ELECTRON TRANSPORT IN SEMICONDUCTOR · PDF fileSilvano De Franceschi – Laboratoire de...

Silvano De Franceschi – GDR Physique Quantique Mésoscopique, Aussois 8-11 décembre 2008

QUANTUM TRANSPORT IN BOTTOM-UP SEMICONDUCTOR NANOSTRUCTURESSilvano De Franceschi

http://www-drfmc.cea.fr/Pisp/55/silvano.de_franceschi.html

INAC/SPSMS/LaTEQS: Laboratory of quantum electron transport and superconductivity

Silvano De Franceschi – Laboratoire de Transport Electronique Quantique et Supraconductivité 217/12/2008

Top-down Quantum Dot Devices

Spathis et al. (poster session)

-2

-1

0

1

2

VS

D (

mV)

-650 -600 -550 -500Vg (mV)

N=0 1 2 3

Vg

Hofheinz, Jehl, Sanquer et al.


I+

I-

V+V-

I+

I-

V+V-

Vgate

SiO2Si (p+)

Catalytic VLS growth

goldparticle

liquideutect

vapor

nano

wire

time

φ

Lsd W

sour

ce

drain

1 μm

Semiconductor nanowires: growth and device fabrication


Bottom-up semiconductor nanowire devices @ LaTEQS

1µm

1 μm

Aluminum bottom gates

Ni silicide

Si nanowires (Mongillo et al.) InAs/InP core/shell nanowires

(Katsaros et al)

200 nm

GaN/AlGaN nanowires(Songmuang et al)

1µm

Mn-GaAs nanowires(Storace et al)


Self-assembled semiconductor quantum dot devices @ LaTEQS

source drain

gate

gate

Ge islands on Si

gate voltage

Sou

rce-

drai

n bi

as

(Katsaros et al)


Hybrid normal-superconductor devices

S SI

S SN

Josephson effect and Andreev reflection

_ _

_ _

Thin insulating (oxide) interlayer

Short (L< LΦ)normal-conductor interlayerAndreev reflection

IS = IC sin(φS - φD )

φS φD

φS φD

IS = IC sin(φS - φD )

L



S SDOT_ _

Nano-link ? ?

Many energy scales involved• Superconducting gap Δ• Charging energy U • Level spacing ΔE • Lifetime broadening Γ• Thouless energy ETh = h/τD• Temperature kBT

How does superconductivity affects transport?Can a supercurrent flow ? What is the current-phase relationship?Can superconductivity provide insight on the electronic properties?



Buizert et al. PRL ‘07

Heersche et al. Nature ‘06

Kasumov et al, Science 284 ’99)Morpurgo et al., Science 286 ’99Buitelaar et al., PRL ’02Jarillo-Herrero et al., Nature ’06Cleuziou et al., Nature Nanotech. ‘06

Metal Nanoparticles in an oxide thin layer: Ralph et al, PRL ’95Atomic-size contacts: Scheer et al., PRL ’97; PRL ’01.

Doh et al. Science ‘05 van Dam et al. Nature ’06Xiang et al., Nature Nanotech. ’06Sand-Jespersen, PRL ‘07


Andreev reflection vs Coulomb blockade

S-N-S devices based on InAs or InP nanowire

DIfferent regimes depending on relative value of the relevant energy scales:

RN/RQ as characteristic parameter(with RN the normal-state resistance and RQ ≡ (2e2/h)-1 ~26 kΩ the quantum resistance)

Y.-J. Doh, SD, et al. Nano Letters, 8 Dec. 2008

• Superconducting gap Δ• Charging energy U • Level spacing ΔE • Lifetime broadening Γ• Thouless energy ETh = h/τD• Temperature kBT


U

U ~ 1 meV

B= 20 mT

dI/dVsd vs (Vsd,Vg)

sd

B= 20 mT

RN >> RQ ≡ (2e2/h)-1 ~26 kΩ => Coulomb blockade

n-type InP nanowire (n~1019 cm-3): weak coupling case

Charging energy:


dI/dVsd vs (Vsd,Vg)

sd

B= 0 B= 20 mT

RN >> RQ ≡ (2e2/h)-1 ~26 kΩ

+Δ

-Δ

+2Δ

-2Δ

Δ << UB = 0

n-type InP nanowire (n~1019 cm-3): weak coupling case


B = 20 mT

Δ

Δ

B = 0

Negative differential conductance due to BCS singularities


DrainSource

Supercond. Supercond.Normal

SiO2

exp( ), ,j j ji j R LϕΨ = Ψ =

sin( ) S C LR LR L RI I whereφ φ ϕ ϕ= ≡ −

(DC Josephson effect)

SD SD S D

Δ , ϕSΔ , ϕS

Δ∗ < Δ(induced gap)

-150 -100 -50 0 50 100 150

-40

-20

0

20

40

IR IC

V (μ

V)

I (nA)

n-doped InAs nanowires (n~1019 cm-3): strong coupling case

T = 40 mK

IC = 136 nARN = 417 ΩICRN = 60 μV ~ Δ0/e

~

S,D

RN as low as ~1 KΩ => No Coulomb blockade


Field-effect control of the supercurrent

-2 -1 0 1 2

-10

0

10

-71 V -61 V -50 V -40 V -30 V -20 V -10 V 0 V

V (μ

V)

I (nA)

Vgate

DrainSource

S SN

Vg< 0

0 4100

101

102

I C(n

A)

RN(kΩ)

Ic for different devices

Ic decreases with RN

Science 309 272 (2005)


Supercurrent fluctuations correlate with normal-state universal conductance fluctations

0 5 10 15 20

dV/dI (kOhm)

0 5 10 15 20

dV/dI (kOhm)

-70 0-2

0

2

I (nA

)

Vg (V)0 30 kΩ

2

4

GN (2e

2/h)

Electron transport through the nanowireis diffusive and phase coherent=> mesoscopic Josephson junctions

Field-effect control of the supercurrent

-2 -1 0 1 2

-10

0

10

-71 V -61 V -50 V -40 V -30 V -20 V -10 V 0 V

V (μ

V)

I (nA)

Vgate

DrainSource

S SN

Vg< 0

Theory: Altshuler & Spivak (‘87)


rms(GB)=√⟨(G(B) - ⟨G(B)⟩)2⟩

rms(GB)= 0.3 e2/h

rms(GB)= 0.29 e2/hI+

I-

V+V-

I+

I-

V+V-B

I+

I-

V+V-

I+

I-

V+V-B

Device 2Device 1L= 440 nm L= 110 nm

Note: rms(GB) ~ (Lφ/L)3/2 e2/h]

• G is not proportional to L! • rms(G) is almost the same [in theory:

Metal contacts are 500 nm wide => L does not correspond to the distance between them

Phase-coherent diffusive transport in InAs nanowires(normal state)


Autocorrelation function: F(ΔB)=⟨G(B)G(B+ΔB)⟩ -⟨G(B)⟩2

(i.e.: F(ΔB)=1/2 F(0) for ΔB = Bc) F(ΔB) decays on a field scale Bc

Bc = 0.214 T Bc = 0.184 T

Lφ ~ wire diameter ~ 100 nm

For the long wire rms(GB) = 2.45 (Lφ/L)3/2 e2/h

Device 2Device 1L= 440 nm L= 110 nm

Bc is independent of channel length and field direction!

=>

= 2.45 (100/440)3/2 e2/h = 0.3 e2/h

Phase-coherent diffusive transport in InAs nanowires(normal state)

[van Houten and Beenakker Solid State Physics ’91]


Enhancement of rms(G) due to combined UCF and Andreev reflection

UCF and Andreev reflection( )( )

0.0 0.3 0.60.4

0.8

rms(

Gg)

(e2 /h

)

V (mV)

-20 -1020

30

dI/d

V (e

2 /h)

Vg (V)

b

0.0 0.3 0.60.4

0.8

rms(

Gg)

(e2 /h

)

V (mV)

-20 -1020

30

dI/d

V (e

2 /h)

Vg (V)

b

V=0; B=0.1T

, @ B=0


Δ

Δ

Andreev regime

RN ~ RQ => expected competition Andreev reflection – Coulomb blockade(+ high-order cotunneling)

n-type InP nanowire (n~1019 cm-3): intermediate coupling case

RN/RQ = 0.77

500 nm


T dependence

Gate dependence

Coulomb blockade affects only the low-bias regime

From fit:


G/Gmax ~ cosh-2[(e(Cg/CΣ)|Vg,peak - Vg|)/2.5kBT]

U = e2/CΣ ~ 13.2 kBT ~ 30 μeV


Sand-Jespersen et al. PRL ’07 (InAs nanowires)

Buizert et al, PRL ’07 (with InAs self-assembled quantum dots)


RN ~ RQ but U>>Δ :

=> Andreev Reflection vs Kondo effect/high-order cotunneling

=> Single-electron supercurrent transistor and π Josephson junction IS = IC sin(φSD+π)

Buitelaar et al. PRL ’02 (carbon nanotubes)

DrainSource

S SVL<0 VR<0

quantum dotinduced gapΔ* ~ Δ

induced gapΔ* ~ Δ

Nature 442, 667 (2006)


Negative and positive supercurrent

Simplest case: single-level quantum dot

initial final

12 34

intermediate

4-th order co-tunneling

initial final

12 3

4

intermediate

N=1

S=1/2

N=2

S=0

)sin()sin(

LRc

LRcs

III

φπφ

−=+=

)sin( LRcs II φ=

(π-junction)

(ordinary junction)

[Bulaevski, Knzii, Sobbianin, JETP Lett. 25, 290 (’77);Spivak and Kivelson PRB 43, 3740 (‘91)]


Summary

Hybrid nanodevices? ?

Γ < ΔE U,Δ ~

RN ~ RQ

RN >> RQ

RN << RQ

Single-electron tunneling, NDC due to BCS density of states (Doh et al. Nano Letters ’08)Case of a diffusive normale conductor (ΔE=0)

Δ, U, ΔE, Γ, ETh, kBTRelevant energy scales:

• pi-junction behavior: IS = IC sin(φSD+π) (van Dam et al., Nature ’06)

•Tunable proximity supercurrent (Doh et al. Science ’05) •Correlation between Ic fluctuations and UCF•Enhance UCF amplitude due to Andreev reflection (at finite bias)Case of a ballistic conductor (quantum dot with finite ΔE)• Resonant supercurrent transistor (Jarillo-Herrero et al. Nature ’06)

Case of a large quantum dot (ΔE~0, U<<Δ)• Clear energy scale separation between Coulomb blockade and Andreev reflection (Doh et al. Nano Letters ’08)

Case of a small quantum dot ( , )


AcknowledgementsINAC/SPSMS/LaTEQS: M. Mongillo (PhD), G. Katsaros (PD), P. Spathis (PD)

F. Lefloch, J.L. Thomassin, X. Jehl, M. Sanquer

S. Rubini, F. Martelli, F. Jabeen (Mn-doped GaAs/InAs NWs, CNR-INFM TASC,Trieste)E. Storace, J. Weis, K. von Klitzing (Mn-doped GaAs/InAs NWs, MPI Stuttgart)

C. Mouchet, E. Rouviere, J.P. Simonato (doped Si NWs, LITEN)P. Gentile, N. Pauc, T. Baron (undoped Si NWs, INAC/LTM)

Collaborators on semiconductor nanowires (NWs):J. Van Dam, Y.J. Doh, S. Sapmaz, L. Kouwenhoven (InAs/InP NWs, TU Delft)E. Bakkers, A. Roest (InAs/InP NWs, Philips Eindhoven)

X. Jiang, C. Lieber (InAs-InP core-shell NWs, Harvard)R. Songmuang, B. Daudin, B. Gayral (GaN-based NWs, INAC/CNRS)

…open positions available at master, PhD and PD level

Collaborators on self-assembled semiconductor quantum dots:M. Stoffel, A. Rastelli, O. Schmidt (IFW Dresden)

Funding: ANR (chair d’excellence & ERC starting grant), EU FP6 (HYSWITCH)


1 μm

VL

VR

200 nm

V(m

V)

1.5

-1.5

VL (mV) -390-410

eVR= - 400 mV

V = δ

δ

Fully tunable quantum dot: intermediate tunnel coupling

Inelastic cotunneling

Can be used for spectroscopy in strong coupling regime [PRL 86, 878 (2001)]

δB=100 mT


1 μm

VL

VR

200 nm

V(m

V)

1.5

-1.5

VL (mV) -390-410

eVR= - 400 mV

δ

B=100 mTLevel spacing: 0.1 – 0.5 meV

Supercond. gap: 0.14 meV

Charging energy: ~ 1 meVQuantum dot parameters:

Fully tunable quantum dot: intermediate tunnel coupling


L R

S DQDΔ* Δ*

VL (mV)-460 -450 -440 -430

V(m

V)

1-1

b

Source

VL

VR

VREF

Drain2µm

Ic,REF = 320 pA (VREF = fixed constant) Ic=Ic,QD+Ic,REF

I c,Q

D(n

A)

00.

5

Study of Josephson Supercurrentthrough an interacting QD

We exploit the independent tunability of nanowire JJs

negative supercurrent!N N+1 N+2 N+3 N+4

Nature 442, 667 (2006)


L R

S DQDΔ* Δ*

Source

VL

VR

VREF

Drain2µm I c,Q

D(n

A)

00.

5

VL (mV)-460 -450 -440 -430

V(m

V)

1-1

b

-432

Φ(Φ

0)

VL(mV)-439

1

5

I c(n

A)

0.4

0.2

Φ (Φ0)1 4

π-junction behaviour

Φ

N N+1 N+2 N+3 N+4

Similar π-behavior seenalso in CNT-SQUIDs[Cleuziou et al. (2006)]


B=0: UCF drops for V>ETh

This is consistent with a Thouless energy ETH ~ 0.14 meV

B=0.1T: UCF drops for kT>ETh

Phase-coherent diffusive transport in InAs nanowires

ELECTRON TRANSPORT IN SEMICONDUCTOR · PDF fileSilvano De Franceschi – Laboratoire de...

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