Materials in 2-dimension and beyond

Philip Kim

Physics Department, Columbia University

Lecture III

Second Lecture: Friday 2/1,

morning

Spin and pseudospin in graphene

First Lecture: Thursday 1/31, afternoon

Bloch, Landau, and Dirac: Hofstadter’s Butterfly in Graphene

Third Lecture: Friday 2/1, afternoon

Materials in 2-dimension and beyond

School on Modern Topics in Condensed Matter Physics, Jan 31- Feb 1st, 2013, Singapore Philip Kim, Department of Physics, Columbia University

Opportunities for Low Dimensional Quantum Material Physics

New Exotic Materials:

Graphene, Topological Insulators, strong spin orbit coupling system,

new strongly correlated system, …

Low Dimensional ‘Mesoscopic’ Correlated systems:

Oxide heterostructures, van der Waals heterostructures, ….

Novel New Experimental Techniques:

Hybrid experimental tools (transport+optics, SPM+transport,

electromechanical+magnetic,…)

Electrolyte gating, novel growth techniques, …

Assembly of Various 2D Systems

X

X

M

C

B

N

graphene

hexa-BN

Metal-Chalcogenide

M = Ta, Nb, Fe, Co, Mo, …

X = S, Se, Te, …

Bi2Sr2CaCu2O8-x

Charge Transfer Bechgaard Salt

(TMTSF)2PF6

Lead Halide Layered Organic

Semiconducting materials: WSe2, NbS2, MoS2, …

Complex-metallic compounds : TaSe2, TaS2, …

Magnetic materials: FeSe2, CoSe2 ,…

Superconducting: NbSe2, Bi2Sr2CaCu2O8-x, ZrNCl,… A

B

A C

A

graphene intercalant

Ca, K, …

FeCl3, AgCl3, …

Br2, I2, …

Graphite Intercalate

Toward Graphene Superconductor?

M. Calandra and F. Mauri PRB(2006)

Tc c

BaC6 : < 0.3 K 5.2 A

SrC6 : 1.65 K 4.9 A

CaC6 : 11.5 K 4.5 A

MgC6: ? 3.9 A (calc)

MgC6 ?

MgxCa1-xC6

Vapor Phase Intercalation of Few Layer Graphene

Bilayer FeCl3 Intercalate

0 100 200 3000.0

0.5

1.0

1.5

R (

)

T (K)

0 2 4 6 8 10 12 14 16 18 200.00

0.05

0.10

0.15

0.20

R (

)

T (K)

Tc ~ 10 K

N. Kim et al. Nano Letters (2011)

Ca Intercalate in Mesoscopic Graphite

N. Kim et al. (2011)

• minimum possible intercalate

• high carrier density (5x1013cm-2)

• mobility ~ 1200 cm2/V sec

• quantum oscillations

• potential 2D magnetism

N. Kim et al. (2012)

• Superconducting Transition @ 11 K

• Hall Carrier density (3x1013cm-2)

Few Layer Graphene

Electrochemically Aided Adsorption / Intercalation

Stage 1 Stage 4 Stage 2 Graphite

Li intercalation in few layer graphene in polymer electrolyte

Time (~ 10 hours)

Electrochemically Aided Adsorption Electrochemically Aided Intercalation

Yinsheng Guo, Dmitri K. Efetov, Kin Fai Mak, Tony F. Heinz, Philip Kim and Louis Brus – (2012)

-5 -4 -3 -2 -1 0

-8

-6

-4

-2

0

Veg

(V)

I(pA

)

Micro Cyclic Voltammetry

Bilayer Graphene

Gate leakage current with slow sweep

Bulk

Microscopic Study: Raman Spectroscopy and Micro Cyclic Voltammetry

Yinsheng Guo, Dmitri K. Efetov, Kin Fai Mak, Tony F. Heinz, Philip Kim and Louis Brus – (2012)

4 Layers

Tim

e (~

10 h

ou

rs)

G peak

Raman Spectroscopy

Diluted phase adsorption

Stage 1 Intercalation

Stage 1 Adsorption

Extremely High Carrier Density in Graphene

D. Efetov and P. Kim, Phys. Rev. Lett. (2010)

Polymer electrolyte: PEO+LiClO4

|n| < 1014 cm-2 ~

0 100 200

T (K)

r (

)

25

50

75

100

125

200

225

Controlling Bloch-Grueneisen Temperature

kF

kph

kF

kph ~ T

phonon sphere

electron sphere

kBTBG=2 hvs kF

D. Efetov and P. Kim (2010)

Ultimate limit of resistivity of

graphene at room

temperature ~20 / □

Multiband Transport in Bilayer Graphene

• Electrolyte Gating (Coarse Control)

~ 5x 1014 cm-2

• Back Gating (Fine Control)

~ 1013 cm-2

Hall measurement yields

the total density nH

Onset of the second subbands

Increased interband scattering Ve = -1.7 V Ve = -.4 V Ve = 1 V

Shubnikov de Haas Oscillations

1st subbands 2nd subbands 2nd subbands

Mobility of the second subband is much higher than that of first subbnad!

Multiband Transport in Bilayer Graphene

D. K. Efetov, P. Maher, S. Glinskis, and P. Kim Phys. Rev. B 84, 161412 (R)

Toward M-point in Graphene

x

E(k2D)

kx ky

2D Brillouin Zone

kx

ky

K

K’

M

M

~ 1.5 eV

~5x1014 cm-2

• Non-linearity and trigonal

warping of the band structure

• Evolution of Fermi Surface –

modification of scattering

processes

• Extended van Hove

Singularities –

Superconductivity, Magnetism,

CDW?

Total Charge

2.2x1016 cm-2

M point Charge

5 x 1015 cm-2

-15 -10 -5 0 5 10 15

-30

-15

0

15

30

G2B2

G3E1

G4B3

G5B4

n

10

13cm

-2

Veg

V

Achieving High Carrier Densities

-15 -10 -5 0 5 10 15

-30

-15

0

15

30

G2B2

G3E1

G4B3

G5B4

n

10

13cm

-2

Veg

V

Increase capacitance and maximal doping

levels on electron side by 2 times !!!

Understanding detailed electrochemical

process is required for further improvement. 2μm

Suspended Graphene samples

- - - - - - - - - -

+ + + + +

+ + + +

Gating from both sides of

suspended graphene samples D. Efetov and P. Kim, Phys. Rev. Lett. (2010) Electrochemical doping

Electrolyte Gating Sr2IrO4: Strongly Correlated Electrons

Samples: Ramesh group @ Berkeley

Sr2IrO2: Mott insulator with strong spin orbit coupling

-4 -3 -2 -1 0 1 2 30

20

40

60

80

100

Re

sis

tan

ce

(x1

03 W

)

Gate Voltage (V)

100 150 200 250 3001

10

100

1000 V

g = 0 V

Vg = -1 V

Vg = -2 V

Vg = -3 V

Vg = -4 V

Vg = -5 V

Re

sis

tan

ce

4w

ire (

kW

)

Temperature (K)

electron

doping

hole

doping

electron doping

• Ionic liquid doping of Mott insulator

• Metal-insulator transition in strong spin

orbit coupled Mott insulator

Ravichandran in progress (2012)

Co-lamination and

Vertical Heterostructures

Co-lamination and Transfer Techniques

1. spin coat substrate with PMMA and

scratch onto top surface

2. Lift off PMMA;

graphene comes with it!

3. Align graphene over target using a micro-

manipulator. PMMA is brought into contact

with target and annealed.

Collaboration: Hone and Shepard groups

Dean et al. Nature Nano (2010)

Flat Graphene on hBN

BN graphene

0.5 um

Roughness

-0.4 -0.2 0.0 0.2 0.40.0

0.4

0.8

1.2

Graphene

BN

fre

qu

en

cy [a

.u.]

height [nm]

0.22 nm

2 um

Room temperature mobility >100,000 cm2V-1s-1

Extremely High Mobility in Graphene/BN

Low temperature mobility >300,000 cm2V-1s-1

Platform for investigating extreme

quantum transport phenomena

Fractional quantum Hall states Hofstadter’s Butterfly Transport in Hydrodynamic Regime

Multi-Stacked Graphene Vertical Heterostructures

0 5 10 15 20 25-10

-5

0

5

10

RD

rag (

Ohm

s)

VBG

(Volts)

225 K

202 K

175 K

148 K

98 K

75 K

48 K

25 K

11 K

Temperature Dependent Coulomb Drag Effect

• Coulomb drag experiment high temperature

ranges for e-e and e-h interactions

• Coulomb drag, counter flow, and excitonic

transport at low temperatures

RXY

Counter flow

VBG (Volts)

VT

G (

Vo

lts)

Rxy (kOhm)

T = 20 mK

B = 20 T

Counter Flow Measurement

Dean et al., in progress (2012)

New Interfaces and

Transport Across

Heterostructures

Yang et al. (SAIT collaboration) Science 336, 1240 (2012)

Graphene/Silicon hybrid Device: Graphene Barristors

Gate Variable Schottky Diode

Invertor and half adder is demonstrated!

MoS2 / graphene Heterojunction

graphene MoS2 (3 nm)

10 mm SiO2

Si

MoS2

graphene

Graphene/MoS2 Schottky Junction

Barreiro et al. in preparation (2013)

Tunable Schottky Diode

-3 0 3-200

-100

0

100

Vg=40V

I (m

A)

V (V)

+V on MoS2

300K

Vg=-40V

-3 0 3-25

-20

-15

-10

-5

0

5

Vg=-30V

I (m

A)

V (V)

+V on MoS2

300K

Vg=-40V

Vg=+40V

Vg=-40V

Gate tunable MoS2/graphene junction

MoS2/graphene/MoS2 metal base transistors Barreiro et al. in preparation (2013)

5 mm

Build vertical MoS2/graphene/MoS2 hetrostacks

-2 0 2 4-0,2

-0,1

0,0

0,1

0,2

Ic (

mA

)

Vc (V)

-9 mA

-6 mA

-3 mA

0 mA

3 mA

6 mA

9 mA

Vg = -40V

emitter: top MoS2

base: graphene

collector: bottom MoS2

• Utilizing graphene as a

metal base in bipolar

junction transistor. α = IC / IE

~ 0.039

α* = α /(ACB /ABE)

= α / 0.05

~ 0.78

NbSe2/Graphene Heterostructures

Efetov et al. (2012)

NbSe2: quasi 2D superconductor

Superconducting transition

Tc = 7 K

Hc2 = 4.5 T

CDW transition

TcCDW= 33 K

-6 -4 -2 0 2 4 6

0.00

0.05

0.10

0.15

R(

)

B(T)

0 10 20 30 40 50

0.0

0.1

0.2

0.3

0.4

0.5

R(

)

T(K)

Tc = 7 K

TcCDW= 33 K

Hc2 = 4.5 T

Tc and Hc2 measurement in mesoscopic samples (~ 30 nm thick)

-1 0 10.0

0.5

1.0

1.5

2.0

B(T

)

VSD

(mV)

Δr Δi dI/dV(mS)

6

10

-1 0 16000

7000

8000

9000

10000

dI/

dV

(mS

)

VSD

(mV)

4K

3.5K

2.9K

-1 0 16000

7000

8000

9000

10000

1.7 K

dI/

dV

(mS

)

VSD

(mV)

Andreev Reflections – between NbSe2 & Graphene Efetov et al. in progress (2012)

Δr Δi

NbSe2 Tc = 7 K

Hc2 = 4.5 T

graphene

5 mm

Andreev Reflections in SS’N junctions

Vg (V)

B (

T)

dRxx/dVg (A.U.)

Potential Interplay between

Superconducting System and QHE

Van der Waals Epitaxy Growth vdW epitaxy can clean interface without chemical mismatch

t=32nm t=20nm

5μm

6~7μm

triangle

BiTe2 growth on hBN substrate

Collaboration with Moon group (Postech)

0 5 10 15

0.3

0.4

Rxx(K

)

B(T)

0.4

0.8

1.2

Rxy(K

)

0 2 4

-3

-2

-1

0

1

2

3

R-R

Poly

nom

ial f

it

1/B(T-1)

Shubnikov de Haas Oscillations

Magneto Resistance and Hall Resistance

Mobility

~ 1,000 cm2/Vsec

Rxx

Rxy

Ghahari et al (2012)

Rubrene on hBN with Graphene Electrodes

organic semiconductor

VG< 0

gate

Graphene source Grapahene drain

H-BN

VD

conducting channel at surface

– – – – – – – – – – – – – – – – – – ID

Graphene electrodes on BN

Rubrene Powder

Rubrene growth on hBN/ graphene

Chulho Lee et al (Nuckolls & Kim)

Rubrene on hBN : Structural Analysis

Chulho Lee et al. (2012)

Glazing incident X-ray diffraction (GIXD)

• Highly oriented rubrene crystal

growth on h-BN

• In-plane orientation & epitaxial

relation under investigation

2 mm

h-BN

Rubrene

Selected -area electron

diffraction (SAED) with TEM

Rubrene a-b plane grown on h-BN

h-BN

Rubrene

Rubrene on hBN with Graphene Electrodes: Transport

Chulho Lee et al. (2012)

20 mm

h-BN

CVD-graphene electrodes

20 mm

Rubrene grown on h-BN & graphene

-40 -30 -20 -10 0 10 20 301E-9

1E-8

1E-7

1E-6

1E-5

1E-4

VG (V)

-ID

S (

A)

VDS

= - 40 V

0.000

0.002

0.004

0.006

0.008

0.010

-I 1/2

DS (A

) 1/2

-40 -30 -20 -10 0-1.0x10

-4

-8.0x10-5

-6.0x10-5

-4.0x10-5

-2.0x10-5

0.0

-40 V

10 V

-30 V

-20 V

-10 V

0 V

20 V

I DS (

A)

VDS (V)

Mobility ~ 11.5 cm2/Vs

Low pressure growth

@ 200 C

Ohmic contact

Hybrid Experimental Tools

Combination of Scanning Probe/ Transport

• Transport

• Atomic force microscopy

• Scanning gate microscopy

• Scanning thermal microscopy

Scanning Kelvin probe microscopy

Y. Yu et al. (2011)

STM on Graphene/hBN

Spectroscopy Map in QHE regime

Mechanical Electromagnetic Measurements

Magnetization measurement

Electromechanical Devices: suspended graphene

Chen at al (2011)

Vikram et al (2012)

Direct experimental access of chemical potential!

(Deshpande et al, with Hone group collaboration)

Chemical Potential Measurement of Graphene Landau Levels

(Deshpande et al, with Hone group collaboration)

Chemical Potential Changes (simulation)

Spring constant (dynamic contribution)

kmag Fmag

z

m

nVg Cg

2

eA

Spring stiffening directly yields electronic compressibility n-2dn/dµ or DOS dn/dµ

(Deshpande et al, with Hone group collaboration)

Chemical Potential Measurement of Broken Symmetry QH States

• Broken Symmetry State

(n=1) are observed

• n=1 is measured to be

scale as B1/2 /

• Partially filled broken

symmetry LL provides

chemical potential

universal scaling of

)(/ nm Fv BF

Kravchenko et al. PRB (1990)

New Exotic Materials:

Graphene, Topological Insulators, strongly correlated system, …

Low dimensional ‘Mesoscopic’ correlated systems:

Oxide heterostructures, van der Waals heterostructures, ….

Novel New Experimental Techniques:

Hybrid experimental tools (transport+optics, SPM+transport,

electromechanical+magnetic,…)

Electrolyte gating, novel growth techniques, …

Summary

Acknowledgement

Funding:

Past Members

Melinda Han (Ph.D. 2010, Frontier of Science Fellow, Columbia University)

Meninder S. Purewal (Ph.D. 2008)

Josh Small (Ph.D. 2006)

Yuanbo Zhang (Ph.D. 2006, Professor, Fundan University)

Yuri Zuev (Ph.D. 2011, IBM Fishkill)

Kirill Bolotin (Assistant Professor, Department of Physics, Vanderbilt University)

Byung Hee Hong (Associate Professor, Department of Chemistry, Seoul National University)

Pablo Jarillo-Herrero (Assistant Professor, Department of Physics, MIT)

Keunsoo Kim (Assistant Professor, Department of Physics, Sejong University)

Namdong Kim (Research Scientist, POSTECH)

Barbaros Oezyilmaz (Assistant Professor, Department of Physics, National University of Singapore)

Current Members

Yue Zhao

Mitsuhide Takekoshi

Andrea Young

Dmitri Efetov

Fereshte Ghahari

Patrick Maher

Young-Jun Yu (jointly with GRL, POSTECH)

Vikram Deshpande (jointly with Hone group)

Paul Cadden-Zimansky (Columbia Frontier of Science Fellow)

Chenguang Lu (jointly with Hone and Herman

Collaborating Students/postodcs

Cory Dean, Inanc Meric, Lei Wang,

Sebastian Sorgenfrei, Kevin Knox, Nayung

Jung, Seok Ju Kang, Jun Yan, Yanwen Tan,

Kevin Knox

Collaborators

Horst Stormer, Aron Pinczuk, Tony Heinz, Abhay

Pasupathy, Latha Venkataraman

Louis Brus, George Flynn, Colin Nuckolls,

Jim Hone, Ken Shepard, Louis Campos, Rick Osgood

T. Taniguchi, K, Watanabe

Andre Geim, Kostya Novoselov, Sanka Das Sarma

Kim group and friends (2011)