Controlling ac transport in carbon- based Fabry-Perot devices

statementdizzyeyedSemiconductor

Nov 1, 2013 (3 years and 11 months ago)

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Controlling ac transport in carbon
-
based
Fabry
-
Perot devices

Claudia Gomes da Rocha


University of Jyvaskyla, Finland

Dresden 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

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

nano

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
)

V
gate

(V)

V
bias

(mV)

Light interferometer

”electron cavity”


Fabry
-
Perot
oscillations

3

28 August 2012

Controlling ac transport in carbon
-
based ...

Controlling

Fabry
-
Perot

patterns



Armchair
-
edge

Energy spectrum

E
1

E
2

E
3

E
4

E
5



L

Adding a time
-
dependent term to the gate

4

28 August 2012

Controlling ac transport in carbon
-
based ...

Theoretical

Model

Tien
-
Gordon
approach for AC transport

AVERAGE CURRENT

J
m



m
th order Bessel
function of the first kind

V
ac

Monitoring the
transmission

changes as a
function of the AC and DC
parameters in AGNRs and
ZGNRs

Solving time dependent
Schrödinger
equation

V
g

V
bias

X

X


Ω

5

28 August 2012

Controlling ac transport in carbon
-
based ...


AC gate in graphene armchair nanoribbon

V
ac

= 0

ac frequency


Ω
=


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 nanoribbon

𝑉
𝑔

=
𝑉
𝑖 𝑠
=
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

=
𝑉
𝑖 𝑠
=
0

8

Noise power

Oscillation
amplitude of the
Noise is
two times
bigger than for
transmission

Magnetic fields

can enrich the conductance
diagrams

Gate

CHANNEL

source

drain

N

N

S

S

Magnetic field can promote
metal
-
semiconductor transition in
ribbons

𝜈
=

𝜙
𝜙
0

28 August 2012

Controlling ac transport in carbon
-
based ...

𝜙
0
=




Quantum flux

𝜙
=

×


Magnetic flux

9

Peierls Phase
Approximation

28 August 2012

Controlling ac transport in carbon
-
based ...


Fabry
-
Perot of graphene armchair nanoribbon

Magnetic 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 nanoribbon

Magnetic 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
-
Pertpattern献




a
c 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

Energy spectrum

E
1

E
2

E
3

E
4

E
5

13

28 August 2012

Controlling ac transport in carbon
-
based ...


AC gate in graphene zigzag nanoribbon

V
ac

= 0

ac frequency


Ω



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 nanoribbon

𝑉
𝑔

=
𝑉
𝑖 𝑠
=
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 V

AC

+ 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



v
an 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 ...

25

Acknowledges

Prof. Dr. G.
Cuniberti

(TUD, Germany)

Dr. L. E. Foa
Torres

(UNC, Argentina)

THANK YOU FOR THE ATTENTION

Prof. Dr. A. Latge

(UFF, Brazil)