Valley polarisation assisted spin polarisation inSi MOSFETs

Vincent Renardvincent.renard@cea.fr

Universite Grenoble Alpes / CEA INAC

0Thanks

1Agenda

Single particle picture

Previous results

Our samples / results

Comparison with Quantum Monte carlo / Discussion

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2Single particle pictureValley unpolarised 2DEG

∆z = gµBB

ps = n↑−n↓n↑−n↓

Bp =2E0

FgµB

3Single particle pictureValley polarised 2DEG

Bp =4E0

FgµB

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

13Role of disorder

Pudalov et al. PRL 88, 076401 (2002)

14Exclusion of disordermagneto- and valley-resistance

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]

17Experiment vs QMC

18DiscussionQMC with valleys in clean 2DEG

E4

E1

E2

Ew

QMC in clean 2DEG by Conti and Senatore EPL (1996)

19DiscussionWhat does our result tell us?

I pv = 0 is more stable vs ferromagnetic instability than pv = 1

I The prediction remains valid in disordered systems

Renard et al. Nature Comm. 6, 7230 (2015)