Electron effective mass in an ultra-high mobility GaAs/AlGaAs
quantum well from MIRO and EPR experiment on DPPH
Sergei Studenikin, Geof Aers, and Andy Sachrajda
National Research Council of Canada, Ottawa, Canada
Q. Shi, and M. A. Zudov
School of Physics and Astronomy, University of Minnesota,
Minneapolis, Minnesota, USA
L. N. Pfeiffer, and K. W. West
Department of Electrical Engineering, Princeton University,
Princeton, New Jersey, USA
1
Three first MIRO/ZRS papers: number of scitations per year
Three first papers in the MIRO field: Number of scitations per year
Number of citations
Zudov PRL PRB 2001
Mani Nature 2002
Zudov PRL2003
Total
100
50
0
2002
2004
2006
2008
2010
2012
2014
Year
2
First time use of “MIRO”
Joan Miró (1893-1983)
3
Niko Pirosmani (1862-1918)
Electron effective mass in an ultra-high mobility GaAs/AlGaAs quantum
well from MIRO and DPPH EPR experiment
Outline
1) Introduction: methods for m*-measurements
2) Sample and Experimental setup
3) B calibration with DPPH in 5-70 mT range
4) m*MIRO measurement
5) Conclusions
5
Why it is interesting to precisely measure m*?
m*0 is a band parameter
m* (w, Ei, B, ….) is sensitive to details
m* is sensitive to e-e interactions
Can MIRO be used as a precise tool for m* ?
What kind of m* is deduced from MIRO ?
6
Rxx=d Vxx/dIdi (arb.un.)
Known methods to measure 2DEG m*: FIR cyclotron resonance
1.84 THz
m*=0.06857m0
m*=0.06849m0
2.5227THz
3.1059 THz
400
2
200
Rxx ()
300
100
=3/2
3
4
5
6
7
8
9
0
Magnetic field (T)
Maan et al. APL 40, 609 (1982).
S.S. et al. Phys. E 34, 73 (2006).
In FIR experiments m* is affected by high B, SdH, plasmons
Important comment: CR resonance is not effected by e-e interactions
Kohn’s theorem - Phys. Rev. 123, 1242 (1961)
7
Remark: CR cannot be reliably measured in high-mobility 2DEG at MW
(1)
(2)
(3)
(1) Calculated reflection/absorbtion by ideal 2DEG
(2) A cavity measurements of absorption in a 1mm
2DEG strip
(3) CR on photo-excited electrons in bulk GaAs by
B.Ashkinadze PRB 52, 17165 (1995)
S.S., et al., Phys. Rev. B 76, 165321 (2007)
8
Known methods to measure m*: magneto-plasmon resonance
n=2.3x1011 cm-2, m=1.2x106 cm2/Vs
m*=0.070 m0
Vasiliadou, Miller, Heitmann, Weiss, von Klitzing, PRB 48, 17145 (1993)
9
Magneto-plasmon resonance experiment on high-mobility samples
n=2.7x1011 cm-2 , m=1.3x107 cm2/Vs
Hatke, Zudov, Watson, Manfra, Pfeiffer, West, PRB 87, 161307(R) (2013)
𝛼𝑐 =e/2π𝑚∗
10
Magneto-plasmon resonance in MW absorption on a high-mobility sample
m*=0.068 m0
w=0.8 mm
n=1.8x1011 cm-2
m=3x106 cm2/Vs
m*  0.068 m0
FEDORYCH, STUDENIKIN, MOREAU, POTEMSKI, SAKU, HIRAYAMA, Int. J. Mod. Phys. B 23, 2698 (2009).
11
Effective mass m* from T-dependence of Shubnikov – de Haas oscillations
BUT:
SdH m* measurements can be affected by side effects…
M. Zudov (not published)
12
Effective mass m* from SdH oscillations: side effects
Tan, Zhu, Stormer, Pfeiffer, Baldwin, PRL 94, 016405 (2005) :
Possible technical issues:
o
o
o
o
SdH sensitive to n-gradients and fluctuations
Possible extra heating
Reliable Te- control in B-field
SdH amplitude may be affected e.g. by spin
splitting
o SdH may be non-sinusoidal: higher harmonics
13
Effective mass m* from SdH oscillations: side effects
Tan, Zhu, Stormer, Pfeiffer, Baldwin, PRL 94, 016405 (2005)
Physical reasons for m* variations:
o
o
o
o
Assumes Lifshitz-Kosevich formula is correct for 2DEG
Depends on LL index i
Non-parabolicity
Different models
o SdH m* depends on e-e interaction
14
MIRO is a beautiful phenomenon: access to new physics?
Dmitriev, Mirlin, Polyakov, Zudov, Rev. Mod. Phys. 84, 1709 (2012):
𝛿𝜌 = −𝐴 sin 2𝜋𝜖
ϵ=
𝜔
,
𝜔𝑐
𝜔𝑐 =
𝑒𝐵
is the cyclotron frequency
𝑚∗
𝜆 = exp(−
𝜋
)
𝜔𝑐 𝜏𝑞
𝒜(𝑇) = 2𝜋𝜌0 (𝜏/(2𝜏∗ ) + 2𝜏𝑖𝑛 /𝜏)
Amplitude vs. B  tq quantum scattering time, e.g.
Amplitude vs. B vs. B|| - tq in B||
Amplitude vs. T scattering mechanism
Amplitude vs. T  scattering mechanisms
Waveform  access to LL shape
Shi, Zudov, Studenikin, Baldwin, Pfeiffer, West (2015)
Precise MIRO positions  m*
(B  10mT, precise B - calibration needed)
15
Example of MIRO T-dependence at 1K<T<4K, m=1.3107 cm2/Vs
Hatke, Zudov, Pfeiffer, West, PRL 102, 066804 (2009)
No signature of the inelastic contribution
16
Example of MIRO T-dependence at 0.35K<T<1.7K, m>3107 cm2/Vs
Shi, Zudov, Studenikin, Baldwin, Pfeiffer, West (2015)
𝒜(𝑇) = 2𝜋𝜌0 (𝜏/(2𝜏∗ ) + 2𝜏𝑖𝑛 /𝜏)
17
Can MIRO be used for precise measurements of m* at large LL?
What kind of m* :
Hatke, MZ, Watson, Manfra, Pfeiffer, West, PRB 87, 161307(R) (2013)
Band parameter (CR)
Modified by e-e
exchange interaction
Else?
m*MPR = 0.066
m*MIRO= 0.059
18
Example of MIROs on m~3x107 sample
Rxx ()
0.30
0.25
0.20
0.15
4
8
12
16
20
Magnetic field (mT)
Many MIRO harmonics observed, but very small field => limited by magnet precision…
19
Sample: n=3.2 x 1011 cm2, m3107 cm2/Vs, tq=46 ps, mq=1.2106 cm2/Vs
AlxGa1-xAs/GaAs/AlGaAs QW
Width 30 nm, x=0.24
Symmetrically doped on both sides
Spacers - 80 nm,
Distance to the surface - 195 nm
Cooling process (~2h) under illumination by a red LED (i=50 mA),
illumination stopped at 25K
n=3.2x1011 (EF=11.4meV)
m*(E1+Ef)=0.06793
20
Self-consistent calculations of m*
Following: Vurgaftman et al., JAP 89, 5815 (2001)
Quantum Codes: GaAs/AlxGa1-xAs QW, EF=11.3 meV, x=0.24
0.074
calculated m*(E1+Ef)
m*
0.072
0.070
m*=0.06793
0.068
QW band edge m*= 0.067016
0.066
0
100
200
300
400
QW Width (Å)
21
Self-consistent calculations of m* vs. E
GaAs/AlxGa1-xAs QW, w=30 nm, EF=11.3 meV, x=0.24
0.074
Emax-en/e0e
calculated m*(E1+Ef)
m*
0.072
0.070
0.068
QW band edge m*= 0.06702
0.066
0
20
40
Electric Field (kV/cm)
22
Chip holder for DPPH+MIRO experiment
DPPH
C18H12N5O6
(1,1-Diphenyl-2-picrylhydrazyl, Free Radical)
g*=2.0036
J. Krzystek, A. Sienkiewicz, L. Pardi, and L. C.
Brunel, "DPPH as a Standard for High-Field EPR,"
Journal of Magnetic Resonance, vol. 125, pp. 207211, 1997.
RuO2 Thermo-resistor:
LakeShore RX-102A-BR
23
Chip and MW antenna arrangement for MIRO experiment
24
MIRO Frequency dependence excited by an antenna
49.62GHz, +5dBm
Nov02050_colflip_s_x10, +3 dBm
0.04
0.10
0.08-5dBm
Nov02200serMIRO_s_colFlip,
0.02
70
0.05
0.10
0.20 50
0.15
Magnetic field (T)
B (mT)
0.00
0.00
B (T)
60
0.06
0.04
40
Nov03200_colflip_s, P=-10 dBm
35
30
25
0.02
20
B (mT)
Rxx ()
0.06
15
10
10
-5
2
4
6
8
10
15
20
25
40
35
30
5
30
45
50
f (GHz)
f (GHz)
12
f (GHz)
0.0
0.0
0.2
0.4
0.6
0.8
Nov03200_colflip_s
0.2
0.4
0.6
0.8
1.0
Nov02050_colflip_s_x10
1.0
25
DPPH resonance from 5 to 70 mT, T=300mK
ddyNov03050DPPH_s
g*=2.0036
d2dyNov050DPPH_s
d2R/dB2
dR/dB
70
70
60
60
50
50
DPPH resonance
B (mT)
RRuO2 (k)
3.40
3.36
3.32
0.15
0.20
0.25
0.30
Magnetic field (T)
B (mT)
f=6.0 GHz
40
40
30
30
20
20
10
10
1.5
1.0
0.5
1.6
gmBB=1.16 meV=13 mK
0.8
0.4
f (GHz)
f (GHz)
At B=10 mT
1.2
-0.0015
-0.0010
-0.0005
0.0000
0.0005
0.0010
0.0015
d2dyNov03050DPPH_s
T=300mK => ( n↑ −𝑛 ↓)/n=1-exp(-g*mBB/kBT)  4%
26
B-field calibration using DPPH resonance from 5 to 70 mT
Sweep down rate 0.01T/min
70
Sweep down callibration:
BDPPH=(0.9804+/-0.0009)Bset+(1.15+/-0.04) mT
BDPPH (mT)
60
BDPPH (mT)
50
40
30
20
10
0
0
10
20
30
40
50
60
70
BIPS120(mT)
90° Angle was optimized by maximizing VHall to the fifth digit.
27
MIRO vs 1/BIPS and 1/BDPPH
B corrected using DPPH
BIPS
Rxx ()
0.4
0.2
0.0
40
80
120
160
-1
1/BIPS, 1/Bcorrected (T )
28
m* from MIRO and DPPH
140
0.6
(Xmin+Xmax)/2
120
47.8GHz, -5 dBm
Peak Centers of C
f=47.800GHz
m*/m0=0.0649 +/- 0.0002
0.4
80
Rxx ()
-1
1/BN (T )
100
Band theory:
m*=0.0679
60
40
Equation
y = a + b*x
Weight
No Weighting
Adj. R-Square
0.99995
Value
(Xmin+Xmax)/2 Intercept
(Xmin+Xmax)/2 Slope
20
0.2
Standard Error
1.16167
0.12699
9.01734
0.01437
0.0
0
0
5
10
15
N
Measured m*=0.0649,
40
80
120
BIPS, Bcorrected (mT)
Theory: m*(E1+Ef)=0.06793
29
Measured m*=0.0649, band theory m*=0.06793
Quantum Codes: GaAs/AlxGa1-xAs QW, EF=11.3 meV, x=0.24
0.074
m*(E1+Ef)
band theory
measured m*
m*
0.072
0.070
m*=0.06793
0.068
QW band edge m*= 0.06702
0.066
m*MIRO=0.0649
0.064
0
100
200
300
400
QW Width (Å)
cos−1 (0.0649/0.0679)=17°
30
Electron effective mass in an ultra-high mobility GaAs/AlGaAs quantum well
from MIROs and EPR experiment on DPPH
Conclusion
1) Measured m*MIRO= 0.0649 is smaller than
theoretically calculated m*theory=0.0679
Question
1) is m*MIRO sensitive to e-e
interactions? Or else?
31