-based valleytronics:

Applications in

Quantum Computing / Communications / FETs

G.-Y. Wu

National Tsing-Hua University

(Aug. 14, 2012)

Coworkers: N.-Y. Lue, M.-K. Lee, L. Chang

References Phys. Rev. B 84, 195463 (2011)

Phys. Rev. B 86, 045456 (2012)

arXiv 1208.0064 (2012) 1 Outline

• introduction - motivation - quantum information - FETs

• graphene-based valleytronics - graphene basics - quantum networks - FETs

• summary

2 Motivation • Si / III-V ------> graphene ? • in graphene ? high coherence vs. weak SOI ?

valleytronics

quantum FETs information 3 Quantum Information

• Benioff, Bennett, Feynman (1980s) . quantum simulations, Feymann (1982) . factorization of large numbers, Shor (1994) . quantum search, Grover (1995)

• - information unit |ψ> = α |↑> + β |↓> (spin)

|ψ> = α (|↑↓> - |↓↑>) + β (|↑↓> + |↓↑>) (decoherence free)

|ψ> = α |σ+> + β |σ-> (photon)

others …… QD spin approach

• Loss, DiVincenzo, Burkard (1998, 1999) spin qubit + qugate ----> universal

• all electrical manipulation Rashba SOI ~ p x (∂V)·σ

• challenges - g-factor engineering: Δg ≠ 0 (computing)

ge = 0 (communication) - spin flip scattering ----> decoherence

5 FETs

• standard FETs gate

x

source source drain

• post-Si FETs - graphene-based FETs (Novoselov et al., 2004) easier to scale (F. Schwierz, Nature Nanotech. 5, 487 (2010)) - spin FETs (Datta & Das, 1990) low power consumption

6 Spin FETs

• structure

Rashba SOI ~ px x (∂V)z·σy

gate

x

↑ … → … ↓ ↑ ↑ source ↓ z↑

→x

FM InAs FM

. challenges

- FM / mismatch → tunnel FETs

- spin-flip scattering (σx) → stray electric fields

7 Graphene-Based Valleytronics

• graphene basics • quantum networks - qubit structure - qubit state - all-electric manipulation - qubit coherence …... • FETs - structure - lead state / injection / detection - all-electric manipulation

8 Graphene Basics-1

• Novoslov, Geim (2004) a) crystal → b) bands →

π-bond K, K' valleys (τv = ±)

9 Graphene Basics-2

. graphene on BN or SiC

2 2 2 E = ±(∆ + vF p ) → massive Dirac particle [cp. E = ±(m2c4 + c2p2)]

c → vF mc2 →Δ

2∆ (energy gap) → QD confinement

10 Graphene Basics-3

. Schrodinger type description (for E ~ ∆) in ε / B fields (Wu et al., 2011)

nonrelativistic part 2 ( 0 )  HV   τ μ B 2m* v v0 normal

e   → valley magnetic moment v 0 2m*

11 Graphene Basics-4

relativistic part (1st order)

2 2 (1) 1  H   τ μ B τ (  V)  * v v0 normal v * 22 m 4m Δ

1  (pV2 ). 8m*

→ valley-orbit interaction ~ τv(p x ∂V)·z cp. spin-orbit interaction ~ (p x ∂V)·σ

12 Valley-based Quantum Networks

• qubit structure / state

• all-electric single-qubit manipulation

• coherence / initialization / readout / qugate

13 Qubit Structure / State

two-electron states: ZS (isospin = 0) → logic 0

ZT0 (isospin = 1) → logic 1

ZT+, ZT- (isospin = 1) 14

Qubit State

• isomorphism valley pair ↔ spin 1/2

ZS ↔ |↓>

ZT0 ↔ |↑>

X- ↔ |←>

X+ ↔ |→> 11 |ZKKKKZKKKK (| '|'    ), |  (| '|'    ) SLRLRTLRLR220 |XKKXKK | '  , |  | '  LRLR 15

Effective Interaction

1 0 1   0i   1 0  HJ x ,,.  y     z    JLR4 1 0  i 0   0 1 

HZ = –g* σ μB|Btotal| + τv μv |Bnormal| spin valley ------> J HB()      eff vL vR normal x2 z

in {0,1} space

16 Single Qubit Manipulation

• DC mode (Bnormal ≠ 0)

µv = µv0 [ 1 – O(E–∆)/∆) ]

→ electric tuning of µv in QDs

x  2( vL  vR )BJ normal /  z  /

→ manipulation time ~ O(ns) 17

Single Qubit Manipulation

• AC mode

(Bnormal = 0)

18 AC Mode

• Bnormal = 0 ----> faithful quantum state transfer

α|σ+> + β|σ-> → α|K> + β|K'>

19

photon → valley pair 20 Graphene + Photon Quantum Network . graphene quantum memory / repeater

hν hν

graphene quantum computer graphene quantum computer

21 Qubit Coherence and Etc.

• coherence phonon-mediated relaxation: L = dot size ~ 350A,

V0 = QD potential depth ~ 70meV, Bnormal = 100mT, T = 10K

valley relaxation time ~ O(ms)

• initialization / readout / qugate operation J. M. Taylor et al, Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins, Nature Phys. 1, 177 (2005)

22 Valley FETs

• structure

• lead state / injection / detection

• all-electric manipulation

23 Structure (a) y gate x

source Q1D channel drain source L …… (b) graphene QW

x

W… W ……

AGNR AGNR

L L 24

Lead State / Injection / Detection

AGNR solution:        A   eiKr  eiK 'r   D, D,  B       ik y y   1   ikx iK  r ikx iK'r  e   v (k  ik)   e e SK '/ K e e  F y  ik y y     e   2  E 

n+1 K' component : K component = SK'/K = (-1)

E = En, ky = kn, 2 2 2 2 2 * (En+Δ) = Δ +ћ (k + kn ) / 2m ,

kn = nπ / W – 4π / 3a0, n = 1.

25 All-electric Manipulation

channel state

    2  ik x ik x exp(y )   e  eiK  r S e  eiK'r   0  K '/ K  2   exp(y )

K' component : K component

i(k  k ) x  SK '/ K e

26

“Rashba” Effect

E0,τ

------>

K' K

E * 3 2m vo 3e 12 k  k  k k k   2 - + vo  *3 3 D y  6.410 eV m

 2m w0 

source ↑ ↑ … → … ↓ ↑

27 Valley FET vs. Spin FET

FET d.o.f. lead channel physical mechanism valley FET valley K,K' AGNR graphene VOI

(all graphene) spin FET spin ↑,↓ FM semiconductor Rashba SOI

(hybrid)

28 Summary • gated device ---> scalable, all-electric manipulation

• VOI mechanism ~ τv(p x ∂V)·z ---> state coherence / fault tolerant ↓↓ graphene + photon quantum networks all-graphene valley FETs ↓↓ EXPERIMENTAL REALIZATION ?  Thank You  29