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Hari ManoharanHari Manoharan
Department of PhysicsGeballe Laboratory for Advanced Materials
Stanford University
Department of PhysicsGeballe Laboratory for Advanced Materials
Stanford University
Manipulating Matter, Charge, and Spinat the Spatial Limit
Manipulating Matter, Charge, and Spinat the Spatial Limit
Les Les Houches Houches Summer School on Quantum Magnetism 2006Summer School on Quantum Magnetism 2006
Lecture 1
• Detection and Manipulation of Atomic Scale Magnetism
• Quantum Mirages and Kondo Lattices
• Atoms, Spins, and Superpositions
Lecture 2
Lecture 3
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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There is Plenty of Room at the Bottom . . .There is Plenty of Room at the Bottom . . .
“But I am not afraid to consider the final question as to whether, ultimately—in the great future—we can arrange the atoms the way we want; the very atoms, all the way down!
What would happen if we could arrange the atoms one by one the way we want them?”
- Richard Feynman, 1959
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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. . . Or Not. . . Or Not
“The individual particle is not a well-defined permanent entity of detectable identity or sameness.
We never experiment with just one electron or atom or (small) molecule. In thought experiments we sometimes assume that we do; this invariably entails ridiculous consequences.”
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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. . . Or Not. . . Or Not
“The individual particle is not a well-defined permanent entity of detectable identity or sameness.
We never experiment with just one electron or atom or (small) molecule. In thought experiments we sometimes assume that we do; this invariably entails ridiculous consequences.”
- Erwin Schrödinger, 1952
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
www.manoharan.org
Quantum MirageQuantum Mirage
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology
SCANNINGPROBE
MICROSCOPES
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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Spanning the Length ScalesSpanning the Length Scales
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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STM
• Microscope resolving power
(Adapted from www.nobel.se)
Scanning Tunneling Microscopy (STM)Scanning Tunneling Microscopy (STM)
Tunnel current
Tip trajectory
SURFACE
TIP
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Scanning “X” MicroscopyScanning “X” Microscopy
• Proximal probe• Feedback loop • Raster scanning
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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(Adapted from www.nobel.se)
Tip DetailTip Detail
• 10x current increase for every Å
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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Tunneling LandmarksTunneling Landmarks
• Lilienfeld: Observation of field emission from metals (1922)
• Oppenheimer: Ionize H by electron tunneling (1928)
• Fowler-Nordheim: Explanation of field emission (1928)
• Zener: Theory of interband tunneling in solids (1934)
• Chynoweth: Observation of Zener tunn. in semiconductors (1957)
• Giaever: Measure superconducting gap (1960)
• Josephson: Cooper pair tunneling (1962)
. . . IETS, Spin-polarized, etc.
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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Apparatus LandmarksApparatus Landmarks
• Müller: Field Emission Microscope (1937)
• Young: Topografiner & Vacuum Tunneling (1971)
• Binnig & Rohrer: Scanning Tunneling Microscope (1982)
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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Vibration Isolation (a.k.a. “The Pit and the Pendulum”)Vibration Isolation (a.k.a. “The Pit and the Pendulum”)
• Three cascaded stages to achieve nG/Hz1/2
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2004H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2004
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Experimental ApparatusExperimental Apparatus
• Specifications
• 4 K / 1 K / 0.5 K UHV Scanning Probe Microscope
Vibration and electronics limits:Current noise ~ 18 fA/√Hz Lateral resolution ~ 100 fmVertical resolution <~ 30 fm/√Hz
Temperature ~ 0.5 KMagnetic Field ~ 11 T
Sample environment:
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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s
simplified schematicMOTA
photo
data
Tunneling EquationsTunneling Equations
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology
EXPLORINGTHE
ATOMIC REALM
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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Cast of Characters: Cu(111) and CoCast of Characters: Cu(111) and Co
300 Åsquaretopo
After surface prep
After Co dose
300 Åsquaretopo
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Formation of Surface State
z
V(z)
Y(z)
surface state inband gap
Electron Standing WavesElectron Standing Waves
• Sulfur atoms on copper surface
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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-.44V
Clean Cu(111)
dI/d
V
0.0V
Near Step edge, Corral, other defects
Cast of Characters: Cu(111) and CoCast of Characters: Cu(111) and Co
300 Åsquaretopo
After surface prep
After Co dose
300 Åsquaretopo
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Cast of Characters: Co AtomCast of Characters: Co Atom
• Bonds to fcc sites on Cu(111)
35 Å
0.8 Å
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Cast of Characters: CO MoleculeCast of Characters: CO Molecule
• Bonds “on-top” to Cu atoms
35 Å
0.5 Å
Cu
C
O
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology
CHARGE: THE OLD WAY
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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SPIN: THE NEW FRONTIER
Probing the Spin Degree of Freedom with STMProbing the Spin Degree of Freedom with STM
Pair breaking
• Magnetic moment on a superconductor
Yazdani et al. (1997)
• Magnetic moment on a normal metal
• Interacting magnetic moments
Tip
Kondo effect
Spin excitations
Li et al. (1998)Madhavan et al. (1998)
Tip
Tip
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Looking “Inside” a ParticleLooking “Inside” a Particle
Charge
Spin
• Quantized degrees of freedom
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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+
Looking “Inside” a ParticleLooking “Inside” a Particle
Charge
Spin
• Quantized degrees of freedom
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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+ + environment
+ environment
Looking “Inside” a ParticleLooking “Inside” a Particle
Charge
Spin
• Quantized degrees of freedom
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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+ + environment
+ environment
+ chargescreening
spinscreening
The Kondo ResonanceThe Kondo Resonance
-500 0 500 -50 0 50
dI /
dV
(a.u
.)
-150 0 150
Sample Bias V (mV)
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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The Kondo Resonance: Co Atom on Cu(111)The Kondo Resonance: Co Atom on Cu(111)
-20 -10 0 10 20
4.0
4.5
5.0
5.5
Off Atom
On Atom
dI /
dV (
arb.
uni
ts)
Sample Bias (mV)H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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The Kondo EffectThe Kondo Effect
Fano resonance
• Kondo ground state
Spin screening cloud
Magneticimpurity
•Kondo effect and STM
• Co on Au(111) [Madhavan et al., Science 280, 567 (1998)].
• Ce on Ag(111)[Li et al., PRL 80, 2893 (1998)].
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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The Kondo TemperatureThe Kondo Temperature
• Fit tunnel spectrum to Fano resonance
-20 -10 0 10 20
1.0
1.1
1.2
1.3
1.4
TK = 56 K
Data Fit
(dI/dV)
/ (dI/dV
at V
= 0
)
Sample Bias [ mV ]
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Fano LineshapeFano Lineshape
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
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2
0 2B K
( ) ,1qF F
k Tε ε αεε′+ −′= =′+
V. Madhavan et al, PRB 64 (2001)
-20 -10 0 10 20
1.0
1.1
1.2
1.3
1.4r =
10 Å6 Å
5 Å
4 Å
3 Å
2 Å
1 Å
0 Å
[ dI /
dV
] /
[ dI
/ dV
] V=0
Sample Bias V (mV)
The Kondo Resonance: Co Atom FlyoverThe Kondo Resonance: Co Atom Flyover
Tip
Co
Cu(111)
r
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Imaging the Kondo ResonanceImaging the Kondo Resonance
Topograph
(V = 5 mV)
dI/dV map
(V = ±5 mV)
• Single Cobalt atom• Simultaneously acquired 35 Å square images
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Kondo Imaging: CoKondo Imaging: Co vsvs COCO
Topograph
(V = 5 mV)
dI/dV map
(V = 5 mV)
• 1 cobalt atom + 1 carbon monoxide molecule• Simultaneously acquired 35 Å square images
Co
CO
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Kondo Imaging for Atom IdentificationKondo Imaging for Atom Identification
Topograph
(V = 10 mV)
dI/dV map
(V = 10 mV)
• 2 Cobalt atoms + 1 Sulfur atom• Simultaneously acquired 27 Å square images
Co
Co
S
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology
ATOMSWHERE YOUWANT THEM
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2003
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Toward Multiple TerminalsToward Multiple Terminals
Tip Tip
Tip
Tip
• Standard two-terminal measurement
Aha!
IV
• Two tips?
• One tip plus weird geometry
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Elliptical Resonator DesignElliptical Resonator Design
170 Å
Eccentricity:e2 = 1 - b2/a2
a-a
b
F1
-b
ae
P
F2
-ae
Path length:F1 P + P F2 = 2a
a = 71.3 Å
e = 1/2
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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AtomAtom--byby--Atom Assembly of NanostructuresAtom Assembly of Nanostructures
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
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180 Å• e = 0.500, a = 71.3 Å elliptical electron resonator
• e = 0.786, a = 71.3 Å elliptical electron resonator 180 Å
Empty Elliptical ResonatorEmpty Elliptical Resonator
Topograph
(V = 10 mV)
dI/dV map
(V = 10 mV)
• e = 1/2, a = 71.3 Å• Simultaneously acquired 150 Å square images
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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The Quantum MirageThe Quantum Mirage
Topograph
dI/dV difference map
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Spectroscopy on Atom and MirageSpectroscopy on Atom and Mirage
-20 -10 0 10 200
1
2
3
4Off Focus∆x = +5 Å
On Focus∆x = 0 Å
Left Focus: Atom
dI /
dV
(a.u
.)
Sample Bias V (mV)-20 -10 0 10 20
0.0
0.1
0.2
0.3
0.4
0.5
Off Focus∆x = -5 Å
On Focus∆x = 0 Å
Right Focus: No Atom
Sample Bias V (mV)H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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EigenmodeEigenmode CalculationsCalculations
0 10 20 30 40 50 60 700.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
EF
E k
[ eV
]
Eigenvalue k
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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EigenmodesEigenmodes
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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EigenmodeEigenmode ModelingModeling
CalculatedEigenmode at EF
(Eigenstate 42)
dI/dVdifference map
• e = 1/2, a = 71.3 Å elliptical resonator• Solve Schrödinger equation with hard-wall boundary
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Elliptical Resonator DesignElliptical Resonator Design
160 Å
Eccentricity:e2 = 1 - b2/a2
Path length:F1 P + P F2 = 2a
a = 71.3 Å
e = 0.786
a
-a
b
F 1
-b
ae
P
F 2
-ae
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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The Quantum MirageThe Quantum Mirage
Topograph
dI/dV difference map
• e = 0.786, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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EigenmodeEigenmode ModelingModeling
CalculatedEigenmode at EF
(Eigenstate 28)
dI/dVdifference map
• e = 0.786, a = 71.3 Å elliptical resonator• Solve Schrödinger equation with hard-wall boundary
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2002
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Eigenvalue Eigenvalue SpectrumSpectrum
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
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1 1.2 1.4 1.6 1.8 2 2.20
100
200
300
400
500
600
700
800
2k A
Ener
gy
/a bμ =Deformation
EigenmodesEigenmodes
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
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EigenmodesEigenmodes: Odd Modes Removed: Odd Modes Removed
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
www.manoharan.org
EigenmodesEigenmodes: Odd Modes Removed: Odd Modes Removed
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
www.manoharan.org
EigenmodesEigenmodes: Even Modes Left: Even Modes Left
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
www.manoharan.org
Quasi-angular nodes
Quas
i-ra
dia
l nodes
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0
1
2
3
4
EigenmodesEigenmodes: Even Modes Left: Even Modes Left
• e = 1/2, a = 71.3 Å elliptical resonator
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
www.manoharan.org
Quasi-angular nodes
Quas
i-ra
dia
l nodes
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0
1
2
3
4
Eigenvalue Eigenvalue SpectrumSpectrum
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
www.manoharan.org
1 1.2 1.4 1.6 1.8 2 2.20
100
200
300
400
500
600
700
800
2k A
Ener
gy
/a bμ =Deformation
Good Good EigenmodesEigenmodes
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2005
www.manoharan.org
1 1.2 1.4 1.6 1.8 2 2.20
100
200
300
400
500
600
700
800
2k A
Ener
gy
/a bμ =Deformation
ThanksThanks
NSF
• The Team
• The Funding
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
www.manoharan.org
ONR DOESloan
Foundation ChevronResearch
CorporationKETI/MOCIE
web:mota.stanford.edu
ThanksThanks
NSF
• The Team
• The Funding
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
www.manoharan.org
ONR DOESloan
Foundation ChevronResearch
CorporationKETI/MOCIE
web:mota.stanford.edu
MOTA subgroup:• Laila Mattos
(Kondo lattices)
ThanksThanks
NSF
• The Team
• The Funding
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
www.manoharan.org
ONR DOESloan
Foundation ChevronResearch
CorporationKETI/MOCIE
web:mota.stanford.edu
MOTA subgroup:• Laila Mattos
(Kondo lattices)• Chris Moon
(State manipulation)
ThanksThanks
NSF
• The Team
• The Funding
H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006H. C. MANOHARAN • DEPARTMENT OF PHYSICS • GEBALLE LABORATORY FOR ADVANCED MATERIALS • STANFORD UNIVERSITY © 2006
www.manoharan.org
ONR DOESloan
Foundation ChevronResearch
CorporationKETI/MOCIE
web:mota.stanford.edu
MOTA subgroup:• Laila Mattos
(Kondo lattices)• Chris Moon
(State manipulation)• Brian Foster• Gabriel Zeltzer• Richard Harris
MERCI!MERCI!
