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Interference in high quality graphene based van der Waals heterostructures Pter Makk http://nanoelectronics.physics.bme.hu/ Nanoelectronics lab Budapest University of Technology and Ecomics - Dept. of Physics Nanoelectronics Group -

  1. Interference in high quality graphene based van der Waals heterostructures Péter Makk http://nanoelectronics.physics.bme.hu/

  2. Nanoelectronics lab Budapest University of Technology and Ecomics - Dept. of Physics Nanoelectronics Group - together with Szabolcs Csonka nanoelectronics.physics.bme.hu

  3. Research interest Quantum dots, topological 2D materials, spintronics superconductivity Circuit QED, FMR, qubits

  4. Facilities Ultra low T measurements, nanofabrication (with MFA)

  5. Properties of graphene K valley K’ valley Castro Neto et al. , Rev. Mod. Phys.. 81 , 109 (2009) Honeycomb lattice with two atom basis At the Fermi energy the spectrum is linear  Dirac fermions Two non-equivalent valleys 5

  6. Properties of graphene 2-dimensional Tunable and flexible Gapless p-n interface Properties tuned by van der Massless “relativistic” Combining ballistic transport Waals stacking: particles with superconductivity, SOI or exchange, etc. Defect-free lattice ferromagnets, mechanical vibrations, photons

  7. Outline • Fabrication of high quality samples • Fabry-Perot Interferences in pn- junctions • Aharonov-Bohm interferometers • Fabry-Perot and supercurrent interference for superlattices • Interference in diffusive samples – weak localization experiment to probe spin-orbit interaction

  8. Fabrication of graphene samples Graphite Scotch tape SiO 2 chip Graphene Novoselov et.al ., Nature 438, 197 (2005)

  9. Fabrication of graphene samples Suspended devices Encapsulated devices • Can have ultra-low residual disorder • More flexible fabrication is possible • Fragile, have to be current annealed • Less fragile R. Maurand, PM . et al., Carbon 79, 486 (2014)

  10. Fabrication of suspended samples Tombros et al. J. Appl. Phys. 109, 093702 (2011) R. Maurand, P. Rickhaus, P. Makk, et. al, Carbon 79, 486 (2014).

  11. Fabrication of encapsulated samples Fabrication of encapsulated devices • encapsulation in hBN using van der Waals pickup • AFM to characterize the stack • e-beam lithography and evaporation • bonding and measurements at low temperature

  12. Fabrication of encapsulated samples Fabrication of encapsulated devices • 1D side contacts to access the stack • shaping using plasma etching • fabrication of top-gates using addition steps • pre-patterned graphite bottomgates pn -junction Wang et al. , Science 342 , 614 (2013); Zomer et al. , APL 105 , 013101 (2014) pnp - junction

  13. Lengthscales         2 2 total t T t t 2 t t cos( ) exp( / )  1 1 2 1 2 L l   L D   t 2 Coherence length L<< l  phase coherent L >> l m diffusive motion, L << l m ballistic motion spin-conserving non- spin-conserving ballistic diffusive L Bohr L e L φ L spin non coherent, coherent diffusive L spin L φ L Bohr L e

  14. Outline • Fabrication of high quality samples • Fabry-Perot Interferences in pn- junctions • Aharonov-Bohm interferometers • Fabry-Perot and supercurrent interference for superlattices • Interference in diffusive samples – weak localization experiment to probe spin-orbit interaction

  15. Gapless pn interfaces p n Hole Electron doping doping

  16. Fabry-Perot interferences Positive interference: For graphene:

  17. Fabry-Perot interferences in p-n junctions F ABRY -P ÉROT Graphene flake 2x2 m m pn nn np pp P. Rickhaus, R. Maurand, M.H. Liu et al. Nature Comm. 4, 2342 (2013)

  18. Fabry-Perot interferences in p-n junctions F ABRY -P ÉROT D G/G: 1% D G/G: 5% P. Rickhaus, R. Maurand, M.H. Liu et al. Nature Comm. 4, 2342 (2013)

  19. Fabry-Perot interferences in p-n junctions F ABRY -P ÉROT Why are the bipolar oscillations better visible? Bias spectroscopy (particle in a box) Similar work: A. L. Grushina, et. al., APL 102, 223102 (2013)

  20. Fabry-Perot interferences in p-n junctions F ABRY -P ÉROT sharp smooth The strong collimation at the smooth p-n interface increases the visibility Smooth : k F d>>1 Sharp : k F d <<1 i p n c p P. Rickhaus, P.M., et al., APL. 107, 251901 (2015) Cheianov, V. & Fal’ko , V. PRB 74, 041403 (2006)

  21. Fabry-Perot interferences in p-n-p junctions F ABRY -P ÉROT Sharp interfaces D G/G: 1% p - n - p n - n’ - n Sharp/smooth interface D G/G: 4 % n - p’ - n p- p’ - p Smooth interfaces D G/G: 12%

  22. Ballistic transport in pnp junctions Ballistic transport in pn – junctions (B=0) Fabry Perot interferences signal ballistic transport C. Handschin, P.M . et al., Nano Lett., 17, 328 (2017)

  23. Ballistic transport in pn junctions Seebeck (a.u.) FP oscillations appear in other quantities - Thermopower (Seebeck coefficient) - Supercurrent etc. (oscillation in R N )? In SC junctions: V. E. Calado et al., Nat. Nano. 10, 761 (2015) M. Ben Shalom et al., Nat. Phys. (2015) M. T. Allen et al., Nat. Phys 12, 128 (2016) R. Kraft et al., Nature Commun. 9, 1722 (2018)

  24. Outline • Fabrication of high quality samples • Fabry-Perot Interferences in pn- junctions • Aharonov-Bohm interferometers • Fabry-Perot and supercurrent interference for superlattices • Interference in diffusive samples – weak localization experiment to probe spin-orbit interaction

  25. Ballistic transport in pn junctions Low magnetic field – Snake states P. M. , et al., PRB. 98, 035413 (2018) and P. Rickhaus, P.M. et al. Nature Comm. 6, 6470 (2015)

  26. Quantum Hall E. Andrei et al., Rep. Prog. Phys, 75 056501 (2012) At high magnetic field Landau levels form Special band-structure of graphene: Landau level at zero energy Landau levels forming in the bulk At the edges Quantum Hall channels conduct current .

  27. Quantum Hall 30 G_xy 2 /h) G diff (e 20 40 10 20 V BG (V) 0 0 -10 -20 -20 -40 -30 0 2 4 6 8 B (T) 18 8 14 6 2 /h) B (T) 4 G 0 (e 10 Conductance plateaus at ...,-6,-2,2,6,... e 2 /h, when E f is between LLs 2 6 0 2 0 10 20 30 V BG (V)

  28. Quantum Hall p-n junctions Junctions formed using local gates In n- n’ or p -n junctions Quantum Hall channels flow in the bulk Where bands meet E f , quantum channels form in the bulk

  29. Edge-state Aharonov-Bohm interference High magnetic field – Aharonov Bohm oscillations Morikawa et al. , APL 106 , 183101 (2015) Wei et al. , Science Adv. 3 , 8 (2017) Different than usual Aharonov-Bohm: Interferometer size changes P. M. , et al., PRB. 98, 035413 (2018) and C. Handschin, P.M. et al., Nano Lett. 17,5389 (2017 )

  30. Edge-state Aharonov-Bohm interference High magnetic field – Aharonov Bohm oscillations Loss of phase coherence P. M. , et al., PRB. 98, 035413 (2018)

  31. Outline • Fabrication of high quality samples • Fabry-Perot Interferences in pn- junctions • Aharonov-Bohm interferometers • Fabry-Perot and supercurrent interference for superlattices • Interference in diffusive samples – weak localization experiment to probe spin-orbit interaction

  32. Graphene superlattices Θ >0° Θ =0° Θ >>0° A. Geim et al. , Nat. Materials 6 , 183 (2007) 32

  33. FP oscillations in a superlattices Peierls distortion New unit cell leads to band distortion Wikipedia Satellite Dirac-peaks C. Dean et al. , Nature 497 , 598(2013) J. Wallbank et al. , PRB 87 , 245408 (2013)

  34. FP oscillations in a superlattices Semi-transparent interface is defined by: E f not present main DP sat. DP (E F >0) sat. DP (E F <0)

  35. Supercurrent Cooper pair Andreev pair Andreev reflections: supercurrent induced through the graphene 0.6 DC Josephson effect (dissapationeless current dV/dI (k  0.4 from phase difference): 0.2 𝐽 = 𝐽 𝐷 f(𝜚 𝑀 − 𝜚 𝑆 ) 0.0 Critical current -400 0 400 𝑱 𝒅 I (nA)

  36. Supercurrent in superlattice • The Andreev pairs decay with time → 𝑺 𝒐 𝑱 𝒅 ∝ ℏ 𝝊 , with τ the traversal time

  37. Supercurrent in superlattice 1 I c / I c,max I c / I c,max 1 0 0 -4 -2 0 2 4 -4 -2 0 2 4 B (mT) B (mT) Supercurrent distributions: Interference experiment: apply out-of plane magnetic field

  38. Supercurrent in superlattice Measurement shows more edge current close to the van Hove singularity points (flat bands, small velocity) Origin? - Topological origin? - Chemical doping D. Indolese, R. Delagrange, P.M. , Phys. Rev. Lett. 121, 137701 (2018)

  39. Outline • Fabrication of high quality samples • Fabry-Perot Interferences in pn- junctions • Aharonov-Bohm interferometers • Fabry-Perot and supercurrent interference for superlattices • Interference in diffusive samples – weak localization experiment to probe spin-orbit interaction

  40. Graphene for spintronics Ideal material for spintronics : long spin lifetime – but no spin orbit Control with electric field? Topological states? Spin-orbit can be engineered using van der Waals heterostructures (e.g. WSe2)

  41. Weak-antilocalization Large samples – diffusive but phase coherent: Weak localization • Coherent wave function leads to interference effects • No SOC, B = 0  • SOC leads to random walk on Block sphere (on average 2 π rotation)  0.00 -0.02 2 /h) -0.04 D 0.25 K - D 30 K (e 2 /h) -0.06 0.6 2 /h) - D 40K (e -0.08 0.25 K 0.4 -0.10 -0.12 0.2 D (e -0.5 V < V BG < 4.5 V -0.14 1.8 K 0.0 -20 -10 0 10 -100 -50 0 50 100 B z (mT) B z (mT)

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