Polarisation Contents: EM Waves Polarisation angle Polaroid filters Brewster’s angle.
Valley polarisation assisted spin polarisation in Si...
Transcript of Valley polarisation assisted spin polarisation in Si...
Valley polarisation assisted spin polarisation inSi MOSFETs
Vincent [email protected]
Universite Grenoble Alpes / CEA INAC
1Agenda
Single particle picture
Previous results
Our samples / results
Comparison with Quantum Monte carlo / Discussion
Advertising
4Determination of BpMagnetoresistance in parallel magnetic fields
2DEG (thin)
0 5 10 15 20
2
4
6
8
10
B [T]
xx [a
.u.]
Bp
97,5%
Okamoto et al. PRL 32, 3875 (1999) , Pudalov et al. PRL 88, 076401 (2002)
4Determination of BpMagnetoresistance in parallel magnetic fields
Real 2DEG
0 5 10 15 20
1
2
3
Bp
B [T]
xx [a
.u]
97,5%
Okamoto et al. PRL 32, 3875 (1999) , Pudalov et al. PRL 88, 076401 (2002)
5Previous resultsAlAs
Shayegan et al. Phys. Rev. Lett. 92 246804 (2004); PRB 78, 161301(R) (2008);
PRB, 81 235305 (2010)
6Our samplesSi quantum wells on insulators
Si Crystal
Diamond structure
Bulk
6 valleys
ml = 0.9m0
mt = 0.2m0
Confined in z direction
2 valleys
7Our samplesSi quantum wells on insulators
thermal oxide
10 nm
SIMOX oxide
Samples from NTT BRL (Atsugi, Japan)
Image by D. Cooper @ Leti
8Our samplesValley polarisation
0 10 20 30 40 50 60 706
4
2
0
-2
-4
-6
-8
-10
-12
B=0T
Back Gate Voltage (V)
No carriers
A
B
Fron
t Gat
e V
olta
ge (
V)
K. Takashina et al. PRL (2006)
B=5T
Back Gate Voltage (V)
A
B
Fro
nt G
ate
Vol
tage
(V
)
n
δn
n = nF + nB ; δn = nB − nF
G ∝ D(EF ) ∆v = αδnα = 0.46 meV/(1015m2)
8Our samplesValley polarisation
0 10 20 30 40 50 60 706
4
2
0
-2
-4
-6
-8
-10
-12
B=0T
Back Gate Voltage (V)
No carriers
A
B
Fron
t Gat
e V
olta
ge (
V)
K. Takashina et al. PRL (2006)
D(E)
E
EF
gsgvD0D(E)
Ef
~gsgvB
~B
A
B
B=0T B
n = nF + nB ; δn = nB − nF
G ∝ D(EF )
∆v = αδnα = 0.46 meV/(1015m2)
8Our samplesValley polarisation
0 10 20 30 40 50 60 706
4
2
0
-2
-4
-6
-8
-10
-12
B=0T
Back Gate Voltage (V)
No carriers
A
B
Fron
t Gat
e V
olta
ge (
V)
K. Takashina et al. PRL (2006)
B=5T
Back Gate Voltage (V)
Fro
nt G
ate
Vol
tage
(V
)
n
δn
n = nF + nB ; δn = nB − nF
G ∝ D(EF )
∆v = αδnα = 0.46 meV/(1015m2)
9Our samplesValley resistance
0 5 10 15 20
2
4
6
8
10
B [T]
xx [a
.u.]
Magnetoresistance
K. Takashina et al. PRL (2011),PRB(2013)
Valleyresistance
10Our samplesSummary
0 10 20 30 40 50 60 706
4
2
0
-2
-4
-6
-8
-10
-12
Partially Valley Polarized
Valley Polarized
Valley Degenerate
11Dependence of Bp on valley polarizationExperiment
Consistent with measurements in AlAs
Shayegan et al. PRL (2004), PRB (2008), PRB (2010)
12Comparison with non-interacting theory
0 1 2 3 4 50
10
20
4567
b
a
pv=1
pv=1p
v=0
B p [T
]
n [1015 m-2]
pv=0
8rs
s
0 1 2 3 4 50369
n [1015 m-2]
B p [
T]
rs = 1(πn−1/2)aB
15Quantum Monte Carlo
Si at pv = 0
ingredients: interactions and white noise disorder
input : sample mobility at high density
Fleury & Waintal PRB (2010)
16Quantum Monte CarloWith Valley polarization
0 1 2 3 4 50
5
10
15
20
25
30
Non interacting µ=106 cm2/Vs µ=105 cm2/Vs µ=104 cm2/Vs
pv=1 p
v=0
B p [T
]
n [1015 m-2]
18DiscussionQMC with valleys in clean 2DEG
E4
E1
E2
Ew
QMC in clean 2DEG by Conti and Senatore EPL (1996)