1. Microwave Radiation-Induced Magnetoresistance Oscillations
in high mobility GaAs/AlGaAs system under
Bichromatic excitation
Presented By : Binuka Gunawardana
Advisor : Dr. Ramesh G. Mani

2. Content
1. Introduction
• 2D Electron Systems (2DES)
• Landau Levels (LL)
• Quantum Hall Effect
• Shubnikov de Hass (SdH) Oscillations
• Microwave Induced Magnetoresistance Oscillations (MIMOs)
2. Theoretical Background
3. Motivation
4. Experimental setup
5. Results
6. Discussion
7. Summary

3. 2D Electron system
𝐸 =
ℏ
2𝑚∗
𝑘 𝑥
2
+ 𝑘 𝑦
2
+ 𝑘 𝑧
2
Energy of free electron with wave vector 𝑘
Allowed quantized energy levels
limits
Z-direction motion
At low temperature (𝑇 < 4𝐾) only lowest energy level is
occupied
2D Electron system (2DES)
1
Ref: http://dx.doi.org/10.18419/opus-6695

4. Landau Levels (LLs)
Quantization
of cyclotron
orbits
(LLs)
Low
Temperature
Perpendicular
𝑩 field
Charged
Particles in
2DES
𝝎 𝒄 =
𝒆𝑩
𝒎∗
• 𝜔𝑐 - Cyclotron Frequency
• 𝑒 - Charge of electron
• 𝐵 - Magnetic Field
• 𝑚∗
- Effective Mass of the electron
𝑬 𝒏 = ℏ𝝎 𝒄 𝒏 +
𝟏
𝟐
2

5. Integer Quantum Hall Effect (IQHE)
Degenerated LL
There are 𝑛 𝑜 =
𝑒𝐵
ℎ
number of degenerated LLs per unit area
Filling factor 𝝂 =
𝒏
𝒏 𝟎
3
𝝆 𝒙𝒚 =
𝟏
𝝂
×
𝒉
𝒆 𝟐
When the filling factor, 𝝂 is an
integer we have an quantum hall
state
Ref: Nobel Lecture by Klaus von Klitzing, 1985

6. QHE and Shubnikov de Hass(SdH) Oscillations 4
Ref: http://dx.doi.org/10.18419/opus-6695

7. Microwave Induced Magnetoresistance Oscillations (MIMOs)
IQHE
SdH
Ref: R. G. Mani, Nature (London) 420, 646 (2002)
MIMOs
𝑅 𝑥𝑥 =
𝑉𝑥𝑥
𝐼𝑖𝑛
5

8. Ref: R. G. Mani, Nature (London) 420, 646 (2002)
6

9. Theoretical Background of MIMOs
MIMOs
Scattered
from
disorder
Photo
excited
electrons
Ref: A. C. Durst, S.Sachdev, N. Read, and S. M. Girvin, Phys.Rev.Lett. 91, 086803 (2003).
Displacement Model
7

10. Inelastic Model
Ref: I. A. Dmitriev, M. G. Vavilov, I. L. Aleiner, A. D. Mirlin, and D. G. Polyakov, Phys. Rev. B 71, 115316 (2005).
8
MWs changes
density of states
Induce Oscillatory
electron distribution
function
MIMOs

11. Radiation Driven Electron Orbital Model
Ref: J. Inarrea and G. Platero, Phys. Rev. Lett. 94, 016806 (2005).
Electron jumps
between fixed
orbits
Orbits oscillates
because of
MWs
MIMOs
9

12. Classical Memory Effect
Ref: Y. M. Beltukov and M. I. Dyakonov, Phys. Rev. Lett. 116, 176801 (2016).
Electrons go in circular
orbits
Gets scattered from
scattering centers
The change in the
direction makes
MIMOs
10

13. MIMOs
Power
Temp
(T)
Density
Polarization
angle
AC/DC
Current
Frequency
MIMOS
Depends on
what
parameters?
11

14. Two Microwave
Frequencies
What happens to
MIMO oscillations
???
Motivation
Previous Studies
Ref: M. A. Zudov, R. R. Du, L. N. Pfeier, and K. W. West, Phys. Rev. Lett. 96,236804 (2006).
• Obeys an Average of two Monochromatic results
• Strongly suppressed at zero resistance states (ZRS)
12

15. • 4 terminal measurement using Lock in
Amplifiers
• GaAs/AlGaAs Sample
• Density, 𝒏 ≈ 𝟑. 𝟑 × 𝟏𝟎 𝟏𝟏 𝒄𝒎−𝟐
• Mobility, 𝝁 ≈ 𝟏𝟓 × 𝟏𝟎 𝟔 𝒄𝒎 𝟐/𝑽𝒔
• Temperature, 𝑻 = 𝟏. 𝟕 𝑲
• 𝟏. 𝟖𝟒 ≤
𝒇 𝟏
𝒇 𝟐
≤ 𝟑. 𝟒
Experimental Setup
Bichromatic Microwave Induced
Magnetoresistance Oscillation
Bichromatic MIMO
13

16. Results : Comparing with Average
This figure shows the
Rxx vs. 1/B
for monochromatic excitation
at
90.6 GHz
48.7 GHz
bichromatic excitation
90.6 GHz & 48.7 GHz
and the numerical arithmetic
average of the
monochromatic signals at
90.6 GHz & 48.7 GHz
14

17. MIMOs for
90.6 GHz
48.7 GHz
bichromatic MIMOs for
90.6 GHz +48.7 GHz
at same Microwave
powers
Region 1
𝑩 𝟏
Region 2
𝑩 𝟐
Region 3
𝑩 𝟑
Results : bMIMO behavior 15

18. MIMOs for
90.6 GHz
41.0 GHz
bichromatic MIMOs for
90.6 GHz +41.0 GHz
at same Microwave
powers
Region 1
𝑩 𝟏
Region 2
𝑩 𝟐
Region 3
𝑩 𝟑
16

19. Low Frequency
𝒇 𝟏 = 𝟓𝟖 𝑮𝑯𝒛
High frequency
component (𝑓2)
takes on the
values
𝟏𝟒𝟏 𝑮𝑯𝒛
𝟏𝟓𝟔. 𝟓 𝑮𝑯𝒛
𝟏𝟔𝟏 𝑮𝑯𝒛
𝟏𝟕𝟒 𝑮𝑯𝒛
17

20. Results : Power dependence of bMIMOs
bMIMOs for frequency pair
90.6 GHz
and
41.0 GHz
for microwave power
4, 2, 1, 0.5 and 0.25 mW
at the lower frequency,
and
constant power at the
higher frequency
(90.6 GHz)
18

21. The variation in
the diagonal
resistance, Rxx,
with the change
in the
microwave
power of the
low frequency
component
under
bichromatic
photo-excitation
conditions for
(a) region (1),
(b) region (2)
and
(c) region (3)
19

22. n
n+1
n+2
n+3
n+4
n+5
n+6
𝒉𝒇 𝟐
𝒉𝒇 𝟏
B1 Region 1
𝑩 𝟏
20Discussion

23. n
n+1
B2
n+2
n+3
n+4
n+5
n+6
𝒉𝒇 𝟐
𝒉𝒇 𝟏
Region 2
𝑩 𝟐
21

24. n+3
n+2
n+1
n
n+4
n+5
B3
n+6
𝒉𝒇 𝟐
𝒉𝒇 𝟏
Region 3
𝑩 𝟑
22

25. Region 1
𝑩 𝟏
Region 2
𝑩 𝟐
Region 3
𝑩 𝟑
23

26. Summary
• Bichromatic response may not be a superposition or average of two monochromatic MIMO responses
• The amplitude of the bichromatic MIMO has a non linear relationship with MW power
• At low magnetic field bichromatic MIMO response is similar to low frequency response, when going to high
magnetic field they both contributes and bichromatic MIMO response goes towards high frequency response
• The model developed can be used to explain the behavior of the bichromatic MIMO responses
24

27. Acknowledgement
• Study more about bichromatic MIMO dependency with MW properties
Future Work
Supervisor : Group Members: Funding Agencies
Prof. Ramesh Mani Dr. Annika Krissa
Han Chun Liu
Committee Members: Zhuo Wang
Prof. Unil Perera Rasanga Samaraweera US Department of Energy
DE-SC001762Prof. Yohannes Abate Rasadi Munasinghe
Prof. Alexander Kozhanov Tharanga Nanayakkara
Prof. Russel White Kushan Wijewardana
Sajith Wijayarathne
Rupesh Ghimire Army Research Office
W911NF-10-1-0450
25

28. Summary
• Bichromatic response may not be a superposition or average of two monochromatic MIMO responses
• The amplitude of the bichromatic MIMO has a non linear relationship with MW power
• At low magnetic field bichromatic MIMO response is similar to low frequency response, when going to high
magnetic field they both contributes and bichromatic MIMO response goes towards high frequency response
• The model developed can be used to explain the behavior of the bichromatic MIMO responses
• Study more about bichromatic MIMO dependency with MW properties
Future Work
26