Pter Makk http://nanoelectronics.physics.bme.hu/ Nanoelectronics - - PowerPoint PPT Presentation

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Pter Makk http://nanoelectronics.physics.bme.hu/ Nanoelectronics - - PowerPoint PPT Presentation

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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 -

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Péter Makk

Interference in high quality graphene based van der Waals heterostructures

http://nanoelectronics.physics.bme.hu/

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

Nanoelectronics lab

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Quantum dots, topological superconductivity 2D materials, spintronics Circuit QED, FMR, qubits

Research interest

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Facilities

Ultra low T measurements, nanofabrication (with MFA)

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5

K valley K’ valley

Castro Neto et al., Rev. Mod. Phys.. 81, 109 (2009)

Properties of graphene

Honeycomb lattice with two atom basis At the Fermi energy the spectrum is linear Dirac fermions Two non-equivalent valleys

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

Properties of graphene

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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

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SLIDE 8

Graphite Scotch tape SiO2 chip Graphene

Novoselov et.al., Nature 438, 197 (2005)

Fabrication of graphene samples

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Fabrication of graphene samples

Suspended devices

  • Can have ultra-low residual disorder
  • Fragile, have to be current annealed

Encapsulated devices

  • More flexible fabrication is possible
  • Less fragile
  • R. Maurand, PM. et al., Carbon 79, 486 (2014)
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SLIDE 10

Tombros et al. J. Appl. Phys. 109, 093702 (2011)

  • R. Maurand, P. Rickhaus, P. Makk, et. al, Carbon 79, 486 (2014).

Fabrication of suspended samples

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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

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SLIDE 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

pnp - junction pn -junction

Wang et al., Science 342, 614 (2013); Zomer et al., APL 105, 013101 (2014)

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Lengthscales Lspin Lφ Le LBohr

ballistic diffusive non coherent, diffusive spin-conserving non- spin-conserving coherent

Lspin Lφ Le LBohr

L

L >> lm diffusive motion, L << lm ballistic motion 1

t

2

t

) / exp( ) cos( 2

L 2 1 2 2 2 1 total 

        t t t t T

Coherence length

 

 D l 

L<< l phase coherent

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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

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SLIDE 15

p Hole doping n Electron doping

Gapless pn interfaces

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Positive interference: For graphene:

Fabry-Perot interferences

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  • P. Rickhaus, R. Maurand, M.H. Liu et al. Nature Comm. 4, 2342 (2013)

FABRY-PÉROT

Graphene flake 2x2mm pn nn pp np

Fabry-Perot interferences in p-n junctions

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SLIDE 18
  • P. Rickhaus, R. Maurand, M.H. Liu et al. Nature Comm. 4, 2342 (2013)

FABRY-PÉROT

DG/G: 1% DG/G: 5%

Fabry-Perot interferences in p-n junctions

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SLIDE 19

FABRY-PÉROT

Why are the bipolar

  • scillations better

visible?

Similar work:

  • A. L. Grushina, et. al., APL 102, 223102 (2013)

Bias spectroscopy (particle in a box)

Fabry-Perot interferences in p-n junctions

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FABRY-PÉROT

sharp smooth

The strong collimation at the smooth p-n interface increases the visibility

Cheianov, V. & Fal’ko, V. PRB 74, 041403 (2006)

Smooth: kFd>>1 Sharp: kFd <<1

Fabry-Perot interferences in p-n junctions

i c p p n

  • P. Rickhaus, P.M., et al., APL. 107, 251901 (2015)
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SLIDE 21

FABRY-PÉROT

Sharp interfaces DG/G: 1% Sharp/smooth interface DG/G: 4 % Smooth interfaces DG/G: 12%

n - n’ - n n - p’ - n p - n - p p- p’ - p

Fabry-Perot interferences in p-n-p junctions

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SLIDE 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)

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Ballistic transport in pn junctions

FP oscillations appear in other quantities

  • Thermopower (Seebeck coefficient)
  • Supercurrent etc. (oscillation in RN)?

Seebeck (a.u.) 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)
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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

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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)

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Quantum Hall

Landau levels forming in the bulk At the edges Quantum Hall channels conduct current. At high magnetic field Landau levels form Special band-structure of graphene: Landau level at zero energy

  • E. Andrei et al., Rep. Prog.

Phys, 75 056501 (2012)

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Quantum Hall

18 14 10 6 2 G0 (e

2/h)

30 20 10 VBG (V)

8 6 4 2 B (T)

30 20 10

  • 10
  • 20
  • 30

VBG (V) 8 6 4 2 B (T)

  • 40
  • 20

20 40 Gdiff (e

2/h)

G_xy

Conductance plateaus at ...,-6,-2,2,6,... e2/h, when Ef is between LLs

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Quantum Hall p-n junctions

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

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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 )
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Edge-state Aharonov-Bohm interference

High magnetic field – Aharonov Bohm oscillations

Loss of phase coherence

  • P. M., et al., PRB. 98, 035413 (2018)
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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

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SLIDE 32

Graphene superlattices

32

Θ>>0° Θ>0° Θ=0°

  • A. Geim et al., Nat. Materials 6, 183 (2007)
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SLIDE 33

FP oscillations in a superlattices

Peierls distortion

Wikipedia

New unit cell leads to band distortion

  • J. Wallbank et al., PRB 87, 245408 (2013)
  • C. Dean et al., Nature 497, 598(2013)

Satellite Dirac-peaks

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SLIDE 34

FP oscillations in a superlattices

Semi-transparent interface is defined by: not present main DP

  • sat. DP (EF>0)
  • sat. DP (EF<0)

Ef

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Supercurrent

Cooper pair Andreev pair

Andreev reflections: supercurrent induced through the graphene DC Josephson effect (dissapationeless current from phase difference): 𝐽 = 𝐽𝐷 f(𝜚𝑀 − 𝜚𝑆)

Critical current

𝑱𝒅

0.6 0.4 0.2 0.0 dV/dI (k

  • 400

400 I (nA)

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Supercurrent in superlattice

  • The Andreev pairs decay

with time → 𝑺𝒐𝑱𝒅 ∝ ℏ

𝝊 , with τ the

traversal time

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Supercurrent in superlattice

1 Ic / Ic,max

  • 4
  • 2

2 4 B (mT) 1 Ic / Ic,max

  • 4
  • 2

2 4 B (mT)

Supercurrent distributions: Interference experiment: apply out-of plane magnetic field

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Supercurrent in superlattice

Origin?

  • Topological origin?
  • Chemical doping

Measurement shows more edge current close to the van Hove singularity points (flat bands, small velocity)

  • D. Indolese, R. Delagrange, P.M., Phys. Rev. Lett. 121, 137701 (2018)
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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

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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)

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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 2π rotation) 

0.6 0.4 0.2 0.0 D (e

2/h) - D40K (e 2/h)

  • 100
  • 50

50 100 Bz (mT) 1.8 K

  • 0.5 V < VBG < 4.5 V
  • 0.14
  • 0.12
  • 0.10
  • 0.08
  • 0.06
  • 0.04
  • 0.02

0.00 D0.25 K - D30 K (e

2/h)

  • 20
  • 10

10 Bz (mT) 0.25 K

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Weak-antilocalization in G/WSe2

graphene hBN WSe2 High quality devices: investigation of SO timescales From fitting procedure

McCann and Fal’ko, PRL 108, 166606 (2012)

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Weak-antilocalization in G/WSe2

Doping dependence allows the identification of relaxation mechanism and relevant spin

  • rbit term

Valley Zeeman term

  • S. Zihlmann, ...,P.M., PRB 97, 045411 (2018)

Martin Gmitra: University of Regensburg Aron Cummings and Jose. H Garcia: ICN2, Barcelona

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Summary

  • K. Zimmermann et al., Nat. Comm. 8,14983 (2017)
  • M. Eich et al., arXiv:1803.02923
  • Y. Cao et al., Nature 556, 43 (2018)
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SLIDE 45

Acknowledgement

  • P. Rickhaus
  • C. Handschin
  • C. Schönenberger

GrapheneMan

Ming-Hao Liu

UNIVERSITÄT REGENSBURG

  • S. Zihlmann
  • D. Indolese

L .Wang

  • R. Delagrange
  • Cs. Szabolcs
  • F. Bálint

K.K. Zoltán

  • K. Máté
  • Sz. Bálint
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Acknowledgement

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Thank you for your attention.