manipulating matter, charge, and spin at the spatial limit · pdf filemanoharan •...

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

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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

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Quantum MirageQuantum Mirage

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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology

SCANNINGPROBE

MICROSCOPES

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Spanning the Length ScalesSpanning the Length Scales

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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

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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

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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)

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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

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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:

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s

simplified schematicMOTA

photo

data

Tunneling EquationsTunneling Equations

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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology

EXPLORINGTHE

ATOMIC REALM

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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

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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

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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

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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

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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

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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology

CHARGE: THE OLD WAY

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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

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Looking “Inside” a ParticleLooking “Inside” a Particle

Charge

Spin

• Quantized degrees of freedom

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+

Looking “Inside” a ParticleLooking “Inside” a Particle

Charge

Spin

• Quantized degrees of freedom

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+ + environment

+ environment

Looking “Inside” a ParticleLooking “Inside” a Particle

Charge

Spin

• Quantized degrees of freedom

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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)

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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)].

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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 ]

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Fano LineshapeFano Lineshape

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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

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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

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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

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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

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Nanoscience Nanoscience and Nanotechnologyand Nanotechnology

ATOMSWHERE YOUWANT THEM

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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

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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

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AtomAtom--byby--Atom Assembly of NanostructuresAtom Assembly of Nanostructures

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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

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The Quantum MirageThe Quantum Mirage

Topograph

dI/dV difference map

• e = 1/2, a = 71.3 Å elliptical resonator

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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

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EigenmodesEigenmodes

• e = 1/2, a = 71.3 Å elliptical resonator

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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

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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

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The Quantum MirageThe Quantum Mirage

Topograph

dI/dV difference map

• e = 0.786, a = 71.3 Å elliptical resonator

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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

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Eigenvalue Eigenvalue SpectrumSpectrum

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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

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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!