controlling ac transport in carbon- based fabry-perot devices claudia gomes da rocha university of...
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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
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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
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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
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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
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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
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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
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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
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AC gate in graphene armchair nanoribbon𝑉 𝑔 (𝑑𝑐 )=𝑉 𝑏𝑖𝑎𝑠=0
1. DC regime 2. Supression 3. Revival and inversion
4. Wagon-Wheel effect
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MAX
MIN
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28 August 2012 Controlling ac transport in carbon-based ...
AC gate in graphene armchair nanoribbon
𝑉 𝑔 (𝑑𝑐 )=𝑉 𝑏𝑖𝑎𝑠=0
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Noise power
Oscillation amplitude of the
Noise is two times bigger than for transmission
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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
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Peierls Phase Approximation
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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)
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Combination of Fabry-Perot and insulator behaviours
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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)
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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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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
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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
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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
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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)
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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)
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18 Applications: quantum pumping devices
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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)
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Charge neutrality point: I 2
van Hove singularity: I
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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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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)