points quantiques et ferromagnétismecoherent non- local effects in disordered mesoscopic devices...

Points quantiques et ferromagnétisme

T. KontosLaboratoire Pierre Aigrain, Ecole Normale Supérieure, Paris

France

Experiment:C. Feuillet-Palma, T. DelattreJ.-M. Berroir, B. Plaçais, G. Fève,D.C. Glattli.

Acknowledgements : A. Thiaville, S. Rohart, H. Jaffrès, G.E.W. Bauer,A. Fert, X. Waintal, C. Mora, M. Brune, J.M. Raimond.

Theory: A. Cottet

Electron spin manipulation in nanocircuits

J. Petta et al. Science ‘05K.C. Nowack et al. Science ‘07

Spin manipulation in confined conductors

Orthogonal (real or effective) magnetic fields needed to perform coherent manipulationsDetection via transport measurement

Use of specific material properties (spin-orbit, nuclear spins…)Can one use ferromagnetic hybrid nanostructures to implement

spin manipulation/detection setups?

Circuit Quantum Electrodynamicswith electronic spins confined in nanoconductors?

Detection via dispersive shift of cavity resonance (not transport)

Manipulation and coupling using cavity QED techniques

Inclusion of electronic spins in superconducting coplanar waveguide cavities (similar to superconducting Qbits)

Use of intrinsic nanoconductor properties possible (spin-orbit, hyperfine interaction)But ferromagnetic contacts can be used to “engineer” spin/photon coupling

Phase coherent spin dependent phenomena in nanoscale conductors

1. Direct (first) experimental demonstration of orbitally phase coherent spintronics (multiterminal spin transport experiment)2. Use of this coupling for spin quantum bit with ferromagnetic contacts for circuit QED

Spin dependent quantum interference expected + electronic phase directlycoupled to local electric field

OUTLINE

pL pRσ,eσ,e

Resonance condition for θ=0 [θ= π] :WW

RWW

L ,][,2 σσ ϕϕδ −++0 Zjπj ∈= ,2

Lke=0δ+

Directly coupled to local electric field

A magnetic tunnel junction…

VSD

HcL < HcRHcRHcL

R

H

Jullière’s model

)(

2222

2

↓↑

↓↑

+∝

∝

NNTG

NNTG

P

AP

2

2

12

PP

RRRTMR

P

PAP

−=

−=

Spin signalTMR

Phase of carriers completely ignored

↓↑

↓↑

+−

=NNNN

P

Spin FET behavior in SWNTs

Oscillations of TMR as a function of gate voltage.

Spin dependent resonant tunneling mechanism (quantitative theory A. Cottet et al.)

S. Sahoo, TK et al., Nature Phys., 1, 99 (2005), H.T. Man et al., Phys. Rev. B R 73, 241401 (2006), A. Cottet, TK et al. Semicond. Sci. Tech. 21, S78 (2006), A. Cottet and M.-S. Choi PRB ‘06

-0,4 -0,2 0,0 0,2 0,4

162

164

166

168

170

R(kΩ

)

B(T)

T= 1.86KVG= +4.328VL=500nm

-0,4 -0,2 0,0 0,2 0,4

2300

2400

2500

R(

kΩ)

B(T)

T= 1.86KVG= +4.302VL=500nm

Both signs of TMR can be observed.

Phase-coherent phenomena particularly visible in multi-terminal devices (non-local effects)

VSD

VGCG

Quantum coherent transport vs spintronics

Coherent non-local effects in disordered mesoscopic devices and non-local spin dependent voltages in disordered incoherent conductors

« Theorist’s blob » experiment

C.P. Umbach et al., APL, 50, 1289 (1987)F.D. Jedema et al., Nature, 416, 713 (2002)See also M. Johnson and R. H. Silsbee, PRL 55, 1790 (1985)

« Non-local » spin injection

Nanotubes ideally suited for the study of the interplay of orbitalcoherence and spin transport


h/e modulations due to Aharonov-Bohm effect in the outer loop (not in the classical path)


C.P. Umbach et al., APL, 50, 1289 (1987)

Small effect here (1 e2/h over 500 e2/h)


Hysteretic switching of non-local voltage as a function of magnetic field

F.D. Jedema et al., Nature, 416, 713 (2002)See also M. Johnson and R. H. Silsbee, PRL 55, 1790 (1985)



Few channel regime in NTs make quantum effect a priori prominent.


C.P. Umbach et al., APL, 50, 1289 (1987)F.D. Jedema et al., Nature, 416, 713 (2002)See also M. Johnson and R. H. Silsbee, PRL 55, 1790 (1985)


Device geometry

Transverse anisotropy for magnetization of NiPd stripesNon-local geometry for charge and spin transport

MFM, S. Rohart, A. Thiaville (LPS,Orsay)

Side gates in addition to back gate to control locally the sections of NTC. Feuillet-Palma et al. PRB 81, 115414 (2010).

Nanotubes based multi quantum dots

e- e-

Reservoir L Reservoir R

Vsd

VSG1VSG1=0 and VSG2=0

e-

VSG2

e-


VSG1=0 and VSG2non zero

e- e-


Vsd

VSG1

e-

VSG2

e-


VSG1non zero and VSG2=0

e- e-


Vsd

VSG1

e-

VSG2

e-


VSG1 non zero and VSG2 non zero Resonances on lignes VSG1 +α VSG2 =cste

e- e-


Vsd

VSG1

e-

VSG2

e-

Non-local voltage signal

-100 -50 0 50 100

-0.2

0.0

0.2VSG2 = -6.0 VVSG1 = -8.76 VVBG = -11.772 V

V 34(µ

V)

H(mT)Tartan pattern for non-local voltage as a function of side gates

Characteristic hysteretic switching of non-local voltage

H

1 2 3 4

Leads to oscillations of non-local voltage in P config as a function of back gatesee also G. Gunnarsson, J. Trbovic, C. Schönenberger PRB 77, 201405(R) (2008)

A priori interplay between non local spin transport and orbital coherence

MG controlled by remote side gate

Sign change in MV specific to coherent case

N-F Non local Conductance F-N Non local Voltage

Anomalous hysteresis in the current

Non local spin transitor action in G and V

-100 -50 0 50 100

0,375

0,4000,600

0,625 VSG2= -0.8V

VSG2= -9.4V

V 34(µ

V)H(mT)

-100 -50 0 50 1000.005

0.010

VSG2= -0.8V

VSG2= 4.8V

G 12(e

²/h)

H(mT)

H

1 2 3 4

MV=V34P-V34APMG=1-G12AP/G12P

G12AP

G12PV34P

V34AP

Resistor network model ?

VV3 V4

R1

R1

R4

R4

↑3R↑2R

↓3R↓2R

R12

R12

R23

R23

R34

R34

↑2r ↑2r

↓2r ↓2r ↓3r↓3r

↑3r↑3r

r1r1

r1 r1 r4 r4

r4 r4

N-F current independent of magnetization relative orientations (also foundIn more sophisticated models e.g. Takahashi & Maekawa).

Non-local spin signal obtained because spin asymmetry

Model conventionally used in incoherent spin transport

N NFF

Multi-terminal scattering appoach

The scattering approach provides an explanation for both non local signals in V and G.

0 2 4 6

-0.01

0.00

∆VM

R (%

)

∆VP / V

δgS

180

210

240

δBg=3π

0 2 4 60.0

0.5

1.0

1.5

GM

R (%

)

GPh

/e2

δSg

-5

0

δBg=3π

A. Cottet, C. Feuillet-Palma and TK Phys. Rev. B 79, 125422 (2009)

Difficult to obtain N-F current magnetic configuration dependent in the diffusiveIncoherent regime

Spectroscopy of conductance

Interference fringes observed in the conductance

Multiple Fabry-Perot electronic interferometers physics

Energy scale correspond to one NT section here

C. Feuillet-Palma et al. PRB 81, 115414 (2010).

Magnetic configuration dependent phase shift

Modulations of GP due to Fabry-Perot physics

Gate modulations of MG phase shifted

Orbitally coherent spintronics

Quantitative agreement with scattering theory

The orbital phase depends on magnetic configuration !

Theory : A. Cottet, C. Feuillet-Palma and TK Phys. Rev. B 79, 125422 (2009)

-30

-20

-10

0

-10 -5 0 5 100.005

0.010

0.015

MG

(%)

G P(e

2 /h)

VSG2 (V)

C. Feuillet-Palma et al. PRB 81, 115414 (2010).

The theorist‘s blob experiment for spintronics

No classical analog of such a spintronic device (no classical signal)

Exact analog of Aharonov-Bohm loop outside classical path

We should observe a « spin signal » between the two N’s

Aharonov-Bohm phase

Spin dependent geometric phase

The theorist‘s blob experiment for spintronics

No signal at 4.2 K for G12 but signal at 1.65K !

Signal both at 4.2K and 1.65K (same amplitude) between the two F‘s

H

1 2 3 4

G

H

1 2 3 4

G

C. Feuillet-Palma et al. in preparation

(preliminary)

Temperature dependence of spin signal

MR between the two ferromagnets essentially constant

Sharp decrease of MR between normal electrodes

Accounted by theory with no adjustment parameters essentiallyC. Feuillet-Palma et al. in preparation

MGNN

MGFF

(preliminary)

Conclusion part I

Observation of local gate controlled “non local” magnetoresistance in mutli-terminal SWNT devices

Multi-terminal devices are multi-electronic interferometers

Anomalous magnetoresistance between a N contact and a F contact in conductance due to delocalization of electronic waves

Observation of spin signals with no classical analog

Orbitally phase coherent spintronics

Behaviour qualitatively and quantitatively reproduced within the scattering approach

A new way to couple the orbital and spin degree of freedom

Cavity Quantum Electrodynamics:from optical systems to superconducting chips

A. Wallraff et, Nature 431, 162 (2004).

Superconducting quantum bit coupled to a superconducting coplanar waveguide

cavity

M. Brune et al., Phys. Rev. Lett. 76, 1800 (1996).

Jaynes-Cummings Hamiltonian

Rydberg atom coupled to asuperconducting mirror cavity

Circuit Quantum Electrodynamicswith spins confined in nanoconductors?

Basic requirements:

- Strong spin/photon coupling g- Local spin manipulation

There exists schemes based on spin-orbit coupling or hyperfine interactionNowack et al. (2007), Trif et al. PRL 101, 217201 (2008), Burkard et al. (2006), etc…

Our motivation:

-A scheme free from external magnetic fields

-A strongly tunable g

∆

+∆

=21

21 112ggJ

First observation with superconducting qubits: J. Majer et al., Nature 449, 443 (2007)

rωω −=∆)2(1

01)2(1

Effective Zeeman fields in nanoconductors with ferromagnetic contacts

A very general effect seen in:

- Thin superconducting layers Tedrow et al., Phys. Rev. Lett. 56, 1746 (1986)

- InAs quantum dots and nanowires Hamaya et al, APL 91, 022107 (2007)L. Hofstetter et al., arXiv:0910.3237

- Single Wall Carbon nanotubes Sahoo et al, Nature Phys. 1, 99 (2005).Hauptmann et al, Nature Phys. 4, 373 (2008).

Here: quantum dots contacted to thick ferromagnetic insulators (FIs)

hybridization of the dot orbitals with the first atomic layers of the FIs

General principle of the ferromagnetic spin qubit

A. Cottet and TK, arXiv:1005.1901

Spin/photon coupling

Transverse effective field due to the (gate controlled) spatial modification of the double dot eigenstates

(1)

Dots L and R controlled by local gates

Hamiltonian of the ferromagnetic spin qubit

H =^

D is a function of VgL and VgR and also possibly Vac

2δL(R) : effective Zeeman splitting in dot L(R)

We assume δL = δR = δ for simplicity

Stability diagram and energy levels of the circuit

t=0

dashed lines: t=0

θ=π/6



t=0

dashed lines: t=0, full lines: t=2δ/3

θ=π/6



θ=π/6

t=0

dashed lines: t=0, full lines: t=2δ/3

DON=2.8δν01=7.7 GHzν12=4.4 GHz

2δ=32µeV


Spin/photon coupling

DON=2.8δ, gON=5.6 MHz

DOFF=20δ, gOFF=13 kHz

gON/gOFF=450π/6

Rabi oscillation possible using an oscillating Vac

Spin/photon coupling g tunable with D and θ

θ=π/6, 2δ=32µeV, Vrms=2µeV

Evaluation of decoherence processes

Example of a Single Wall Carbon Nanotube Based Setup

Description with a Dirac-like hamiltonianwith realistic parameters

Several decoherence sources:

Spin orbit coupling T1~ ms [Bulaev et al., PRB 77, 235301 (2008)]

Low frequency charge noise

PhononsSpecific to our setup

∆ K-K‘ ~3meV [Liang (2002), Sapmaz (2005)]

Dephasing due to low-frequency charge noise

ν01~2δL

Charge noise mediated by fluctuations of D

Charge noise mediated by fluctuations of δL

Estimates using a semiclassical approximation and extrapolating the charge noiseamplitude given in Herrman et al., Phys. Rev. Lett. 99, 156804 (2007)

π/6

Chemical potential of dot L (meV)

Relaxation due to phonons

Suspended carbon nanotube:

Non-suspended carbon nanotube:

Stretching vibrons confined in dots L and R

λ=100 nm

Expected performances

Non-suspended carbon nanotube setup:

DON=2.8δ, gON =5.6MHz, T2=1.2µs strong coupling regime reached

DON=20δ, gOFF=13kHz, T2=2ms quantum register at the OFF point

A generic setup Our setup does not require spin-orbit coupling or hyperfine interaction

A relatively robust setup δ can be adjusted by choosing the dot size and the active dot orbital,regardless of the FI contact properties

These performances may be further enhanced with suspended nanoconductors


Conclusion part II

New scheme for manipulating single electronic spins in nanocircuits

Prediction of observation of strong coupling regime for realistic parameters

Theoretical proposal based on orbitally phase coherent spintronics

Possibility to explore cavity QED with electronic spins

Maybe a new platform to study decoherence in strongly correlatedsystems ?

Strongly tunable coupling g + quantum register behavior


C. Feuillet-Palma et al. PRB 81, 115414 (2010)

A. Cottet, C. Feuillet-Palma and TK Phys. Rev. B 79, 125422 (2009)

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points quantiques et ferromagnétismecoherent non- local effects in disordered mesoscopic devices...

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