Controlling ac transport in carbonbased Fabry-Perot devices
Claudia Gomes da Rocha
University of Jyvaskyla, Finland
Dresden University of Technology, Germany
Jyvaskyla, 28 August 2012
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Outline
System: graphene nanoribbon devices
AC driven devices
Theoretical model
Results: probing the control
Conclusions / Perspectives
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Controlling ac transport in carbon-based ...
Graphene nanodevices
nano
X. Wang et. al., PRL
100 (2008)
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Understand the transport
properties of nanodevices
composed of graphene
nanoribbons
Controlling ac transport in carbon-based ...
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Carbon-based interferometers
• Good quality contacts, ballistic transport (no scattering)!
Vbias (mV)
W. Liang et al., Nature 411, 665 (2001)
Light interferometer
Fabry-Perot
oscillations
Vgate (V)
”electron cavity”
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Controlling ac transport in carbon-based ...
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4
Controlling Fabry-Perot patterns
Energy spectrum
Armchair-edge
E5
E4
E3
∆
E2
E1
L

Adding a time-dependent term to the gate
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Controlling ac transport in carbon-based ...
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Theoretical Model
Tien-Gordon approach for AC transport
Hˆ  Hˆ 0  eV ac cos  t 

I 

Solving time dependent
Schrödinger equation
J m e V ac    I 0 eV dc  m   
2
m  
Vg
G   , eV ac 
X
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Vac

G V
X
Vbias
dc
g
, V bias

ℏΩ
Controlling ac transport in carbon-based ...
AVERAGE CURRENT
Jm – mth order Bessel
function of the first kind
Monitoring the
transmission changes as a
function of the AC and DC
parameters in AGNRs and
ZGNRs
AC gate in graphene armchair nanoribbon
Vac = 0
ℏΩ = ∆
ac frequency
Quantum Wagon-Wheel effect
C.G. Rocha et. al., Phys. Rev. B 81, 115435 (2010)
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AC gate in graphene armchair nanoribbon
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𝑉𝑔 𝑑𝑐 = 𝑉𝑏𝑖𝑎𝑠 = 0
MAX
MIN
1. DC regime
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2. Supression
4. Wagon3. Revival and
inversion Wheel effect
Controlling ac transport in carbon-based ...
AC gate in graphene armchair nanoribbon
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Noise power
𝑉𝑔 𝑑𝑐 = 𝑉𝑏𝑖𝑎𝑠 = 0
Oscillation
amplitude of the
Noise is two times
bigger than for
transmission
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Magnetic fields can enrich the conductance
diagrams
Peierls Phase
Approximation
N
S
𝜙
𝜈=
𝜙0
ℎ
𝜙0 =
𝑒
source
CHANNEL
drain
Quantum flux
𝜙 =𝐵×𝐴
Magnetic flux
Gate
N
S
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Magnetic field can promote
metal-semiconductor transition in
ribbons
Controlling ac transport in carbon-based ...
Fabry-Perot of graphene armchair nanoribbon
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Magnetic fields can enrich the conductance diagrams
System is at dc
condition
Combination of Fabry-Perot and insulator
behaviours
C.G. Rocha et. al., EPL 94, 47002 (2011)
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Fabry-Perot of graphene armchair nanoribbon
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Magnetic fields can enrich the conductance diagrams
System is at
supression state
System is at
Wagon-Wheel
state
C.G. Rocha et. al., EPL 94, 47002 (2011)
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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).
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Controlling Fabry-Perot patterns
Energy spectrum
Zigzag-edge
E5
E4
E3
E2
E1
Adding a time-dependent term to the gate
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AC gate in graphene zigzag nanoribbon
Vac = 0
ℏΩ ≅ ∆
ac frequency
Regular energy level spacing only at high energy
ranges
NO Quantum Wagon-Wheel effect in zigzag-edge
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AC gate in graphene zigzag nanoribbon
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𝑉𝑔 𝑑𝑐 = 𝑉𝑏𝑖𝑎𝑠 = 0
(a) DC regime
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(b) ”Supression”
Controlling ac transport in carbon-based ...
(c) Partial recovery
of DC state
Lessons taken so far from graphene ribbons
under ac/dc conditions
Zigzag and armchair-edge ribbons: atomic details
on the edges are important.
F. Miao et al. Science 317, 1530 (2007)
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Controlling ac transport in carbon-based ...
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Applications: quantum pumping devices
(Possibility of generating DC current at zero bias)
Altshuler et al. Science 283,
1864 (1999)
AC
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Dissipated power ~ I x V + f()
Controlling ac transport in carbon-based ...
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Applications: quantum pumping devices
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Applications: quantum pumping devices
Current is amplified when the pumping is tuned nearby van
Hove singularity.
Charge neutrality point: I  2
van Hove singularity: I  
L.E.F. Foa Torres, C.G. Rocha, et. al., APL 99,
092102 (2011)
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Controlling ac transport in carbon-based ...
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.
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Acknowledges
Prof. Dr. G. Cuniberti
Dr. L. E. Foa Torres
(TUD, Germany)
(UNC, Argentina)
THANK YOU FOR THE ATTENTION
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Controlling ac transport in carbon-based ...
Prof. Dr. A. Latge
(UFF, Brazil)