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