We examine the radiation induced modification of the Hall effect in high
mobility GaAs/AlGaAs devices that exhibit vanishing resistance under microwave
excitation. The modification in the Hall effect upon irradiation is
characterized by (a) a small reduction in the slope of the Hall resistance
curve with respect to the dark value, (b) a periodic reduction in the magnitude
of the Hall resistance, $R_{xy}$, that correlates with an increase in the
diagonal resistance, $R_{xx}$, and (c) a Hall resistance correction that
disappears as the diagonal resistance vanishes.Comment: 4 pages text, 4 color figure

A.A. Koulakov

A.C. Durst

A.V. Andreev

D.C. Tsui

F.S. Bergeret

I.A. Dmitriev

J. H. Smet

J. Shi

J.C. Phillips

K. von Klitzing

M.A. Zudov

M.E. Cage

R. G. Mani

R.G. Mani

T. Ando

V. Narayanamurti

V. Ryzhii

V. Umansky

V.I. Ryzhii

W. B. Johnson

X.L. Lei

English

arXiv

We examine the radiation induced modification of the Hall effect in
 high-mobility GaAs/AlxGa1-xAs devices that exhibit vanishing resistance
 under microwave excitation. The modification in the Hall effect upon
 irradiation is characterized by (a) a small reduction in the slope of
 the Hall resistance curve with respect to the dark value, (b) a
 periodic reduction in the magnitude of the Hall resistance R-xy that
 correlates with an increase in the diagonal resistance R-xx, and (c) a
 Hall resistance correction that disappears as the diagonal resistance
 vanishes

Mani, R. G.

Narayanamurti, V.

von Klitzing, K.

Smet, J. H.

Johnson, W. B.

Umansky, V.

Max Planck Society eDoc Server

Radiation-induced oscillatory Hall effect in high-mobility GaAs/AlxGa1-xAs devices

Crossref

Radiation-induced oscillatory Hall effect in high-mobility
                    
                      
                        
                          
                            G

We examine the radiation induced modification of the Hall effect in high-mobility GaAs/AlxGa1-xAs devices that exhibit vanishing resistance under microwave excitation. The modification in the Hall effect upon irradiation is characterized by (a) a small reduction in the slope of the Hall resistance curve with respect to the dark value, (b) a periodic reduction in the magnitude of the Hall resistance Rxy that correlates with an increase in the diagonal resistance Rxx, and (c) a Hall resistance correction that disappears as the diagonal resistance vanishes

Klitzing, K. Von

Publications of the IAS Fellows

RAPID COMMUNICATIONS
PHYSICAL REVIEW B 69, 161306~R! ~2004!Radiation-induced oscillatory Hall effect in high-mobility GaAsÕAlxGa1ÀxAs devices
R. G. Mani,1,* V. Narayanamurti,1 K. von Klitzing,2 J. H. Smet,2 W. B. Johnson,3 and V. Umansky4
1Harvard University, Gordon McKay Laboratory of Applied Science, 9 Oxford Street, Cambridge, Massachusetts 02138, USA
2Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany
3Laboratory for Physical Sciences, University of Maryland, College Park, Maryland 20740, USA
4Braun Center for Submicron Research, Weizmann Institute, Rehovot 76100, Israel
~Received 20 October 2003; revised manuscript received 7 January 2004; published 22 April 2004!
We examine the radiation induced modification of the Hall effect in high-mobility GaAs/AlxGa12xAs de-
vices that exhibit vanishing resistance under microwave excitation. The modification in the Hall effect upon
irradiation is characterized by ~a! a small reduction in the slope of the Hall resistance curve with respect to the
dark value, ~b! a periodic reduction in the magnitude of the Hall resistance Rxy that correlates with an increase
in the diagonal resistance Rxx , and ~c! a Hall resistance correction that disappears as the diagonal resistance
vanishes.
DOI: 10.1103/PhysRevB.69.161306 PACS number~s!: 73.21.2b, 73.40.2c, 73.43.2fVanishing electrical resistance has served to introduce
new physical phenomena in condensed matter physics such
as, for example, quantum Hall effects ~QHE!, which
stemmed from the studies of zero-resistance states at low
temperatures ~T! and high magnetic fields ~B! in the two-
dimensional electron system ~2DES!.1,2 Recently, the high-
mobility 2DES provided an unexpected surprise by exhibit-
ing novel zero-resistance states upon irradiation by low-
energy photons. In this instance, vanishing diagonal
resistance occurred about B5(4/5)B f and B5(4/9)B f ,
where B f52p f m*/e , m* is an effective mass, e is the elec-
tron charge, and f is the radiation frequency, while the resis-
tance minima followed the series B5@4/(4 j11)#B f with j
51,2,3, . . . .3 Remarkably, vanishing resistance induced by
microwave excitation of the 2DES did not produce plateaus
in the Hall resistance, although the diagonal resistance ex-
hibited activated transport and zero-resistance states, similar
to QHE.3,4 These striking features have motivated substantial
theoretical interest in this phenomenon.5–10
It is well known from the experimental studies of trans-
port that the changes in the diagonal conductivity sxx such as
those induced by the radiation in this context, can produce
small corrections, in the strong field limit, in the Hall resis-
tivity rxy , via the tensor relation rxy5sxy /(sxx2 1sxy2 ).11
Durst and co-workers have also mentioned the possibility of
an oscillatory Hall effect from their theoretical perspective.7
Experimental results reported here examine in detail a
radiation-induced modification of the Hall effect, which oc-
curred in Fig. 1~b! of the article from the year 2002 of Ref. 3
and Fig. 1~b! of Ref. 12. In particular, it is demonstrated that
microwave excitation changes the slope of the Hall resis-
tance Rxy vs B curve by <1.5%. Further, there appears to be
an oscillatory variation in Rxy , where a reduction, in magni-
tude, of the Hall resistance correlates with an increase in the
diagonal resistance Rxx . It is also demonstrated that the cor-
rection to the Hall resistance disappears as Rxx→0. Finally,
the oscillatory variation in the Hall resistance is comparable,
in magnitude, to the radiation-induced change in the diagonal
resistance, although the change DRxy is small (<5%) in
comparison to Rxy .0163-1829/2004/69~16!/161306~4!/$22.50 69 1613Measurements were performed on standard devices fabri-
cated from GaAs/AlxGa12xAs heterostructure junctions. Af-
ter a brief illumination by a red light-emitting diode, the best
material was typically characterized by an electron density,
n(4.2 K)’331011 cm22, and an electron mobility
m(1.5 K)’1.53107 cm2/V s. Lock-in based four-terminal
electrical measurements were carried out with the sample
mounted inside a waveguide and immersed in pumped liquid
He-3 or He-4, as the specimens were excited with electro-
magnetic ~EM! waves in the microwave part of the spectrum,
27< f <170 GHz. In this report, we illustrate the character-
istics of the radiation-induced modification of the Hall effect
and point out a similarity to the situation in the quantum Hall
limit.
Figure 1~a! shows measurements of the diagonal (Rxx)
and Hall (Rxy) resistances where, under microwave excita-
tion at 50 GHz, Rxx and Rxy exhibit the usual quantum Hall
behavior for B>0.3 T.1,2 In contrast, for B,0.25 T, see in-
set of Fig. 1~a!, a radiation-induced signal occurs and the
resistance vanishes over a broad B interval about B50.1 T.
Further high-resolution measurements are shown in Fig.
1~b!. Without EM-wave excitation, Rxx exhibits
Shubnikov–de Haas ~SdH! oscillations for B.100 mT @Fig.
1~b!#. The application of microwaves induces resistance os-
cillations, which are characterized by the property that the
Rxx under radiation falls below the Rxx without radiation,
over broad B intervals.3,4,12 Indeed, Rxx appears to vanish
about (4/5)B f .3 Although these zero-resistance states exhibit
a flat bottom as in the quantum Hall regime,1,2 Rxy under
radiation does not exhibit plateaus over the same B interval.
Yet, the Rxy data of Fig. 1~b! show perceptible oscillations
in the Hall resistance that are induced by the radiation.3,12,13
Indeed, an edgewise inspection of the data shows that there
is an antisymmetric oscillatory component in Rxy , in addi-
tion to a small radiation-induced change in the slope of the
Hall curve.12 In order to highlight these changes in the Hall
effect, the radiation-induced portion of the Hall resistance
DRxy5Rxy
excited2Rxy
dark is shown along with Rxx in Fig. 1~c!.
Here, Rxy
dark is the Hall resistance obtained without ~w/o!©2004 The American Physical Society06-1
RAPID COMMUNICATIONS
R. G. MANI et al. PHYSICAL REVIEW B 69, 161306~R! ~2004!radiation, and Rxy
excited is the Hall resistance with ~w/! radia-
tion. As this procedure for extracting the radiation-induced
Hall resistance involves the subtraction of two large signals
Rxy
dark and Rxy
excited and since DRxy is only a few percent of
the dark Hall signal it is necessary to realize a stable low-
noise experimental setup that minimizes parameter drifts
with time in order to obtain noise-free reliable DRxy data.
The plot of Fig. 1~c! confirms a robust DRxy signal. Indeed,
the observed characteristics in Fig. 1~c!, namely, a DRxy sig-
nal that vanishes as B→0, and odd symmetry in DRxy under
field reversal, help to rule out the possibility that DRxy origi-
nates from a mixture of the diagonal resistance with Rxy , as
a result of a misalignment of the Hall voltage contacts. Fur-
ther, the observation of quantized Hall effect in Fig. 1~a!
under radiation, and the radiation-intensity-independence of
the period of the radiation-induced oscillations, helps to rule
FIG. 1. ~Color online! ~a! The Hall (Rxy) and diagonal (Rxx)
resistances are plotted vs the magnetic field B for a
GaAs/AlxGa12xAs device under excitation at 50 GHz. Quantum
Hall effects ~QHE! occur at high B as Rxx vanishes. ~inset! An
expanded view of the low-B data. ~b! Data over low magnetic fields
obtained both with ~w/! and without ~w/o! microwaves at 50 GHz.
Here, radiation-induced vanishing resistance about (4/5)B f does not
produce plateaus in the Hall resistance, unlike in QHE. Yet, an
edgewise inspection reveals that there are antisymmetric-in-B oscil-
lations in Rxy that correlate with the Rxx oscillations. The w/o ra-
diation Hall data have been offset here for the sake of clarity. ~c! A
comparison of the radiation-induced Rxx oscillations with the
radiation-induced change DRxy in the Hall resistance. Note the fi-
nite slope ~dotted line! in DRxy , and the odd symmetry under field
reversal, which is characteristic of the Hall effect.16130out parallel conduction as the origin of nonvanishing DRxy .
These resistances scale to resistivities with a scale factor of
one.
The data of Fig. 2 illustrate this same effect when the
specimen is excited with microwaves at f 5108 GHz. In Fig.
2~a!, the Hall data without radiation have been offset with
respect to the Hall data with radiation in order to bring out
the oscillatory portion of the Hall effect. Once again, an
edgewise inspection of the irradiated Rxy data identifies an
antisymmetric oscillatory Hall resistance, while it also re-
veals a small reduction in the slope of the Hall resistance. A
comparison of Fig. 2~a! with Fig. 2~b! shows clearly that Rxy
is reduced in magnitude over the B intervals where Rxx is
enhanced by the radiation. On the other hand, as the diagonal
resistance vanishes upon microwave excitation, as in the vi-
cinity of B5(4/5)B f , for example, the correction DRxy also
vanishes. The dotted line in the plot of DRxy in Fig. 2~b! also
confirms that there is an approximately 1.5% reduction in the
slope of Rxy that is induced by the radiation. The small field
reversal asymmetry that is observable in the w/ radiation Rxx
data of Fig. 2 could be related to this radiation-induced
change in the slope of Rxy . All these features are also ob-
servable in Figs. 1~b! and 1~c!. Our studies indicate that the
FIG. 2. ~Color online! ~a! Data over low magnetic fields ob-
tained both with ~w/! and without ~w/o! microwave radiation at 108
GHz. Here, once again, radiation-induced vanishing resistance
about (4/5)B f and (4/9)B f does not produce plateaus in the Hall
resistance, although antisymmetric-in-B oscillations in Rxy correlate
with the Rxx oscillations. The slope of the Rxy is reduced by the
radiation. The w/o radiation Hall data have been offset for the sake
of clarity. ~b! The radiation-induced portion of the Hall resistance
DRxy is shown along with Rxx . There is a slope to the DRxy curve
~dotted line! because the radiation reduces the slope of the Hall
curve in ~a!. The correction to the Hall resistance DRxy vanishes
over the B interval of the Rxx zero-resistance states. Shubnikov–de
Haas type resistance oscillations, which are observable in the DRxy
trace in the vicinity of the (4/5)B f zero-resistance state, are attrib-
uted to the dark signal.6-2
RAPID COMMUNICATIONS
RADIATION-INDUCED OSCILLATORY HALL EFFECT . . . PHYSICAL REVIEW B 69, 161306~R! ~2004!radiation induced reduction in the slope of the Hall curve
brings with it a corresponding small shift ~at the percent
level! in the positions of the extrema in the SdH oscillations
to higher magnetic fields. A straightforward interpretation
suggests that the change in the Rxy slope, and the shift of the
SdH extrema, result from a radiation-induced change in the
cross-sectional area of the Fermi surface.
Figure 3 illustrates the frequency dependence, and the
correlation between DRxy and Rxx , at microwave frequen-
cies f 530, 40, and 50 GHz. Here, and also in Fig. 4, the
exhibited Hall resistances represent an antisymmetric combi-
nation of the signal obtained for the two directions (1B ,
2B) of the magnetic field. In each case shown in Fig. 3, it is
observed that ~a! the magnitude of DRxy is approximately the
same as the magnitude of Rxx , ~b! an increase in Rxx under
microwave excitation leads to a decrease in the magnitude of
Rxy , i.e., DRxy<0 for B>0, ~c! DRxy shows a finite slope
as B→0, and ~d! the correction DRxy vanishes as the diag-
onal resistance vanishes in the vicinity of B5(4/5)B f . These
data also confirm that the characteristic field scale for the
oscillatory Hall effect follows the microwave frequency in
the same way as Rxx .
We exhibit the power dependence of the Hall resistance at
a fixed microwave frequency in Fig. 4. Figure 4~a! shows
Rxy for various microwave intensities in units of dBm, with
0 dBm51 mW. Here, it is evident that increasing the radia-
tion power produces progressively stronger variations in
FIG. 3. ~Color online! The radiation-induced change in the Hall
resistance DRxy is shown on the left ordinate and the diagonal re-
sistance Rxx is shown on the right ordinate for microwave excitation
at ~a! 50 GHz, ~b! 40 GHz, and ~c! 30 GHz. Here, DRxy tends to
vanish as the diagonal resistance becomes exponentially small in
the vicinity of (4/5)B f . In addition, a finite slope is evident in DRxy
for B<30 mT, as in Figs. 1~c! and 2~b!.16130Rxy . This is confirmed by Fig. 4~b!, which demonstrates that
the minima in DRxy become deeper with increased power,
consistent with the results of Figs. 1~c!, 2~b!, and 3.
There appear to be some similarities between the Hall
resistance correction reported here and the experimental ob-
servations under quantum Hall conditions. In the vicinity of
integral filling factors in the quantum Hall situation, the mea-
sured Hall resistivity rxy is expected to approach the quan-
tum Hall resistance, RH(i)5h/(e2i), in the limit of vanish-
ing diagonal resistivity, i.e., rxx→0, at zero temperature.14
At finite temperature, experiment has indicated corrections to
the Hall resistivity that are proportional to the magnitude of
the diagonal resistivity, Drxy52srxx , with s a device-
dependent constant.14 That is, a finite ~nonvanishing! rxx can
lead to a reduction in the magnitude of rxy . This is analo-
gous to the effect reported here since an increase in Rxx due
to microwave excitation leads also to a decrease in the mag-
nitude of the Hall resistance, i.e., DRxy;2Rxx in Fig. 3,
and, as the Rxx vanishes, so does the correction to the Hall
resistance. Indeed, experiment suggests some device depen-
dence to this radiation-induced Hall resistance correction just
as in the quantum Hall situation.14 Thus, one might suggest
that increased backscattering due to the radiation,5,7,9 leads to
an increased dissipative current over the Rxx peaks, which
loads the Hall effect, similar to suggestions in Ref. 14. It
might then follow that the suppression of the backscattered
current over the Rxx minima, eliminates also the correction to
the Hall effect in our experiment.
The radiation-induced change in the slope of the Hall
FIG. 4. ~Color online! ~a! The Hall resistance Rxy is shown as a
function of the magnetic field B for radiation intensities, given in
units of dBm. The data indicate progressively stronger modulations
in Rxy with increased radiation intensity. Data have been offset for
the sake of clarity. ~b! This plot shows the radiation-induced change
in the Hall resistance DRxy obtained from the data of ~a!. The inset
illustrates the B dependence of DRxy for B<30 mT.6-3
RAPID COMMUNICATIONS
R. G. MANI et al. PHYSICAL REVIEW B 69, 161306~R! ~2004!curve appears to fall, however, outside the scope of this anal-
ogy, and this helps to identify the dissimilarities between the
radiation-induced effect reported here and the quantum Hall
situation: In the quantum Hall situation, the effect of finite
temperature is to mainly increase the diagonal resistance,
which leads to a decrease in the observed Hall resistance.14
In the case of the radiation-induced resistance oscillations,
the radiation, which plays here a role that is similar to the
temperature in the quantum Hall situation, can serve to both
increase and decrease the diagonal resistance. Theory would
suggest the existence of both a downhill and uphill radiation-
induced current with respect to the Hall field.7 Naively, one
might then expect both an enhancement and a diminishment
of the magnitude of the Hall resistance if the quantum Hall
analogy carried over to this case. Yet, we have found that the
magnitude of Rxy is mainly reduced by the radiation. The
radiation-induced change in the slope of the Hall resistance
*Email address: mani@deas.harvard.edu
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The results seem to hint at different transport pictures for the
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In summary, high-mobility GaAs/AlxGa12xAs devices
that exhibit vanishing Rxx under microwave radiation also
show a radiation-induced modification of the Hall effect. The
modification is characterized by ~a! a small reduction in the
slope of the Rxy vs B curve upon microwave excitation, with
respect to the dark value, ~b! a reduction in the magnitude of
the Hall resistance that correlates with an increase in the
diagonal resistance Rxx . The radiation-induced changes in
Rxx and Rxy are comparable in magnitude, although DRxy is
small compared to Rxy , and ~c! a Hall resistance correction
that disappears as the diagonal resistance vanishes. These
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P.H. Rivera and P.A. Schulz, cond-mat/0305019 ~unpublished!;
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~Amsterdam! 22, 1 ~2004!.
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Radiation-induced oscillatory Hall effect in high-mobility GaAs/Al<SUB>x</SUB>Ga<SUB>1-x</SUB>As devices

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Radiation induced oscillatory Hall effect in high mobility GaAs/AlGaAs
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Radiation induced oscillatory Hall effect in high mobility GaAs/AlGaAs devices

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