reading and manipulating valley quantum states in graphene arindam ghosh department of physics...
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Reading and manipulating valley quantum states in Graphene
Arindam GhoshDepartment of Physics
Indian Institute of Science
Atin Pal et al. ACS Nano 5, 2075 (2011)Atin Pal and Arindam Ghosh PRL 102, 126805 (2009)Atin Pal, Vidya Kochat & Arindam Ghosh PRL 109, 196601 (2012)
Atindra Nath Pal Vidya Kochat
Layout• A brief introduction to Graphene – The valleys
• Uniqueness in the structure of graphene – Valleys and new effects in quantum transport
• Graphene as an electronic component
• Valley manipulation with disorder and gate
• Valley reading: Mesoscopic conductance fluctuations in Graphene
• Graphene on crystalline substrates: Manipulating valleys at atomic scales
• Conclusions
Graphene
Graphene excitement
Electronics of Graphene Backbone of post-Silicon nanoelectronics, Flexible Higher mobility, speed, robustness, miniaturization > 100 GHz transistors (Can be upto 1.4 THz) Electrical sensor for toxic gas Novel Physics – Astrophysics, Spintronics… more?
Strongest material known – Electromechanical sensingBio-compatibility: Bio sensing, DNA sequencingTransparent – Application in solar cells
What is different in Graphene?
Existence of valleys
Single layer graphene: Sublattice symmetry
AB
B
A
B
A
yx
yxF E
i
ivi
0
0
EkvF ).(
Pseudospin
Single layer graphene: Valleys
EkvF ).(
K’ K
EkvF ).(
sskv
kv EF
F
.0
0.
k
E
Valleys
Implications to Random Matrix Theory and universality class
Valley symmetry
Removed
Preserved Effective spin rotation symmetry preserved
Effective spin rotation symmetry broken
Wigner-Dyson orthogonal symmetry class
Wigner-Dyson symplectic symmetry class
Suzuura & Ando, PRL (2002)
Valley-phenomenology in graphene
• Valleytronics Valley-based electronics, equivalent to SPIN (generation and detection of valley state)
• Valley Hall Effect Analogous to Spin Hall effect (Berry phase supported topological transport)
• Valley-based quantum computation Example: Zero and One states are valley singlet and triplets in double quantum dot structures
Phenomenology
'
'
A
B
B
A
s
ObservedBerry phase
Half-integer integer Quantum Hall effect
Absence of backscattering
Klein Tunneling
Antilocalization
MagnetismTime reversal symmetry
Valley Hall Effect
Universality of mesoscopic fluctuations?
Nontrivial universality class
Edges , magnetic impurities, adatoms, ripples…
Valley Physics
Graphene: An active electrical component
The Graphene field-effect transistor
Heavily doped Silicon (Gate)
300 nm Silicon dioxide (dielectric)
Au contact pads
VBG
Exfoliation of Graphene
Typical HOPG (highly oriented pyrolitic graphite ) surface prior to exfoliation
The Graphene field-effect transistor
Heavily doped Silicon (Gate)
300 nm Silicon dioxide (dielectric)
Au contact pads
-40 0 400
1
2
3
(
k)
VBG
(V)
VBG
Effect of valleys on quantum transport in graphene
Disorder in graphene
Doped silicon
Silicon oxide
Graphene
Atomic scale defects: Grain boundaries, topological defects, edges, vacancies…
Charged impurity 1. Long range scattering2. Substrate traps, ion drift, free charges3. Does not affect valley degeneracy4. Linear variation of conductivity
1. Source of short range scattering2. Removes valley degeneracy
-3 -2 -1 0 1 2
0.5
1.0
1.5
Con
duct
ivity
(m
S)
n2D
(1012/cm2)
Valley symmetry: Quantum transport
Presence of Valley symmetry
Broken valley symmetry
Isospin singlet
Isospin singlet
Isospin triplet
)()2(
2 02
22
CCCCqdDe zyx
Quantum correction to
conductivity
Weak localization correction in Graphene
)()2(
2 02
22
CCCCqdDe zyx
zi BB
BF
BB
BF
B
BF
eB
22
2)0()(
2
Short range scattering
sContributeC
GappedCCC zyx
0
,,
Long range scattering
ContributeCCCC zyx 0
Negative MR: Localization
Positive MR: Anti-Localization
PRL (2009): Savchenko Group
Effect of valleys on mesoscopic fluctuations in graphene?
Universal Conductance FluctuationsIn a regular disordered metal
L
Aperiodic yet reproducible fluctuation of conductance with magnetic field, Fermi Energy and disorder configuration
For L < L: dG e2/h Quantum interference effect, same physics as weak localization Independent of material properties, device geometry: UNIVERSAL
Bi film (Birge group, 1990)
-40 0 400
1
2
3
(
k)
VBG
(V)
Conductance fluctuations at low temperatures
-20 -19 -1810
11
12
VBG
(V)
G (
e2/h
)4.5K
1K
500mK
10mK
DG e2/h Universal conductance fluctuations
-60 -30 0 30 6010-5
10-4
10-3
VBG
(V)
G2 /<
G>
2
Density dependence of conductance fluctuations
Need to find Conductance variance in single phase coherent box
10 mKB = 0
-40 0 400
2
4
6
8
G (
mS
)
VBG
(V)
Evaluating phase coherent conductance fluctuations in Graphene
Lf
L
W
2
2
2
21
G
G
NG
G
box
GL
LWNbox ,
Classical superposition
10-5
10-4
10-3
-60 -40 -20 0 20 400
2
4
6
2 /
2G
2 ((e
2 /h)2 )
VBG
(V)
-40 0 400.0
0.5
1.0
1.5
Li
L
VBG
(V)
L (
m)
T = 10mKB = 0
0
2
4
6
G (m
S)DEVICE 1
-80 -40 0 40 800.0
0.2
0.4
0.6
0.8
1.0
G2 (
(e2 /h
)2 )
VBG
(V)
0.5
1.0
1.5
2.0
G (
mS
)
0.5
1.0
1.5
2.0
Li
L (
m)
L
DEVICE 2
Valley symmetry: UCF
Universal Conductance fluctuations
DEG
CDGraphene
GNG2
22
Number of gapless diffuson and Cooperon modes
Low density: Valley symmetry preserved
4CDN
1CDN
High density: Valley symmetry destroyed
Implications to Random Matrix Theory and universality class
Valley symmetry
Removed
Short range scattering
Preserved
Long range scattering
Effective spin rotation symmetry preserved
Effective spin rotation symmetry broken
Wigner-Dyson orthogonal symmetry class
Wigner-Dyson symplectic symmetry class
Suzuura & Ando, PRL (2002)
Intervalley scattering by atomically sharp defects
Long range Coulomb potential from trapped charges
Temperature dependence
-70 0 700
4
-70 0 70 -70 0 70 -70 0 70
G2 /
G
VBG
(V)
10mK 330mK
1K
4.5K
1
Factor of FOUR enhancement in UCF near the Dirac Point Possible evidence of density dependent crossover in universality class
BINARY HYBRIDS GRAPHENE ON BN (INSULATOR)
GRAPHENE
BORONNITRIDE
GRAPHENE/BN
GRAPHENE/BN BINARY HYBRIDS VERTICALLY ALIGNED OVERLAY
15 µm
EL9Tape
Glass
GRAPHENE
15 µm
Si/SiO2
h-BN (exfoliated)
Aligner
GRAPHENE on h-BN
Dr. Srijit Goswami Paritosh Karnatak
GRAPHENE/BN
GRAPHENE-hBN HYBRIDS ULTRA-HIGH MOBILITY
-2 -1 0 1 2
0.0
0.2
0.4
0.6
0.8
4.2K
~ 30000 cm2/Vs
Resis
tanc
e (k
)
density (1012 cm-2)
300 K 77 K 4.2 K
300K
~ 12000 cm2/Vs
DOPED SILICON
SiO2
Graphene
h-BN
GRAPHENE/BN
GRAPHENE-hBN HYBRIDS QUANTUM HALL EFFECT
0 2 4 6 8 10 120
100
200
300
Rxx ()
B (T)
Vg = -30 V
-20 -10 0 10 20 300
2
Vg (V)
Rxx (k)
-1.0
-0.5
0.0
0.5
1.0
-6-5 -4
6543-3
B = 12 TT = 4,2 K
Ryx (h
/e2)
-1 1
-2 2
LIFTING OF 4-FOLD DEGENERACY
1/Rxy = gsgv(n+1/2)e2/h = 2x2 (n+1/2)e2/h
n = 0, 1, 2,…
Summary• A new effect of valley quantum state on the quantum transport
in graphene revealed• The valley states are extremely sensitive to nature of scattering
of charge in graphene• The degeneracy of the valley and singlet states can be tuned
with external electric field• Universal conductance fluctuations can act as a readout of the
valley states• Single layer graphene shows a density dependent crossover in it
universality class , along with a exact factor of four change in its conductance fluctuation magnitude
• Valley degeneracy can be tuned with other means as well, such as external periodic potential from the substrate
THANK YOU
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