1. 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

2. 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

3. 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

4. 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

5. 28 August 2012 Controlling ac transport in carbon-based... Controlling Fabry-Perot patterns  Armchair-edge Energy spectrum E1E1 E2E2 E3E3 E4E4 E5E5 ∆ L Adding a time-dependent term to the gate 4

6. 28 August 2012 Controlling ac transport in carbon-based... Theoretical Model Tien-Gordon approach for AC transport AVERAGE CURRENT J m – mth 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 VgVg V bias X X 5

7. 28 August 2012 Controlling ac transport in carbon-based... AC gate in graphene armchair nanoribbon V ac = 0 ac frequency C.G. Rocha et. al., Phys. Rev. B 81, 115435 (2010) Quantum Wagon-Wheel effect 6

8. 28 August 2012 Controlling ac transport in carbon-based... AC gate in graphene armchair nanoribbon 1. DC regime 2. Supression 3. Revival and inversion 4. Wagon- Wheel effect 7 MAX MIN

9. 28 August 2012 Controlling ac transport in carbon-based... AC gate in graphene armchair nanoribbon 8 Noise power Oscillation amplitude of the Noise is two times bigger than for transmission

10. Magnetic fields can enrich the conductance diagrams Gate CHANNEL source drain N N S S Magnetic field can promote metal-semiconductor transition in ribbons 28 August 2012 Controlling ac transport in carbon-based... Quantum flux Magnetic flux 9 Peierls Phase Approximation

11. 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

12. 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

13. 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

14. 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 E1E1 E2E2 E3E3 E4E4 E5E5 13

15. 28 August 2012 Controlling ac transport in carbon-based... AC gate in graphene zigzag nanoribbon V ac = 0 ac frequency Regular energy level spacing only at high energy ranges NO Quantum Wagon-Wheel effect in zigzag-edge 14

16. 28 August 2012 Controlling ac transport in carbon-based... AC gate in graphene zigzag nanoribbon (a) DC regime(b) ”Supression” (c) Partial recovery of DC state 15

17. 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)

18. 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)

19. 28 August 2012 Controlling ac transport in carbon-based... 18 Applications: quantum pumping devices

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24. 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  

25. 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

26. 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)