Controlling ac transport in carbon-based Fabry -Perot devices

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


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


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

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

Vgate (V)

Vbi

as (m

V) Light

interferometer

”electron cavity”

Fabry-Perot oscillations

3


Controlling Fabry-Perot patterns

Armchair-edge

Ener

gy sp

ectru

m

E1

E2

E3

E4

E5

∆

L

Adding a time-dependent term to the gate

4


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


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


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


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


𝜙0=h𝑒

Quantum flux

𝜙=𝐵× 𝐴Magnetic flux

9

Peierls Phase Approximation


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


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


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


Controlling Fabry-Perot patterns

Adding a time-dependent term to the gate

Zigzag-edge

Ener

gy sp

ectru

m

E1

E2

E3

E4

E5

13


AC gate in graphene zigzag nanoribbon

Vac = 0

ac frequency

ℏΩ≅ ∆Regular energy level spacing only at

high energy rangesNO Quantum Wagon-Wheel effect in

zigzag-edge

14


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.


16

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


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)


18 Applications: quantum pumping devices


19


20


21


22


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.


24


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)

Documents

Controlling ac transport in carbon-based Fabry -Perot devices