Controlling ac transport in carbon- based Fabry-Perot devices Claudia Gomes da Rocha University of...

Controlling ac transport in carbon-based Fabry-Perot devices

Claudia Gomes da Rocha

University of Jyvaskyla, FinlandDresden University of Technology, Germany

Jyvaskyla, 28 August 2012

Outline

28 August 2012 Controlling ac transport in carbon-based ...

System: graphene nanoribbon devices

AC driven devices

Theoretical model

Results: probing the control

Conclusions / Perspectives

1

28 August 2012 Controlling ac transport in carbon-based ...

Graphene nanodevices

DC source

X. Wang et. al., PRL 100 (2008)

nano

Gate voltage

Understand the transport properties of nanodevices

composed of graphene nanoribbons

2

28 August 2012 Controlling ac transport in carbon-based ...

Carbon-based interferometers• Good quality contacts, ballistic transport (no scattering)!

W. Liang et al., Nature 411, 665 (2001)

Vgate (V)

Vbi

as (

mV

) Light interferometer

”electron cavity”

Fabry-Perot oscillations

3

28 August 2012 Controlling ac transport in carbon-based ...

Controlling Fabry-Perot patterns

Armchair-edge

Energ

y s

pect

rum

E1

E2

E3

E4

E5

∆

L

Adding a time-dependent term to the gate

4

28 August 2012 Controlling ac transport in carbon-based ...

Theoretical ModelTien-Gordon approach for AC transport

m

dcacm meVIVeJI 02 AVERAGE CURRENT

Jm – mth order Bessel function of the first kind

biasdcg VVG ,

Vac Monitoring the transmission changes as a function of the AC and DC parameters in AGNRs and

ZGNRs

teVHH ac cosˆˆ0

Solving time dependent Schrödinger equation

aceVG ,Vg

Vbias

XXℏΩ

5

28 August 2012 Controlling ac transport in carbon-based ...

AC gate in graphene armchair nanoribbon

Vac = 0

ac frequency

ℏΩ=∆

C.G. Rocha et. al., Phys. Rev. B 81, 115435 (2010)

Quantum Wagon-Wheel effect

6

28 August 2012 Controlling ac transport in carbon-based ...

AC gate in graphene armchair nanoribbon𝑉 𝑔 (𝑑𝑐 )=𝑉 𝑏𝑖𝑎𝑠=0

1. DC regime 2. Supression 3. Revival and inversion

4. Wagon-Wheel effect

7

MAX

MIN

28 August 2012 Controlling ac transport in carbon-based ...

AC gate in graphene armchair nanoribbon

𝑉 𝑔 (𝑑𝑐 )=𝑉 𝑏𝑖𝑎𝑠=0

8

Noise power

Oscillation amplitude of the

Noise is two times bigger than for transmission

Magnetic fields can enrich the conductance diagrams

Gate

CHANNELsource drain

N

N

S

S

Magnetic field can promote metal-

semiconductor transition in ribbons

𝜈=𝜙𝜙0

28 August 2012 Controlling ac transport in carbon-based ...

𝜙0=h𝑒

Quantum flux

𝜙=𝐵× 𝐴Magnetic flux

9

Peierls Phase Approximation

28 August 2012 Controlling ac transport in carbon-based ...

Fabry-Perot of graphene armchair nanoribbonMagnetic fields can enrich the conductance diagrams

System is at dc condition

C.G. Rocha et. al., EPL 94, 47002 (2011)

10

Combination of Fabry-Perot and insulator behaviours

28 August 2012 Controlling ac transport in carbon-based ...

Fabry-Perot of graphene armchair nanoribbonMagnetic fields can enrich the conductance diagrams

System is at Wagon-Wheel state

System is at supression state

C.G. Rocha et. al., EPL 94, 47002 (2011)

11

28 August 2012 Controlling ac transport in carbon-based ...

Lessons taken from graphene armchair nanoribbon under ac/dc conditions

Regular energy spectrum regular Fabry-Perot patterns.

ac fields can guide the systems to three different transport states: (i) suppression, (ii) inversion and (iii) Stroboscopic condition.

Noise is sensitive to the phase of the transmission amplitude.

Magnetic fields enrich the FB diagrams by opening an energy gap (resonator and semiconductor behaviours coexist).

12

28 August 2012 Controlling ac transport in carbon-based ...

Controlling Fabry-Perot patterns

Adding a time-dependent term to the gate

Zigzag-edge

Energ

y s

pect

rum

E1

E2

E3

E4

E5

13

28 August 2012 Controlling ac transport in carbon-based ...

AC gate in graphene zigzag nanoribbon

Vac = 0

ac frequency

ℏΩ≅ ∆Regular energy level spacing only at

high energy ranges

NO Quantum Wagon-Wheel effect in zigzag-edge

14

28 August 2012 Controlling ac transport in carbon-based ...

AC gate in graphene zigzag nanoribbon𝑉 𝑔 (𝑑𝑐 )=𝑉 𝑏𝑖𝑎𝑠=0

(a) DC regime (b) ”Supression”(c) Partial recovery

of DC state

15

Lessons taken so far from graphene ribbons under ac/dc conditions

Zigzag and armchair-edge ribbons: atomic details on the edges are important.

28 August 2012 Controlling ac transport in carbon-based ...

16

F. Miao et al. Science 317, 1530 (2007)

28 August 2012 Controlling ac transport in carbon-based ...

17 Applications: quantum pumping devices

(Possibility of generating DC current at zero bias)

Dissipated power ~ I x VAC + f()

Altshuler et al. Science 283, 1864 (1999)

28 August 2012 Controlling ac transport in carbon-based ...

18 Applications: quantum pumping devices

28 August 2012 Controlling ac transport in carbon-based ...

19

28 August 2012 Controlling ac transport in carbon-based ...

20

28 August 2012 Controlling ac transport in carbon-based ...

21

28 August 2012 Controlling ac transport in carbon-based ...

22

28 August 2012 Controlling ac transport in carbon-based ...

Applications: quantum pumping devices

Current is amplified when the pumping is tuned nearby van Hove singularity.

L.E.F. Foa Torres, C.G. Rocha, et. al., APL 99, 092102 (2011)

23

Charge neutrality point: I 2

van Hove singularity: I

Lessons taken from graphene-based quantum pumping

Graphene nanoribbons are promising transmission channels for quantum pumping;

When pumped nearby a van Hove singularity, its current is amplified;

The current scales linearily with the frequency.

28 August 2012 Controlling ac transport in carbon-based ...

24

28 August 2012 Controlling ac transport in carbon-based ...

25Acknowledges

Prof. Dr. G. Cuniberti

(TUD, Germany)

Dr. L. E. Foa Torres

(UNC, Argentina)

THANK YOU FOR THE ATTENTION

Prof. Dr. A. Latge (UFF, Brazil)