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Extreme Straintronics of Graphene
2DCC-MIP Webinar29 January, 2019
Riju BanerjeePenn State
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January 29, 2019 2DCC-MIP Webinar
Berry, Mat. Today (2016)
New questions in FlatlandOne of the most fundamental properties of matter:How it deforms under stress
2004: Discovery of graphene -How are deformations of atom thick materials different from bulk?
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January 29, 2019 2DCC-MIP Webinar
• Graphene sustains strains >20%, while silicon breaks at 1.5%. How do materials deform under such extreme strains?
me-mechanicalengineering.com
New questions in FlatlandOne of the most fundamental properties of matter:How it deforms under stress
2004: Discovery of graphene -How are deformations of atom thick materials different from bulk?
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January 29, 2019 2DCC-MIP Webinar
• Graphene sustains strains >20%, while silicon breaks at 1.5%. How do materials deform under such extreme strains?
• Large Deformations also affect the electronic properties endowing certain versatility. Engineer novel electronic properties under extreme strain?
Castro Neto et. al., RMP (2009)
Modify??
New questions in FlatlandOne of the most fundamental properties of matter:How it deforms under stress
2004: Discovery of graphene -How are deformations of atom thick materials different from bulk?
![Page 5: Extreme Straintronics of Graphene · 1/29/2019 · Graphene sustains strains >20%, while silicon breaks at 1.5%. How do materials deform under such extreme strains? • Large Deformations](https://reader035.vdocuments.site/reader035/viewer/2022062605/5fd854285c2f1d7bce7a4722/html5/thumbnails/5.jpg)
January 29, 2019 2DCC-MIP Webinar
• Graphene sustains strains >20%, while silicon breaks at 1.5%. How do materials deform under such extreme strains?
• Large Deformations also affect the electronic properties endowing certain versatility. Engineer novel electronic properties under extreme strain?
• How are ripples in a lattice different from those in a continuous fabric?
me-mechanicalengineering.com
New questions in FlatlandOne of the most fundamental properties of matter:How it deforms under stress
2004: Discovery of graphene -How are deformations of atom thick materials different from bulk?
![Page 6: Extreme Straintronics of Graphene · 1/29/2019 · Graphene sustains strains >20%, while silicon breaks at 1.5%. How do materials deform under such extreme strains? • Large Deformations](https://reader035.vdocuments.site/reader035/viewer/2022062605/5fd854285c2f1d7bce7a4722/html5/thumbnails/6.jpg)
January 29, 2019 2DCC-MIP Webinar
• Graphene sustains strains >20%, while silicon breaks at 1.5%. How do materials deform under such extreme strains?
• Large Deformations also affect the electronic properties endowing certain versatility. Engineer novel electronic properties under extreme strain?
• How are ripples in a lattice different from those in a continuous fabric?
me-mechanicalengineering.com
New questions in FlatlandOne of the most fundamental properties of matter:How it deforms under stress
2004: Discovery of graphene -How are deformations of atom thick materials different from bulk?
Take graphene, apply extreme strain and vary it at the
nanoscale and probe effects
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Traditional method of straining
January 29, 2019 2DCC-MIP WebinarPamela C. Burnley
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Traditional method of straining
January 29, 2019 2DCC-MIP WebinarPamela C. Burnley
Difficult for atom thick materials
Cannot measure/probe resulting deformations and other physical properties down to atomic scale
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Engineering nanoscale ripples in suspended graphene
January 29, 2019 2DCC-MIP Webinar
Grow graphene on Copper Substrate with Step Edges
Step Edges
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Preferred tool – Scanning tunneling microscopy
January 29, 2019 2DCC-MIP Webinar
Try to maintain constant current while scanning
𝐼𝐼 ∝ 𝑒𝑒−𝜅𝜅𝑧𝑧
Å change in z gives order of magnitude change in 𝐼𝐼
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Scanning tunneling microscope
January 29, 2019 2DCC-MIP Webinar
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Scanning tunneling microscope
January 29, 2019 2DCC-MIP Webinar
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What does a STM ‘see’?
January 29, 2019 2DCC-MIP Webinar
Measures current 𝐼𝐼 ∝ local electron density
Sharp tip sensitive to electron density at sub-Angstrom length scale
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What does a STM ‘see’?
January 29, 2019 2DCC-MIP Webinar
Measures current 𝐼𝐼 ∝ local electron density
Sharp tip sensitive to electron density at sub-Angstrom length scale
Maps out topographic features by running a feedback loop on current
Record how z needs to change to keep 𝐼𝐼 constant
Z-he
ight
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What does a STM ‘see’?
January 29, 2019 2DCC-MIP Webinar
Measures current 𝐼𝐼 ∝ local electron density
Sharp tip sensitive to electron density at sub-Angstrom length scale
Maps out topographic features by running a feedback loop on current
Record how z needs to change to keep 𝐼𝐼 constant
Z-he
ight
Pristine Graphene lattice
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What does a STM ‘see’?
January 29, 2019 2DCC-MIP Webinar
Measures current 𝐼𝐼 ∝ local electron density
Sharp tip sensitive to electron density at sub-Angstrom length scale
Maps out topographic features by running a feedback loop on current
Record how z needs to change to keep 𝐼𝐼 constant
Z-he
ight
Dirac cone
Pristine Graphene lattice
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January 29, 2019 2DCC-MIP Webinar
Mechanical properties
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Studying nanoscale deformations by STM
January 29, 2019 2DCC-MIP Webinar
Levy, et. al Science (2010) Xu, et. al Nano. Lett (2010)Yeh, et. al Surf.Sci. (2011)
Bao, et. al Nat.Nano. (2009) Tapaszto, et. al Nat. Phys. (2012)Zhu, et. al PRB (2014)
• Experimental Nanoscale Strain Manipulation still in its Infancy
• Engineering at nm scale is hard and Wrinkling is inherently somewhat messy
• Ideally : On a suspended sheet, vary, measure and relate wavelength λ, Amplitude, Curvature – This Talk!
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Sculpting atomic step edges
January 29, 2019 2DCC-MIP Webinar
Graphene pushes Cu to form higher step edges
Our samples grown by T.G. Nakajima, (Terrones group)
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Extreme strain measurement
January 29, 2019 2DCC-MIP Webinar
Measured strain >10%, consistent with first principle calculations
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Ripples in a classical fabric
January 29, 2019 2DCC-MIP Webinar
Ripples form due to compressive stress
Wavelength λ ~ Amplitude AWavelength λ ~ 1/Amplitude A
Direct Application Indirectly by Poisson Compression
Cerda et. al, PRL, (2003)
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Nanoscale graphene ripples – local curvature
January 29, 2019 2DCC-MIP Webinar
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Nanoscale graphene ripples – Draping angle
January 29, 2019 2DCC-MIP Webinar
Δz
Δx
Conserved draping angle
35°
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Nanoscale graphene ripples – Rippling angle
January 29, 2019 2DCC-MIP Webinar
~168°
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Nanoscale graphene ripples – Beyond classical theory
January 29, 2019 2DCC-MIP Webinar
λ
𝐿𝐿
Classically,𝐿𝐿 ∝ 𝜆𝜆2
A1B1
B2A2
Classical theory of rippling assumes thick, continuous material possible breakdown for 2D material at atomic scale?
𝐿𝐿𝐵𝐵 ≠ 4𝐿𝐿𝐴𝐴
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January 29, 2019 2DCC-MIP Webinar
Electronic properties
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Graphene electronics
January 29, 2019 2DCC-MIP Webinar
High electron mobility in graphene Attractive for making electronics
Functionalizing by dopants Van der Waals heterostructures Lateral heterostructures
Zhao et. al., Science (2011)
N dopants in graphene
Atomic Lego blocks
X-sec TEM of graphene-hBN
Haigh et. al., N. Mat. (2012)
Zhao et. al., N. Nano (2016)
MonolayerGraphene -MoS2assembly
Graphene -hBN
Levendorf et. al., Nature (2012)
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Electronics
January 29, 2019 2DCC-MIP Webinar
B ~ +10 T
B ~ -10 T
Impossible to realize with present technology !
Large fields are uniformStanford University
Non-uniform fields are weak
Kamalakar et. al., Nat. Comm. (2015)
Nanoscale variation of fields ispossible by strain engineering
Manipulate electrons by precise application of Electric and Magnetic fields – ideally down to atomic scale
Present day electronics predominantly use E fields. B fields are often non-trivial to engineer in devices
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Graphene – pseudospin and valley
January 29, 2019 2DCC-MIP Webinar
Linear dispersion near Fermi energy
2 inequivalent K points
Can be thought of as a spin
Ψ = 𝜓𝜓𝐴𝐴𝜓𝜓𝐵𝐵
= 𝑒𝑒𝑖𝑖𝑖𝑖.𝑟𝑟/ℏ
21
±𝜉𝜉 𝑒𝑒𝑖𝑖𝑖𝑖
𝜃𝜃 = 𝑡𝑡𝑡𝑡𝑡𝑡−1𝑝𝑝𝑦𝑦𝑝𝑝𝑥𝑥
𝜉𝜉 = ±1 for K,K’
Pseudospin - A new degree of freedom
Castro Neto et. al., RMP (2009)
B
A
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What does strain do? Pseudovector potentials
January 29, 2019 2DCC-MIP Webinar
KK’
Reciprocal space
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What does strain do? Pseudovector potentials
January 29, 2019 2DCC-MIP Webinar
Reciprocal space
𝐾𝐾 → 𝐾𝐾 + 𝛿𝛿𝛿𝛿𝐾𝐾′ = −𝐾𝐾 → −𝐾𝐾 − 𝛿𝛿𝛿𝛿
For K valley
𝐾𝐾 → 𝐾𝐾 + 𝛿𝛿𝛿𝛿 = 𝐾𝐾 +𝑝𝑝𝑝𝑝𝑐𝑐
For K’ valley
𝐾𝐾′ → 𝐾𝐾′ − 𝛿𝛿𝛿𝛿 = 𝐾𝐾′ −𝑝𝑝𝑝𝑝𝑐𝑐
Like generating magnetic fields of opposite directions
in K and K’ valleys!
𝑝𝑝𝑥𝑥𝑝𝑝𝑦𝑦
∝𝑢𝑢𝑥𝑥𝑥𝑥 − 𝑢𝑢𝑦𝑦𝑦𝑦2𝑢𝑢𝑥𝑥𝑦𝑦
Ando et. al., PRB (2002), Geim et. al., N. Phys (2010)
Vector potential
Pseudo vector potential from strain
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What does strain do? Pseudoscalar potentials
January 29, 2019 2DCC-MIP Webinar
Real space
𝑡𝑡𝑖𝑖𝑖𝑖𝑖𝑖 changes ⇒ 𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 changes to maintain charge neutrality
As 𝑉𝑉 ∝ 𝑒𝑒 𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒, 𝑉𝑉 changes
Ando et. al., PRB (2002)
Scalar potential
Like generating electric fields!𝑉𝑉 ∝ 𝑢𝑢𝑥𝑥𝑥𝑥 + 𝑢𝑢𝑦𝑦𝑦𝑦
Pseudo scalar potential from strain
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What does strain do? Pseudo gauge fields
January 29, 2019 2DCC-MIP Webinar
Pseudo gauge fields are created by strain gradients
𝐵𝐵 = ∇ × 𝑝𝑝 ∝ 𝜕𝜕𝑢𝑢𝐸𝐸 = −∇𝑉𝑉 ∝ 𝜕𝜕𝑢𝑢
𝑝𝑝𝑥𝑥𝑝𝑝𝑦𝑦
∝𝑢𝑢𝑥𝑥𝑥𝑥 − 𝑢𝑢𝑦𝑦𝑦𝑦2𝑢𝑢𝑥𝑥𝑦𝑦
𝑉𝑉 ∝ 𝑢𝑢𝑥𝑥𝑥𝑥 + 𝑢𝑢𝑦𝑦𝑦𝑦
Pseudo scalar potential from strainPseudo vector potential from strain
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Landau Levels from Pseudomagnetic fields
January 29, 2019 2DCC-MIP Webinar
Electrons in 2D form Landau levels under external B fields
𝐸𝐸𝑖𝑖 ∝ |𝑡𝑡|
Strain induced pseudo magnetic fields
Levy, et. al Science (2010)https://www.nist.gov/programs-projects/measuring-magneto-electronic-properties-graphene-nanometer-scale
Graphene Nanobubbles on Pt
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Manipulating electronic states
January 29, 2019 2DCC-MIP Webinar
A
B
𝐸𝐸𝑖𝑖 ∝ 𝑡𝑡
B-A
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Electronic states
January 29, 2019 2DCC-MIP Webinar
1
1223
34
45566778
89
910
1011
11
12
1213
1314
1415
1516
1617
17
18
1819
1920
2021
2122
2223
2324
2425
2526
2627
27
Drap
ed R
egio
n
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Electronic states
January 29, 2019 2DCC-MIP Webinar
LDOSAmplitudeIncreases at kinks ⇒ Strain
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2 models of graphene bending - Calculations
January 29, 2019 2DCC-MIP Webinar
Graphene bending: out of plane and curvature induced in-plane distortions
High LDOS at peaks/troughs
Low LDOS at peaks/troughs
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Pseudo electromagnetic superlattice
January 29, 2019 2DCC-MIP Webinar
Large C-C bonds
Small C-C bonds
+/- pseudo B for K/K’
-/+ pseudo B for K/K’
Pseudo E field in-plane
x
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Pseudo electromagnetic superlattice
January 29, 2019 2DCC-MIP Webinar
Large C-C bonds
Small C-C bonds
+/- pseudo B for K/K’
-/+ pseudo B for K/K’
Pseudo E field in-plane
LDOS of graphene lattice
+periodic strain
Effective 𝐵𝐵𝑚𝑚𝑚𝑚𝑥𝑥 ≈ 200 𝑇𝑇
LDOS of Unstrained graphene
lattice +
periodic E, B fields
First principle calculations
X (n
m)
X (n
m)
x
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Pseudo electromagnetic superlattice
January 29, 2019 2DCC-MIP Webinar
STRained Electromagnetic Modulated Superlattices (STREMS)
Usually superlattices require interfacing different materials
Stacked superlattice
Lateral Heterostructures
Same material modulated by strain!
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Snake states – theoretical prediction/implication
January 29, 2019 2DCC-MIP Webinar
Oroszlány et. al., PRB (2008)
Non uniform B fields create snake states
K and K’ electrons see opposite pseudomagnetic fields
Counterpropagating snake states akin to topological insulators
K
K’
Settnes et. al., PRL (2016)
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Summary
January 29, 2019 2DCC-MIP Webinar
1. Developed a technique to study mechanical and electrical properties of nanoscale ripples in suspended Graphene
2. Draping and Rippling angles seems to be Conserved for a wide range of parameters.
3. Possible breakdown of continuum elasticity theory
4. Spectral signatures of strong nonuniform pseudo gauge fields
5. Demonstrated STRained Electromagnetic Modulated Superlattices (STREMS)
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Thank You
January 29, 2019 2DCC-MIP Webinar
Questions?
&All of You
Eric HudsonLavish PabbiAnna BinionBill DuschVincent Crespi
Tomotaroh Granzier-NakajimaMauricio TerronesViet-Hung NguyenJean-Christophe CharlierYuanxi Wang