that a steady magnetic field does slightly alter the distribution of currents in most conductors so that the statement must be regarded as only approximately true."
It is now known that the magnitude, and even the sign, of the Hall voltage depends on the material properties of the conductor -- the gold leaf in Hall's experiment. That made the Hall effect an important diagnostic tool for investigating the carriers of electric current. Eventually it pointed to the concept of positively charged holes as current carriers in solids.
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QUANTUM PHYSICS: A 2-DIMENSIONAL QUANTIZED HALL INSULATOR
In classical physics, the *Hall effect is the development of a transverse voltage across a current-carrying conductor in a magnetic field, the voltage being perpendicular to both the direction of the current and the direction of the magnetic field. In quantum physics, there are two other Hall effects, an integer charge quantum Hall effect, and a fractional charge quantum Hall effect, these quantum Hall effects being observed at extremely low temperatures (a few degrees Kelvin) and extremely high magnetic fields (at least several tesla). Both quantum Hall effects were first noted in the 1980s. In the quantum Hall effect, the Hall resistance, the ratio of the voltage to the current, is precisely related to Planck's constant, the electronic charge, and an integer or rational fraction.
Concerning the electrical properties of matter, the general theoretical definition of an insulator is a material in which the conductivity vanishes at the absolute zero of temperature. In classical insulators, vanishing conductivities lead to infinite resistivities. But other insulators can show more complex behavior, particularly in the presence of a high magnetic field, where different components of the resistivity can display different behaviors. For example, in magnetoresistive systems the *magnetoresistance becomes infinite as the temperature approaches zero, but the transverse (Hall) resistance remains finite. Such systems are known as "Hall insulators".
M. Hilke et al (Nature 1998 395:675) report experimental evidence for a *quantized Hall insulator in a 2-dimensional electron system confined in a *semiconductor quantum well. The authors report the Hall resistance is quantized in the quantum unit of resistance of given by the ratio of Planck's constant to the square of the electronic charge. At low fields, the sample reverts to a normal Hall insulator. The authors suggest the existence of these insulators can serve as guidelines for a complete understanding of 2-dimensional systems in strong magnetic fields.
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Notes by ScienceWeek:
Hall effect: The importance of the classical Hall effect, discovered by E. H. Hall in 1879, is that it indicates the sign of the charge carriers in a conductor. Hall placed a metal strip carrying a current in a magnetic field, and observed a voltage difference produced across the strip. The side of the strip at the higher voltage depends on the sign of the charge carrier, and Hall's observations demonstrated that in metals the charge carriers are negative. It was only later that the metal charge carriers were identified as electrons. The Hall effect again became an active area of research with the discovery of the quantized Hall effect by Klaus von Klitzing, who received the Nobel Prize in Physics for his discovery in 1985. Before von Klitzing's discovery, it was believed that the amount of voltage difference across the conducting strip varied in direct proportion to the strength of the magnetic field. Von Klitzing demonstrated that under the special conditions of low temperature, high magnetic field, and two-dimensional electron systems in which electrons are confined to move in a plane, the voltage difference is quantized, increasing in a series of steps with increasing magnetic field.
magnetoresistance: A change in the electrical resistance of a conductor or semiconductor upon the application of a magnetic field, a property of magnetoresistive systems.
quantized: In experimental physics, a quantized variable is a variable taking only discrete multiple values of a quantum mechanical constant. In theoretical physics, "quantizing" means the consistent application of certain rules that lead from classical to quantum mechanics. In general, "quantization" is a transition from a classical theory or a classical quantity to a quantum theory or the corresponding quantity in quantum mechanics.
semiconductor: This experiment involved a silicon-germanium system doped with boron.
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