Spin and Charge transport in Ferromagnetic Graphene

Transcription

1 Spin and Charge transport in Ferromagnetic Graphene Hosein Cheraghchi School of Physics, Damghan University Recent Progress in D Systems, Oct, 4, IPM

2 Outline: Graphene Spintronics Background on graphene : monolayer, bilayer and nanoribbons Magnetoresistance and spin polarization in ferromagnteic bilayer graphene : Spin transport through bilayer graphene nanoribbons : Introduction on Pure spin and charge non-adiabatic pumping through ferromagnetic graphene nanoribbons Conclusion

3 Spectrum of Monolayer Graphene ) 3 ( ) 3 ( 4 ) 3 ( 4 ) ( a k Cos a k Cos a k Cos t k E x y y ) ( ) ( O k k v k E F Empty-antibonding Occupied-bonding

4 Bilayer Graphene: the Tight Binding model 4 3 B B A A B A B A B A B A H H H H H H B A Dimer sites:b-a Non-Dimer sites:a-b B E. Mccann, et al. 3 Rep. Prog. Phys

5 Effective 4-band Hamiltonian at low energy / 3 & / 3 / 3 &, a v a v a v ip p y x 4 Neglecting Mexican hat structure M. Mucha-Kruczynski M, et al. Semicond. Sci. Technol, 5,33

6 Tunable Band gap in Bilayer Graphene [Y. Zhang, et al, Nature, 9]

7 Graphene nanoribbon: Chemical Method [X. Li et al., Science 39, 9 (8)]

8 Graphene nanoribbon : Unzipping Carbon nanotubes [Jiao, et al. Nature, 458, 877 (9)]

9 Proximity induced spin polarization in graphene Spin transport in MLG Giant Rashba Splitting in Graphene with Au [D. Marchenko et al, Nature 3 3 ]

10 Possible mechanisms of the emergence of magnetism in graphene Point defect-induced magntisms in graphene Yazyev O V and Helm L 7 Phys. Rev. B ZGNR and finite fragments of graphene Coulomb Interaction and doping: 5 Phys. Rev.B By applying an external electric field in the transverse direction in nanoribbons: Son Y W, Cohen M L and Louie S G 6 Nature PRL,, 66 (3)

11 Spin transport in proximity of FM insulators on graphene The exchange splitting induced by the FM insulator Euo in graphene was estimated to be of the order of 5 mev. [H. Haugen, et al,phy. Rev. B. 77, 546 (8)] The exchange energy for a graphene electron interacting with the nearest stratum of magnetic ions is estimated as 5-65 mev. [Y. G. Semenov et al, Phys. Rev. B. 77, 3545 (8)]

12 Transport through ferromagnetic graphene V V t V t V H t t [H. Cheraghchi, F. Adinehvand, JPCM, 4, 4533 ()] Local Magnetoresistance measurements

13 Four band Tunneling If we assume plane wave for the Schroedinger equation, the wave function in each region is written as: x i x i x i x i A B B A e e e e M h g h g h g h g h h h h f f f f G D C B A GM ) ( ) ( () ) ( 3 3 w G M w G M G M G M N ] / [ t T N N N N t NA 3 A Continuity of wave function at the boundaries:

14 Transmission through bilayer nanojunction W= 4 nm V= 5 mev ε εt ky ε εt E V v F

15 Spin polarization in parallel configuration Parallel Configuration G( E) G / T( E, )cos( ) / d [H. Cheraghchi, F. Adinehvand, JPCM, 4, 4533 ()]

16 Magnetoresistance in bilayer graphene mev w 4nm V 5meV E 4meV

17 Spin polarized transport in ferromagnetic gated bilayer ZGNR Parallel and anti-parallel configuration Band structure +M +M +M Parallel -M Anti-Parallel [V. Derakhshan, H. Cheraghchi, JMMM, 357, 9 (4)]

18 Landauer Formalism: Tight-binding Green s function approach M=.5t

19 Conductance in Parallel and Anti-Parallel Configurations Left Central part Right Left Central part Right

20 Electrical Control of Spin Polarization and Magnetoresistance Spin polarization for parallel configuration a) V= b) V=. t a) b) Full Magnetoresistance Complete spin polarized regions [V. Derakhshan, H. Cheraghchi, JMMM, 357, 9 (4)]

21 Quantum pumping:adiabatic and non-adiabatic regimes Quantum Pumps Two time scales: Quantum pump is a mesoscopic device generating dc current in response to a local and periodic in time perturbation in the absence of any dc/ac bias Classical Pumps ) electronic traversal time through the sample ) the period of the time-periodic potential - Adiabatic Regime: D T T D P. Brouwer, PRB Non-adiabatic Regime: D T Exact Description by Floquet Theorem Driving fast h f Single Parameter Pumping

22 Experimental Realization: Quantum Pump through GaAs open quantum dot [M. Switkes, et al. Science 83, 95 (999)] A=mV A=6mV I dc ~ sin Pure Quantum Spin Pump f=mhz [S. K. Watson, et al, 9, 583 (3)]

23 Quantum Pumping in Graphene induced by Klein Tunneling Single Paramtere Pumping in Graphene [E. Prada, et al, Phys. Rev. B. 8, 4544 (9) ] [P. San-Jose, et al, Phys. Rev. B () ]

24 Floquet Formalism of Quantum Pumping Floquet Theory Spatially Periodic Systems Time periodic Hamiltonian Bloch Theorem quasi-momenta associated with Block functions Floquet Theorem quasi-energy associated with Floquet states Hˆ ( t) Hˆ ( t T), ( Hˆ ( x, t) i ) ( x, t) t Note: Energy is not conserved. There is a complete set of solutions as: Floquet State ( x, t) ( x, t ( x, t) exp( i t ) ( x, t) T) quasi-energies

25 Floquet Space H F ( x, t) ( x, t) ( x, t) The same as time-independent Schroedinger equation Floquet Hamiltonian H F ( x, t) H( x, t) i t n=+ n=+ n= n=- n=- Hilbert Space Floquet or Sambe Space:, space and time R T n n e in t First Brillouin Zone Time-independent Replica Picture

26 Averaged Current I T T I( t) dt e h n [ T n LR ( ) f L ( ) T n RL ( ) f R ( )] d Introduction to Graphene-Based Nanomaterials, L. E. F. Foa Torres, et al, ISBN , Cambridge University Press (4) ( R, n),( L,) n n Transmission Probability: r ( ) 4 ( ) T G ( ) F Floquet Green s Function: G r F ( ) ( H F ) T T When? e At Zero temperature, I h n n T ( ) [ T ( ) T ( )] Pump n LR RL E F Spatial Asymmetry T Pump ( ) d OR DOS( E) lim Dynamical breaking of a time reversal symmetry Im[ i { r G F } n ii ]

27 Graphene nanoribbons as quantum pump V g t I V ac in adiabatic regime

28 Level Spacing and driven frequency Competition between level spacing and driven frequency determines the pumped current. At VHs, there is small level spacing so with a small driven frequency we have large pumped current. For one dimensional example: 3

29 Pure Spin and Charge Pumping I C =I S I C = I C =-I S I, I = I =- I I =, I 3 4 ZGNR(6,4) ZGNR(,4) at low frequencies E=, V=.

30 Pumped Current in terms of Fermi energy

31 Conclusion Weak spin-orbit and long spin flip length in Graphene is promising spintronic applications based on graphene. Spin polarization can be controlled by application of prependicular electric field in bilayer graphene (infinite sheets and also nanoribbons). Spin polarization in bilayer graphene sheets emerges at evanescent modes. Pure spin and charge pumping is achievable in Graphene nanoribbons by using an electrical control over driven frequency.

32 Acknowledges Collaborators: F. Adinehvand (PhD Student, Damghan University) V. Derakhshan (PhD Student, Damghan University) F. Pasha (M.Sc Student, Damghan University) With Special Thanks: Dr. R. Asgari (IPM, Tehran) Dr. L. E. Foa Torres (UNC, Argentina) THANK YOU FOR THE ATTENTION

33 Gigahertz quantized charge pumping in graphene quantum dot [M. R. Connolly et al, Nature Nanotechnology, 8, 4 (3)]

34 At zero phase lag there is still nonzero current [B. Wang, et al. PRB, 65, 7336 ()]

35 Energy Gap in Graphene Nanoribbons E g / N a Based on tight-binding approximation, AGNRs are metal if N=3p+, while it is semiconductor if N=3p,3p+. The energy gap appeared in armchair ribbons is induced by the quantum confinement of graphene strips and also edge effects. Moreover, in this approach, zigzag edge ribbons are metal regardless of their Widths. The first principles calculations, however, show that both armchair and zigzag GNRs have a direct band gap. Band gap of ZGNR arises from a potential induced by spin ordered states at the edges. PRL,97,683(6)