condensed matter physics at low dimensions
DESCRIPTION
Condensed Matter Physics At Low Dimensions. Philip Kim Department of Physics Columbia University. Condensed Matter Physics. ~10 23 electrons ~10 23 ions. Atomic orbital sp 2. 0D. 1D. 2D. 3D. Carbon Nanotubes. Fullerenes (C 60 ). p. s. SP 2 Carbon: 0-Dimension to 3-Dimension. - PowerPoint PPT PresentationTRANSCRIPT
Condensed Matter Physics At Low Dimensions
Philip Kim
Department of PhysicsColumbia University
Condensed Matter Physics
~1023 electrons~1023 ions
SP2 Carbon: 0-Dimension to 3-Dimension
Atomic orbital sp2s
p
Fullerenes (C60) Carbon Nanotubes GraphiteGraphene
0D 1D 2D 3D
Benzenemolecule
x
E(k2D)
kx
ky
Electronic Band Structure of Graphene
kvE F
Band structure of graphene (Wallace 1947)
Zero effective mass particles moving with a constant speed vF = c/300
2D Brillouin Zone
kx
ky
K
K’
ccBAtHmn
mn .ˆ),(
kx'
ky'
E
empty
filled
A B
Single Layer Graphene: Pseudo Spinor
‘A’ sublattice: pz orbitals
‘B’ sublattice : pz orbitals
A
B
q
Spinor Representation
Pseudo spin
Graphene Lattice Structures
BeA iqSuperposition:
Two inequivalent lattice sites!
[ ] Cs
Spin
X
Dirac Fermions in Graphene : “Helicity”
KK’
momentumpseudo spin
E
kx
ky
E
kx
ky
E
ky
kx
G. Semenoff PRL (1984)
Effective Dirac Equations
kvvH FFeff
s
0
0
yx
yx
ikkikk
qk = tan-1(ky / kx)
21
k = eik r.
eiqk
1
ccBAtHmn
mn .ˆ),(
Vxy
Hall Effect
I
Vxx
+
+
+
+
-
-
--
B
Quantized Cyclotron Orbit
Rxy
Rxx
s
s
Rxx = Vxx / I
Rxy = Vxy / I = B/enQuantum Hall Effect:
Klitzing (1980)
Hall (1879)
Quantum Hall Effect in Graphene (2005)
Quantization:4 (n + )Rxy
=-1 ___ eh
2
21
spin (2) X pseudo-spin (2)
pseudo-spin rotation
kx' ky'
E
Klein Tunneling (1928)
Step Potential problemV>m: transmission via negative energy states
x
V
0
Klein result: barrier sharpness ~Compton wavelength
eT Em
2p
x
V
0x
V
0E
filed
1T
Klein Tunneling and Pseudo spin
Chiral tunneling in graphene pn junctions
Katsnelson et al. (2006)
n
np n
p
p
VBG > 0VTG < 0
VBG < 0VTG > 0
graphene
electrode
1 mm
20 nmYoung et al. (2009)
|n2| (1012 cm-2)
1 2 3 4
0
2
B (T
)
Gosc (e2/h)-1 0 +1
Magnetic field modulation of FP
Spin ½ and Electron Interaction
“Triplet”
“Singlet”
Pseudo Spin
“Quantum Hall bilayer”
“Valley spin”
…
21 cc
ji ssjjiiji
Xedd ,
**
,
2
)()()()(||2
1 rrrrrr
rr
Exchange Interaction:
SU(4) Quantum Hall Ferromagnet in Graphene
q
Valley spinSpin
X
SU(4)<
K
K’
K’
K
Yang, Das Sarma and MacDonal, PRB (2006);
K’ K’
kx
ky
E
Magnetic Wave Function
Under magnetic fields:pseudospin = valley spin
Degree of freedom:
Spin (1/2), Valleys
Charge Density WaveKekule DistortionAnti FerroMagneticFerroMagnetic
Possible SU(4) Quantum Hall Ferromagnetism at the Neutrality
Spin & pseudo spins: many body physics in graphene
5 mm
Dean et al. Nature Physics (2011)
• SU(4) hierarchical Fractional Quantum Hall Effect
• Spin and Pseudospin Ferromagnetic Quantum Hall Effect
• Spin Skyrmion and Valley Skyrmions
Mobility > 300,000 cm2/Vsec
Phase Transitions Among Fractional Quantum Hall States
Maher*, Wang* et al. submitted
Bilayer GrapheneEncapsulated with top & bottom gate
mobility > 106 cm/Vsec
sxx (S)
0.5 1.0 1.5 2.00
2000
4000
6000
8000
10000
12000B=18TSiGate = +40V Rxx
Rxy
Vg (Volts)
Rxx
()
0
10
20
30
40
50
60
70
432
Rxy
(k
)
1
2/34/3
5/37/3
8/3 10/311/3
20 mK
Bilayer graphene: Fractional Quantum Hall effect Rxx (k)2/31 2 3 4 5 6
5/3 8/3
E-field tunable FQHEPhase Transitions in Lowest Landau Levels
X
X
M
C
BN
graphene
hexa-BN
Metal-Chalcogenide
M = Ta, Nb, Mo, W, Eu …
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: EuS2, EuSe2 ,…Superconducting: NbSe2, Bi2Sr2CaCu2O8-x, ZrNCl,… A
BA
CA
Assembly of Various 2D Systems
-40 -20 0 20 400.96
0.98
1.00
1.02
1.04
1.06
1.08
VSD(mV)
(dI/d
V)/(d
I/dV(
10K)
)
Andreev Reflection btw graphene/NbSe2
1.5 K2.5 K3.5 K4.5 K5.5 K6.5 K6.8 K7.0 K7.2 K7.5 K
Andreev Reflections – between NbSe2 & GrapheneEfetov et al. (2014)
NbSe2Tc = 7 KHc2 = 4.5 T
graphene
5 mm
Tomasch Oscillations
Andreev Reflection
Andreev Reflection into QH edge states are more efficient!
Superconductivity and QHE
Vertical & Lateral Channels
- Al contact to MoS2 for electron injection
- Pd contact to WSe2 for hole injection
-60 -40 -20 0 20 40 6010-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
WSe2
MoS2
I ds (A
)
Vg (V)
Vds
= 0.5 V
Lateral Transport in Channels
C. Lee et al, submitted
Atomically Thin vdW p-n junction
Forward
Lateral and vertical electron band alignment
Interlayer recombination by inelastic tunneling process
Gate Tunable Diode Characteristic
Graphene Materials and Applications
Large-ScaleCVD Graphene
+Graphene
NanoplateletComposites
Composites
Cars,AerospaceAppliations
Semi-conductors
Ultrafast Transistors, RFIC,
Photo/Bio/Gas Sensors
Transparent ElectrodesFlexible/Transparent
Electrodes/Touch Panels
PrintableInks Conductive Ink,
EMI shields
EnergyElectrodes
Super Cap./Solar CellsSecondary Batteries
Fuel Cells
HeatDissipation
LED Lights, BLUECU, PC …
GasBarriers
Gas barriers fo Displays,Solar Cells
Images: Royal Swedish Academy Courtesy: B. H. Hong
CERN Electro-Positron Collider
Relativistic QM: High Energy Physics
Conclusions
Kim Lab @ Columbia in City of New York
Quasi Relativistic QM: Low Energy Physics
Dirac Equation:.
Majorana Equation: ??
Acknowledgement
Past MembersMelinda 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 MembersYue ZhaoMitsuhide TakekoshiAndrea YoungDmitri EfetovFereshte GhahariPatrick MaherYoung-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/postodcsCory Dean, Inanc Meric, Lei Wang, Sebastian Sorgenfrei, Kevin Knox, Nayung Jung, Seok Ju Kang, Jun Yan, Yanwen Tan, Kevin Knox
CollaboratorsHorst Stormer, Aron Pinczuk, Tony Heinz, Abhay Pasupathy, Latha VenkataramanLouis Brus, George Flynn, Colin Nuckolls, Jim Hone, Ken Shepard, Louis Campos, Rick OsgoodT. Taniguchi, K, WatanabeAndre Geim, Kostya Novoselov, Sanka Das Sarma
Kim group and friends (2011)
Funding:
Amelia Barreiro Chul-ho Lee (jointly with Nuckolls group)Jean-Damien Pillet Jayakanth Ravichandran Adam Wei Tsen (jointly with Pasupathy group)Dmitri EfetovFereshte Ghahari
Patrick MaherCarlos ForsytheGiselle Elbaz (jointly with Brus group)Austin Cheng Frank Zhao Xiaomeng Liu
Collaborations: Brus, Dean, Heinz, Hone, Nuckolls, Shepard