Physics Today, volume 56, Number 4, page 24, April 2003
Microwaves Induce
Vanishing Resistance in TwoDimensional Electron Systems
At modest magnetic fields and microwave excitations,
the resistance of a 2D semiconductor can oscillate all the way to zero.
Zero resistance is a rare
phenomenon in condensed matter systems, and its observation heralds interesting
physics. Heike Kamerlingh Onnes
was the first to see a transition to a zeroresistance state, when he
discovered superconductivity in mercury in 1911. Nearly 70 years later, Klaus
von Klitzing observed the quantum Hall effect (QHE)
accompanying vanishing longitudinal resistance in twodimensional electron
systems (2DES) at high magnetic fields. So when Ramesh
Mani (now at Harvard University) and collaborators
submitted a paper to Nature on "zeroresistance states" last
June^{1} and Michael Zudov
and RuiRui Du (University
of Utah) and colleagues posted a preprint with "evidence for a new dissipationless effect" in October^{2}both groups studying 2DES irradiated with
microwaves at lower magnetic fieldsmany people were intrigued.
At first glance, the new observations bear
enticing resemblances to the QHE. For example, the resistance in the two
effects approaches zero with similar temperature dependences. But there are
significant differences. Most noticeably, not only is the Hall resistance not
quantized in the recent experiments, but the microwaves appear to have
virtually no effect on the Hall resistance. And while the QHE is typically seen
in magnetic fields of several tesla, the new effects
are seen in fields a factor of 50 or so lower, about 0.1 T. In addition, the
QHE is an equilibrium effect, whereas the lowfield state is a nonequilibrium one induced by microwave irradiation.
First sightings
In 2DES, electrons are typically confined
at interfaces between two different semiconductors, or within a quantum well
formed in a threelayer semiconductor sandwich. When a magnetic field is
applied perpendicular to the 2D plane of such systems, the electrons' orbital motion
is quantized, which leads to flat bandssocalled Landau levelsin the energy
spectrum. The energy levels are evenly spaced with a separation of w_{c}, where the cyclotron frequency w_{c }= eB/m*.
Here, m* is the effective electron mass in the semiconductor (for
gallium arsenide, about 0.067 of the bare electron mass). The strength of the
magnetic field can be expressed in terms of the filling factor n, which
specifies the number of filled Landau levels. The higher the field, the more
states there are in each Landau level, and the lower the filling factor for a
given electron density.
Figure 1 Resistance of a twodimensional electron system with very
high mobility under microwave irradiation. Shubnikovde
Haas oscillations are seen in the longitudinal resistance R_{xx} for fields
above 0.2 T. Below that, R_{xx} without microwaves (red) is featureless;
with microwaves, R_{xx}
oscillates dramatically (purple), although the transverse Hall resistance R_{xy}_{
}(green) remains essentially unaffected. The positions of the resistance
minima are proportional to B_{f }=
wm^{*}/e, where w is the microwave
frequency and m^{*}
is the effective electron mass. (Adapted from ref.
1.) 
Landaulevel quantization leads to a
variety of effects in 2DES. At large fieldstypically several teslathe resistance is dominated by the QHE: At fields
corresponding to filled Landau levels, that is, integer values of n, the
longitudinal resistance R_{xx}measured
in the direction of the applied currentgoes to 0 while the transverse or Hall
resistance R_{xy}_{ }shows
plateaus at h/ne^{2}. And in clean samples, Hall plateaus are also
found at fractional values of n. Meanwhile, at lower magnetic fields
(corresponding to higher filling factors), socalled Shubnikovde
Haas (SdH) oscillations appear in the resistance as
the fielddependent Landaulevel energies pass through the Fermi energy of the
2DES.
The QHE and SdH
oscillations are well understood and are essentially DC effects. The first
report of microwaveinduced features was made by Zudov
and Du, using samples supplied by Jerry Simmons and
John Reno (Sandia National Laboratories).^{3} Peide Ye (now at Agere Systems) and colleagues subsequently saw similar
features.^{4} Those two early
experiments saw radiationinduced oscillations in the resistance at low
magnetic fields, below the onset of SdH oscillations.
In those experiments, though, the microwave response did not reach zero
resistance.
The strength of the induced behavior
appears to depend on the electron mobility, a measure of how "clean"
the sample is. In the earlier experiments, the mobility was about 3 ´10^{6 }cm^{2}/Vsconsidered
quite a high value. Continuing improvements in sample quality have made the new
work possible: The sample made by Vladimir Umansky (Weizmann Institute of Science) for Mani
and coworkers had a mobility five times higher, and
the sample by Loren Pfeiffer and Ken West (Lucent Technologies' Bell Labs) for
the
Figure 1
illustrates the effect of microwave irradiation on the lowfield resistance, as
measured by Mani and colleagues at the Max Planck
Institute for SolidState Physics in
Probing the effect

Figure 2 Microwaveinduced oscillations in
the resistance are periodic in 1/B,
where B is the applied
magnetic field. (a) Experimenters at Harvard University and the Max
Planck Institute for 
When the resistance is plotted in terms of
inverse field (or, alternatively, inverse cyclotron frequency), the
oscillations are regularly spaced, as shown in figure
2, with a period set by the microwave frequency. Much attention has been
paid to the phase of the oscillations. In their early experiments, Zudov and Du and also Ye and colleagues found that, for microwaves of frequency w, the
oscillations were periodic with maxima at º w/w_{c }= j and minima at = j +
1/2, for j an integer. Mani and company also
saw regular oscillations, but with a "1/4cycle phase shift": The
maxima occurred at = j 
1/4 and the minima at j + 1/4. In the recent
Both the HarvardStuttgart group and the
Utah group have studied the various dependencies of the resistance. Oscillations
were observed at all microwave frequencies they examined, from 27 GHz through
150 GHz. And at the American Physical Society's March meeting in Austin, Texas,
Robert Willett (Bell Labs) reported observing oscillations at frequencies down
to 3 GHz. The resistance is independent of the bias current applied to the
2DES, and the oscillations grow in amplitude as the microwave power is
increased.
The more interesting dependence is that on
temperature. Figure 3 shows the temperature
dependence of the oscillations, as measured by Zudov
and Du for a GaAs/AlGaAs
quantum well sample irradiated at 57 GHz. The behavior of the resistance minima
resembles that of the QHE: an activated temperature dependence of the form
exp(E_{A}/k_{B}T),
where k_{B} is Boltzmann's
constant. Surprisingly, the activation energies E_{A} observed
by both groups are very high: The HarvardStuttgart group found E_{A}/k_{B} up to 10 K and the Utah group up to 20
Kalmost an order of magnitude larger than the Landaulevel spacing or the
microwave photon energy. For fixed microwave frequency, both groups find a
roughly linear relationship between the activation energy and the magnetic
field at which the minima occur.
Figure 3 Activated behavior is seen in the temperature dependence
of the microwaveinduced vanishing resistance. When plotted on a logarithmic scale
against inverse temperature, the normalized resistance minima (red) for the
first four oscillations show a thermally activated dependence of the form
exp(E_{A}/k_{B}T), where k_{B}
is Boltzmann's constant. The activation energies
are surprisingly large, up to an order of magnitude higher than any other
energy scale in the system. The resistance maxima are plotted in blue.
(Adapted from ref. 2.) 
Some researchers have questioned whether the
resistance is truly zero in the microwaveirradiated samples. At the March
meeting, Willett reported measuring negative, not zero, voltages between some
electrodes placed around the edges of his samples.
Theorists chime in
Word of the observations of vanishing
resistance spread quickly, and many theorists began trying to understand the
origins of the behavior. The arXiv.org eprint server has been functioning as a
clearinghouse of ideas over the past several months. A complete understanding,
though, has yet to emerge.
Adam Durst and colleagues (
Figure 4 Impurity scattering is one explanation being proposed for
the microwaveinduced behavior. In a twodimensional electron system, an
applied voltage V will give a
spatial tilt to Landaulevel energies (blue). Microwaves of frequency w can excite
an electron to a higher Landau level. If the photon energy is slightly higher
than an integral multiple of the level spacing w_{c}, energy can still be conserved if the
electron scatters laterally in the "upstream" direction. Such
scattering would reduce the conductivity and could drive it to zero or even
to negative values. (Adapted from ref. 5.) 
As illustrated in figure 4, a voltage bias applied to the 2DES
will produce a spatial gradient in the Landaulevel energy. An electron can
absorb a microwave photon whose energy is a multiple of the Landaulevel
spacing, and the electron will stay in the same place. If the photon energy is
offresonance, energy can be conserved if impurities or other imperfections in
the 2DES scatter the electron laterally. The "upstream" or
"downstream" motion will reduce or increase the conductivity of the
sample. If scattering events are frequent enough, the conductivity could be
driven to zero or even to negative values when the microwave frequency is above
a multiple of the cyclotron frequency. (In 2DES, if the transverse Hall
conductivity dominates the DC response, the longitudinal resistance is actually
proportional to the longitudinal conductance.) A similar effect has been
observed in a different symbol: James Allen (
The Yale group's calculations using a
simplified model for the impurity potential reproduce not only the period of
the observed resistance oscillation, but also the phase found by Mani and company. An explicit connection between the
calculations and the observed zero resistance was put forward by Anton Andreev (University of Colorado) and colleagues at Columbia
University,^{10} who noted that a
negative conductivity makes the 2DES unstable (a point also made by Anderson
and Brinkman^{7} and by Anatoly Volkov of the University of Bochum,
Germany^{11}). Andreev
and coworkers showed that this instability causes the symbol to develop a
domain structure with an inhomogeneous current pattern, for which the measured
resistance would be zero. Andreev notes that the
resistance oscillations indeed look like they could have swung negative but
have instead been truncated at 0. Willett's observation of negative voltages
may lend support to the idea of inhomogeneous current flow.
Other explanations have also been
proposed. James Phillips (
Richard Fitzgerald
1. R. G. Mani, J. H. Smet, K. von Klitzing, V. Narayanamurti, W. B.
Johnson, V. Umansky, Nature 420, 646
(2002); http://arXiv.org/abs/condmat/0303034.
2. M. A. Zudov, R. R. Du, L. N. Pfeiffer, K. W. West, http://arXiv.org/abs/condmat/0210034; Phys. Rev. Lett. 90,
046807 (2003).
3. M. A. Zudov, R. R. Du, J. A. Simmons, J. L. Reno, http://arXiv.org/abs/condmat/9711149 ; Phys. Rev. B. 64,
201311 (2001).
4. P. D. Ye, L. W. Engel, D. C. Tsui, J. A. Simmons, J. R. Wendt, G. A.
Vawter, J. L. Reno, Appl. Phys.
Lett. 79, 2193 (2001).
5. A. C. Durst, S. Sachdev, N. Read, S. M. Girvin, http://arXiv.org/abs/condmat/0301569.
6. V. I. Ryzhii, R. A. Suris, B. S. Shchamkhalova, Sov.
Phys. Semicond. 20, 1299 (1986); V. I. Ryzhii, Sov. Phys.
Solid State 11, 2078 (1970).
7. P. W. Anderson, W. F.
Brinkman, http://arXiv.org/abs/condmat/0302129.
8. J.
Shi, X. C. Xie, http://arXiv.org/abs/
condmat/0302393;condmat/0303141.
9. See, for example, B. J.
Keay et al., Phys. Rev. Lett. 75, 4102 (1995).
10. A. V. Andreev, I. L. Aleiner, A. J. Millis, http://arXiv.org/abs/condmat/0302063.
11. A. Volkov, http://arXiv.org/abs/condmat/0302615.
12. J. C. Phillips, http://arXiv.org/abs/condmat/0212416;condmat/0303181.
13. A. A. Koulakov, M. E. Raikh, http://arXiv.org/abs/condmat/0302465.
14. S. A. Mikhailov, http://arXiv.org/abs/condmat/0303130.
© 2003 American Institute of Physics