The microwave induced resistance response of a high mobility 2DEG from the quasi-classical limit to the quantum Hall regime

Abstract

Microwave induced resistance oscillations (MIROs) were studied experimentally over a very wide range of frequencies ranging from ~20 GHz up to ~4 THz, and from the quasi-classical regime to the quantum Hall effect regime. At low frequencies regular MIROs were observed, with a periodicity determined by the ratio of the microwave to cyclotron frequencies. For frequencies below 150 GHz the magnetic field dependence of MIROs waveform is well described by a simplified version of an existing theoretical model, where the damping is controlled by the width of the Landau levels. In the THz frequency range MIROs vanish and only pronounced resistance changes are observed at the cyclotron resonance. The evolution of MIROs with frequency are presented and discussed. Comment: 4 pages, presented at EP2DS, to be published in Physica E

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Sergei Studenikin Page 1 12/08/2005
1
The microwave induced resistance response of a high mobility
2DEG from the quasi-classical limit to the quantum Hall regime
S. A. Studenikin,a,* M. Byszewski,b D. K. Maude,b M. Potemski,b A. Sachrajda,a
Z. R. Wasilewski, M. Hilke,c L. N. Pfeiffer,d K. W. Westd
aInstitute for Microstructural Sciences, NRC, Ottawa, Ontario K1A-0R6, Canada
bGrenoble High Magnetic Field Laboratory, MPI/FKF and CNRS, Grenoble 38-042, France
cDepartment of Physics, McGill University, Montreal H3A 2T8, Canada
Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974-0636, USA

Abstract
Microwave induced resistance oscillations (MIROs) were studied experimentally over a very wide range of
frequencies ranging from ~20 GHz up to ~4 THz, and from the quasi-classical regime to the quantum Hall effect
regime. At low frequencies regular MIROs were observed, with a periodicity determined by the ratio of the
microwave to cyclotron frequencies. For frequencies below 150 GHz the magnetic field dependence of MIROs
waveform is well described by a simplified version of an existing theoretical model, where the damping is
controlled by the width of the Landau levels. In the THz frequency range MIROs vanish and only pronounced
resistance changes are observed at the cyclotron resonance. The evolution of MIROs with frequency are
presented and discussed.

Keywords: 2DEG; microwaves; zero-resistance states; Landau levels

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1. Introduction
Microwave induced resistance oscillations
(MIROs) observed on very high mobility samples
have attracted considerable interest, partly because of
the existence of zero-resistance states under certain
conditions1,2,3 Several theoretical models were
suggested to explain this phenomenon.4,5,6,7 It was
recently shown [8] that a simplified version of the
model based on spatially indirect inter-Landau level
(LL) transitions4,5 describes the MIROs waveform
accurately in the quasi-classical regime of large
filling factors. It should be noticed that other
theoretical approaches based on a non-equilibrium
distribution function6 or the quasi-classical electron
orbit dynamics7 produced similar results in regards to
the waveform and phase of the oscillations. On the
other hand, neither of the existing theories can
explain other MIROs characteristics, such as: (i) the
absence of dependence of the waveform on the
right/left circular polarization9, (ii) the absence of
dependence on the LL index change ∆n for the
probabilities of the inter-Landau level transitions
contributing to the MIROs8, and (iii) the very high
frequency dependence of the MIROs, in particular,
where these oscillations have never been observed at
optical or sub-millimeter frequencies.
In this work we experimentally investigate the
frequency dependence of the MIROs and their
evolutions over a very wide range of frequencies,
ranging from ~20 GHz up to ~4 THz, starting with
the quasi-classical regime and up the quantum Hall
regime. We show that MIROs start to deviate from
the theoretical model at frequencies above ~120 GHz
and vanish at higher frequencies above ~200 GHz.
2. Experimental results
Experiments were performed on two samples of
GaAs/AlGaAs hetero-structures with a high mobility
two dimensional electron gas (2DEG) confined at the
interface. After a brief illumination with a red LED,
the 2DEG in the first sample attained mobility of
4×106 cm2/Vs and in the second sample
8×106 cm2/Vs at a temperature of 2 K. The electron
concentration was around 2.0×1011cm-2 in both
samples. The samples were placed in a 4He cryostat
equipped with a superconducting solenoid. Three
sources of microwave radiation were employed
depending on the frequency range. In low-frequency
experiments between 20 and 50 GHz an Anritsu
signal synthesizer (model 69377B) was used and the
microwaves were delivered to the sample by means
of a semi-rigid coaxial cable equipped with a small
antenna at the end.8 In the medium frequency range
between 80 and 220 GHz a tunable klystron
microwave generator (model ΓC-03) in tandem with
a frequency doubler was used.
For higher frequencies in the tera-Hertz range a far-
infrared gas laser pumped with a CO2 laser was
employed. In these last two cases the MW radiation
was delivered into the cryostat using an oversize thin-
wall stainless steal pipe. For each set of experimental
traces the MW power at the sample was maintained
at a constant level which was controlled by a carbon
thermo sensor for all frequencies.10
Typical experimental traces of the MIROs on the
first sample (µ≈4×106 cm2/Vs) at low frequencies are
shown in Fig. 1 (a) and the corresponding theoretical
curves are presented in Fig. 1(b) which were
calculated using the following equation:8



where (1)

is the electron density of states in a quantizing
magnetic field, and Γ is the width of the Landau
levels. It is evident from the figure that in this
frequency range the theory fits the data very well,
where we used the same value of Γ=28 µeV for all
curves.
Figure 2 shows experimental (a) and simulated (b)
traces of the MIROs on sample 2 (µ≈8×106 cm2/Vs)
in the medium frequency range from 80 to 226 GHz.
As we can see from the figure, at frequencies higher
than ~150 GHz the MIROs progressively become
smaller and completely vanish at frequencies higher
than 230 GHz that sets the upper frequency limit for
the observation of the MIROs. It is clear that the
theoretical model fails to describe this behavior.
Figure 3 shows the microwave induced changes in
the resistance in the THz range along with the
magnetoresistance trace for the Shubnikov-de Haas
oscillations Rxx. In this frequency range, pronounced
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Sergei Studenikin Page 3 12/08/2005
3
resistance changes are observed in the form of
relatively sharp peaks under the condition of a
cyclotron resonance at ω=ωc but no evidence for
MIROs is seen. The observed resistance changes can
be qualitatively understood in terms of the
bolometric-type response of the 2DEG resistance.
Let us examine what happens with the fitting
parameter Γ by following the evolution of MIROs
from low to high frequencies. Figure 4 shows the
plot of the LL width Γ as a function of the MW
frequency obtained by fitting of the data in Fig. 2
with eq.(1). Since the fitting was done in
approximately the same magnetic field range from
~0.02 to 0.4 T, the changes in Γ cannot be due to a
possible dependence of Γ on magnetic field. Indeed,
as seen from the plot, Γ remains constant for
frequencies below 120 GHz, as mentioned above,
where the model works. Between 120 and 156 GHz
the LL width Γ increases stepwise from 25 to 60 µeV
and at 226 GHz it increases even further and MIROs
vanish at higher frequencies. Such behaviour is not
addressed in existing theoretical models and has to be
understood. Qualitatively, the damping of MIROs
(equivalently, effective broadening of the LL width)
can be explained if an additional coulping is involved
in the interaction between light and the electrons.
Most likely, this additional coupling is related to
magneto-plasmon excitations in a finite size sample
due to the strong electrodynamic interaction between
radiation and mobile charges.8,11 If the lifetime of the
plasmon excitation depends on the MW frequency,
which would lead to the experimentally observed
broadening of the total effective width Γtot=Γ+Γp.
This additional coupling might also be at the source
for the lack of dependence of MIROs on circular
polarization9 and the transition probability
insensitivity to the LL index change ∆n.8
3. Conclusion
We studied the evolution of the MIROs over a wide
range of frequencies. At MW frequencies below 150
GHz the MIROs are well described by an existing
theoretical model, where the only fitting parameter is
the LL width Γ, which remains constant for f<120
GHz but increases rapidly for higher frequencies.
At even higher frequencies the MIROs disappear and
only the cyclotron resonance is observed.









































Fig. 1. MIROs traces for different MW frequencies
from 20 to 50 GHz on GaAs/AlGas sample 1
(µ≈4×106 cm2/Vs); (a) experiment, (b) calculated
with eq. (1) using the same Landau level width Γ=28
µeV. Traces are shifted vertically for clarity.
0.00.1
Magnetic field (T)
0.20.3
0
2
4
6
8
20 GHz
25 GHz
30 GHz


∆Rxx (Ω)
f=50 GHz
40 GHz
Experiment
µ=4×10
T=1.6 K
6cm
2/Vs
(a)
0.0 0.1
Magnetic field (T)
0.20.3
0
2
4
6
8
δ δ=0.028 meV
T=1.6 K
Theory
20 GHz
25 GHz
30 GHz


∆Rxx (Ω)
f=50 GHz
40 GHz
(b)

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Sergei Studenikin
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Fig. 2. MIROs (∆Rxx=Rxx(MWs on)-Rxx(no MWs)) for
different MW frequencies from 80 to 226 GHz using
GaAs/AlGas sample 2 (µ≈8×106 cm2/Vs); (a)
experiment, (b) theory eq. (1) with the same Landau
level width Γ=30 µeV.
Traces are shifted vertically for clarity.














Fig. 3. Photo-response of the high mobility 2DEG in
the quantum Hall regime at THz frequencies.
















Fig. 4. Landau level width determined from MIROs
and fitted by eq. (1).

[1] R. G. Mani et al., Naure 420 (2002) 646.
[2] M. A. Zudov et al., Phys. Rev. Lett. 90 (2003) 046807.
[3] S. A. Studenikin et al., Solid State Commun. 129 (2004)
341.
[4] A. C. Durst et al., Phys. Rev. Lett. 91 (2003) 086803.
[5] V. Ryzhii, Phys. Rev. B 68 (2003) 193402.
[6] A. Dmitriev et al. Phys. Rev. B 71 (2005) 115316.
[7] J. Inarrea, G. Platero, Phys. Rev. Lett. 94 (2005)
016806.
[8] S. A. Studenikin et al., Phys. Rev. B 71 (2005) 245313.
[9] J. H. Smet et al., cond-mat/0505183 (2005).
[10] S. A. Studenikin et al. IEEE Transactions on
Nanotechnology 4 (2005) 124.
[11] S. A. Michailov et al., Phys. Rev. B 70 (2004) 165311.
0.00.20.4 0.60.8
0
2
4
6
8
10
12


∆Rxx (arb.un.)
Magnetic field (T)
Theory
δ=30µeV
f=80 GHz
110 GHz
156 GHz
192 GHz
226 GHz
(b)
0.00.2
Magnetic field (T)
0.40.6 0.8
0
20
40
60
80


∆Rxx (Ω)
80 GHz
100 GHz
110 GHz
156 GHz
192 GHz
f=226 GHz
Experiment
(a)
50100 150200250
0
20
40
60
80
100


Γ (µeV)
Frequency (GHz)
Γ in µeV
0
100
200
300
400
3456789
ν=3/2
ν=2
1.84 THz
2.52 THz
3.10 THz

∆Rxx=d
2Vxx/dIdi (arb.un.)
Magnetic field (T)
ν=3

Rxx (Ω)