Evidence for current-flow anomalies in the irradiated 2D electron system at small magnetic fields.

Abstract

We report experimental transport results in 2D electron systems exposed to dipole radiation up to 20 GHz. Magnetoresistance oscillations occur as seen with higher frequency radiation; however, minima here can be seen to extend to negative biases, and zeros are not observed persistently around sample perimeters. Under radiation, voltages are generated from internal to external contacts in the absence of applied driving currents. These findings may be consistent with theoretical pictures of current instabilities due to local negative resistivities.

Full text

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Evidence for current flow anomalies in the irradiated 2D electron system at
small magnetic fields

R.L. Willett, L.N. Pfeiffer, K.W. West
Bell Laboratories, Lucent Technologies

Abstract

We report experimental results of low temperature magnetotransport in high mobility 2D
electron systems exposed to radiation up to 20GHz frequency using a simple dipole
configuration. Magnetoresistance oscillations are observed as in previously reported
higher frequency radiation on 2D systems, however minima here can be seen to extend to
negative biases, and zeroes previously reported are not observed persistently around the
full sample perimeters. In addition, under radiation, voltages are observed from internal
to external contacts in the absence of applied driving currents not due to simple
rectification. These findings are consistent with micro- and macroscopic theoretical
pictures of radiation induced transport and current instabilities due to local negative
resistivities. However, the temperature dependent development of minima is shown to be
severely power dependent, and outside of present theoretical understanding.

Simple irradiation in the GHz range on 2D electron systems has been shown to
have remarkable consequences on the transport at low magnetic fields. It was found by
Zudov, et. al. [1] that radiation from 30 to 120GHz imposed on a high quality
heterostructure resulted in a series of oscillations periodic in ω/ωc with ω the radiation
frequency and ωc the cyclotron frequency, using bare GaAs electron mass. Subsequently
it was observed by Mani, et al [2] and Zudov, et al [3] that in high mobility samples the
minima can form apparent zeroes, with the temperature dependence activated. The
series of minima, formed at ω/ωc = j +α, j = 1,2,3…, α = ½ [1] or ¼ [2], and showed for
the primary minima (j = 1, 2) activation energies substantially larger than the incident
radiation.
Multiple theoretical addresses of these results have been made [4-7], with one
microscopic picture [4] developed that describes radiation induced, disorder facilitated
magnetotransport oscillations. In this model radiation raises an electron over multiple
Landau levels, with disorder scattering providing a preferential boost or reduction to the
conductivity dependent upon the relative position of the new high energy level to the
adjacent Landau levels. Numerical calculations from the diagrammatic expansions show
an oscillatory magnetotransport with the appropriate period of ω/ωc. Significantly, these
calculations showed that under high radiation power, the conductivity minima could be
seen to become negative. Further work by Andreev, et al. [7], described the macroscopic
consequences of this negative conductivity. It was shown that current instabilities will
result, with current inhomogeneities or circulations possible: current vortices may result
under sufficient radiation power.
We report in our experimental work here prominent magneto-oscillations at low
frequencies (<20GHz) and in ultra-high mobility samples that demonstrate the essential
physics of the previously observed effects. In our studies, however, we study in detail
the oscillatory resistance and observe minima consistent with the previously reported

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“zeroes”, but also note minima in which the voltage drop is distinctly negative. We have
mapped the resistivity properties around sample perimeters and find that all samples
show variation in minima, with no samples showing all zeroes around the perimeter. We
then tested voltage drops from internal contacts to external contacts with radiation but
without applied driving current: substantial voltages were observed, consistent with large
currents induced by the radiation yet not consistent with a simple rectification of the
radiation. These findings are in sum supportive of both the microsopic and macroscopic
pictures developed to describe radiation induced magnetoresistance oscillations.
However, an important property of the radiation-induced minima is the temperature
dependence: the previous experimental work [2,3] showed activated transport consistent
with an energy gap in the transport spectrum. We examined the transport minima and
found a complicated temperature dependence: hysteresis in the minima are possible, with
temperature development not necessarily activated over a large temperature range. In
addition, we find all temperature dependence is severely dependent upon the incident
radiation power.

The samples used in these experiments all have mobilities in excess of
15x106cm2/V-sec., with densities near 2x1011cm-2 and were taken from 3 different MBE
produced GaAs/AlGaAs wafers. Contacting to the 2D electron system is accomplished
with diffused In or Ni/Au/Ge contacts. The Ni/Au/Ge contacts have a particular layering
scheme that allows highly efficient contacting in that a large percentage of the area
covered by the contact diffuses to the 2D layer. Unlike previous work [1-3], radiation is
not applied to the sample by rigid wave-guide but rather by a linear dipole antenna hung
over the sample. The dipole is greater than 7mm in extent, and the samples range from
400µm to 5mm in largest dimension. Frequencies applied can range continuously from 2
to 20GHz. Measurements were made in a He3 refrigerator providing temperatures down
to 280mK with radiation.

The lower frequency range accessed here examines fundamentally the same
physics as the higher frequency range (30-120GHz), as shown by the data in Figure 1.
Using indium contacts the oscillations are observable down to near 3GHz at this
temperature and the apparent zeroes can be observed at near 8GHz. Such a minimum
demonstrating this saturation near zero but at 20GHz was examined for its temperature
dependence near full incident power: see Figure 1b. It demonstrates an activated
temperature dependence with activation energy E, (ρ∼e-(E/kT)) of 6K. This scales well
with the results of Zudov et al [3] where with incident radiation of 54GHz, an activation
energy of 18K was derived. One novelty at the lower frequencies is an apparent
minimum in resistivity at roughly twice the magnetic field value of the principal (j=1)
minimum. Beyond this difference, these results indicate that the process of magneto-
oscillation due to incident radiation appears continuously over a large frequency range.
One of the findings of this work is that negative bias can be observed across
longitudinal resistivity contacts as shown in Figure 2. The measurement configuration
here is constant current driven at low frequency (3 to 13Hz) through a van der Paaw
configuration of contacts with voltage tapped along one side of the sample. The
magneto-transport of Fig. 2a shows distinct negative bias for the minimum at j=1 as the
incident radiation power and frequency are increased. In another sample (Fig. 2b),

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negative bias is again observed but as incident radiation power is increased structure in
the center of the minimum appears and the minimum becomes positive. These negative
bias minima have been observed in samples from all three wafers examined. The
structure of the minima change with thermal cycling. Better contacting of the 2DES
allows observation of the negative bias, as our Ni/Au/Ge contacts with uniform metal
diffusion to the conducting layer tend to demonstrate the negative bias with higher
prevalence. These results of negative bias can be understood in terms of a current path
counter to the net current flow occurring locally near the contacts tested. This picture
would suggest that not all contacts would necessarily show negative bias, and this is as
we have observed – only a limited number of contact pairs demonstrate this type of
negative bias on any given sample.
To further understand possible complicated current flow patterns under
illumination we have mapped the voltage differences around the periphery of several high
mobility samples. Figure 3 shows the results of such a measurement: similar minima do
not occur around the entire periphery of the sample. In the sample of Figure 3 minima
along one side of the sample show the “zeroes” while the opposite side shows a positive
bias where the “zeroes” are anticipated. When the B-field direction is reversed the
minima on the two sides of the sample are reversed in properties – “zeroes” now occur
where the positive bias was previously observed and the vise-versa. This reversal of
properties is symmetric about the line determined by the radiation dipole direction. All
samples examined to date, including the 400µm x 400µm square samples, have
demonstrated this lack of zeroes completely around the sample perimeter and the reversal
of zero positions with change in magnetic field direction. This type of voltage mapping
shows that a homogeneous resistance is not present throughout the samples upon
illumination and the reversal of the minima with B-field reversal shows that improper
contacting is not the source of the non-“zero” minimum.
An important property to determine is whether significant currents are generated
within the samples upon radiation but in the absence of driving currents. To this end we
produced a series of samples with contacts internal to the periphery and also standard
peripheral contacts. The voltage difference between this internal and an external contact
can be measured; with no external current input, if radiation generates a current within
the sample that has a net value between those contacts, that Hall voltage generated may
be measurable. The results of such measurements are shown in Figure 4: in these the
voltage between the labeled contacts is measured with differential input to a preamplifier
(PAR 113) over a series of frequency windows, from d.c. to several Hz. A substantial
voltage is indeed generated, with features reflecting properties observed in the standard
longitudinal resistivity measurement (Fig. 4a), and representing a large induced current.
The voltage generated at the j=1 feature corresponds to a current of roughly 5µA flowing
between the contacts. At low frequencies (d.c. to 3Hz) a significant rectification signal
is present, but as the frequency detection range is raised (0.1 to 3Hz) this rectification
signal becomes weaker, particularly at the j=1 feature. This rectification is minimal
between peripheral contacts and distinctly different in form from the internal to external
contact voltage (Fig. 4c). While all samples examined have shown induced voltages
from center to external contacts under radiation, a particularly surprising result is shown
in Figure 4d: for this sample, the feature at j=1 is either a minimum or maximum
dependent upon the sweep direction of the B-field. This suggests a marked instability in

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the current paths due to the radiation, with these results in sum showing that large low
frequency currents are induced by radiation.
The findings of negative bias, inconsistent oscillatory minima around the sample
perimeters, and large induced voltages from center to external contacts under radiation all
suggest that substantial current instabilities and anomalous current paths are produced
within the 2D gas at low B-field. Such current pathologies are generally consistent with
the theoretical macroscopic picture [7] and by inference the microscopic picture [4]
developed describing radiation induced photoconductivity and the current instabilities
that should result from negative resistivities [4,7]. Further development of these
theoretical pictures is needed to account for these specific experimental findings. While
we can generally deduce that substantial current variations occur across the sample, it is
not possible to attribute these currents to a homogenous response of the 2DES to the
radiation, an intrinsic but inhomogeneous response to the radiation, or an extrinsic input
that does not allow homogenous radiation of the sample, such as interference from the
sample leads.
An open issue within the standing theoretical models is the temperature
dependence of the minima. We examined the temperature dependence of the j=1
minimum at 20GHz but for a range of incident radiation powers. A first observation was
a B-field sweep hysteresis effecting the minimum, with data taken in both sweep
directions for completeness (Fig. 5a). At minimum attenuation of the incident radiation
the temperature dependence is activated over two orders of magnitude in resistance.
When less power is incident this activated property is present only for one B-field sweep
direction, with the low temperature resistivity showing marked deviation. For lower
incident powers the activation energies are clearly of lower value, indicating a strong
power dependence to the minimum formation. The activation energies are plotted as a
function of incident power (Fig. 5c) showing a linear relationship. This power
dependence and the presence of hysteresis indicate that the activated transport may not
reflect a microscopic property of the system, but rather a process related to macroscopic
features in the transport, such as current path formation or switching.
In conclusion, “zeroes” may not be an appropriate description of resistance in
radiation exposed samples as these results are not consistent over entire samples,
suggesting inhomogeneous current paths. The current instabilities picture is supported by
our results, with local reverse current possibly responsible for the negative voltage
measured at some peripheral contact pairs. Other tests for current instabilities, such as
large internal to external contact potentials, are consistent with this picture. The
oscillation minima demonstrate incident power temperature dependence, which further
complicates the description of the minima as zeroes. It remains an open question as to
what determines this temperature dependence.
We gratefully acknowledge discussions with N. Read, A. Durst, and A. Andreev.

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