Graphene electronics

Transcription

1 Graphene electronics Alberto Morpurgo Main collaborators J. Oostinga, H. Heersche, P. Jarillo Herrero, S. Russo, M. Craciun, L. Vandersypen, S. Tarucha, R. Danneau, P. Hakkonen

2 A simple tight-binding H Two inequivalent C atoms = t A B + δ δ i, j R R B A + R + R i i j i Solutions are plane waves i ( ) ( ) ikri ikri ψ k >= α k e A + β k e B 0> Ri Rj i i OR αk A ikr Ri ψ i k >= e 0 > i βk B Rj pseudo spin

3 Band-structure H ψ >= E( k) ψ > Fermi surface: six discrete points H ψ >= E( k) ψ > E > 0 solutions conduction band Zero gap semi-metal Fermi energy: at the Dirac points E < 0 solutions conduction band

4 Conduction at the charge neutrality point Fermi energy can be tuned with a gate electrode 200 Rn Delft data 150 R (Ω) Vg (V) Resistance remains finite when E F is at the Dirac point Metal or Insulator?

5 Effective hamiltonian near one K-point H ψ >= E( q) ψ > with q = K + k q v F q Long wavelength limit (small k ) Δ kx iky αk αk E( k) kx iky = + Δ βk βk Δ=0 E( k) =± v k F Δ 0 Ek v k 2 ( ) =± Δ + F ( ) 2 Gapless = zero mass Dirac fermions Gap open = Chiral fermions with mass

6 H ( k + ik ) Gap in biased bilayers ( k ik ) x y = α 2 x Δ y Δ 2 McCann & Falko 2006 Low-energy effective Hamiltonian Same potential Different potential Δ=0 Δ 0

7 Device Fabrication Room-Temperature Mobility: cm 2 /Vs 10 x Silicon Graphite Micromechanical cleaving AFM Find flakes Attach Contacts

8 Multi-layered flakes Graphene: different thickness Recognition: under optical microscope Devices: single- bi- tri-layer

9 Double-gated devices

10 Double-gated graphene devices We will compare single and double layer In bilayer double gate needed to Create difference in electrostatic potential between layers Maintain the layer at the charge neutrality point (keep E F in the gap)

11 Single-layer devices: gate-voltage dependence Fixed top-gate voltage Fixed back-gate voltage Dirac peak shifts with voltage applied to second gate, but peak height does not change

12 Single-layer devices: temperature dependence Unbiased Asymmetrically biased No temperature dependence irrespective of gate voltage configuration

13 Bilayer devices: gate-voltage dependence Fixed top-gate voltage Fixed back-gate voltage Dirac peak shift with voltage applied to second gate and peak height increases for oppositely biased gates

14 Bilayer devices: temperature dependence Unbiased gates : No temperature dependence Oppositely biased gates: appearance of tempereture dependence

15 Bilayer at millikelvin Gate-voltage dependence Temperature dependence Oppositely biased gates 3 orders of magnitude increase in R with lowering T Unbiased gates No temperature dependence

16 I-V Characteristics Evolution of I-V curves: Non-linearity appears for oppositely biased top and bottom gates Charge neutrality line Non linearity expected for gapped material

17 Gap determined directly by optical spectroscopy: much larger than estimates from transport

18 +V Gate electrode Gate insulator Topological confinement +V with I. Martin and Ya. M. Blanter -theory Lateral confinement in Bilayer graphene +V -V -V -V -V +V Normal confinement Topological confinement Chiral zero modes

19 Double-gated trilayer graphene

20 Trilayer in perpendicular E-field Height of resistance peak decreases with perpendicular E-field

21 Tri-layer vs Bi-layer Tri-layer Bi-layer Trilayer different from - bi-layer: resistance increases with E-field - single-layer: resistance constant with E-field Trilayer is a semimetal with a gate tunable band overlap

22 Zero-energy evanescent states in graphene sinle-layers

23 Conduction at the charge neutrality point 200 Rn What happens here? 150 R (Ω) Vg (V) Fermi energy can be tuned with a gate electrode Resistance remains finite when E F is at the Dirac point Metal or Insulator?

24 How does the charge neutrality point looks? Scanning potentiometry Charge Density Map: Spread in charge density At charge neutrality: Network of pn junctions Yacoby group 2007

25 Evanescent states at the Dirac point y v F 0 k ik α x y α k E( k) k kx iky 0 = + βk βk at E=0 ( ) = 0 i β x y k Solution κ x ik y e e y x Barrier along x due to kinetic energy along y W/L >> 1 - Otherwise result depends on boundary conditions

26 Predictions for ballistic motion At the Dirac point Conductivity = 4e 2 /πh Shot-noise: Fano factor = 1/3 Away from Dirac point Fano factor decreases with increasing carrier density Tworzydlo et al 2006

27 Ballistic motion indeed! Contact separation = nm; W/L = 3, 10, 24 (three samples) Conductivity Fano Factor Consistent with ballistic evanescent states Gate voltage dependence: scale larger than simple theory

28 Main results Gate tunable-band gap and insulating state in bilayer graphene Predition of topological confinement in bilayer graphene Evanescent states and ballistic transport at small length scales