Tunneling Spectroscopy of Quantum States in Nanoparticles and Single Molecules • Quantized Electronic States in Metals -- How Interactions Affect the Spectra Spin-Orbit Effects Superconducting Interactions Non-Equilibrium Effects and Electron-Electron Interactions Ferromagnetism and Magnetic Anisotropy Forces • Tunneling via a Single Cobalt Atom in one Molecule Jason Petta, Mandar Deshmukh, Sophie Guéron, Chuck Black Abhay Pasupathy, Jiwoong Park, Jonas Goldsmith Héctor Abruña, Paul McEuen, Dan Ralph Thanks to Piet Brouwer, Jan von Delft, many others
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Tunneling Spectroscopy of Quantum Statesin Nanoparticles and Single Molecules
• Quantized Electronic States in Metals -- How Interactions Affectthe Spectra
Spin-Orbit Effects
Superconducting Interactions
Non-Equilibrium Effects and Electron-Electron Interactions
Ferromagnetism and Magnetic Anisotropy Forces
• Tunneling via a Single Cobalt Atom in one Molecule
Jason Petta, Mandar Deshmukh, Sophie Guéron, Chuck BlackAbhay Pasupathy, Jiwoong Park, Jonas Goldsmith
Héctor Abruña, Paul McEuen, Dan Ralph
Thanks to Piet Brouwer, Jan von Delft, many others
Introduction to tunneling spectroscopyMeasuring “electrons-in-a-box” levels in a metal nanoparticle
o c c u p ie d u no c c u p ie dodd number of electrons even number of electrons
01234567
0.25 0.50 0.75 1.00 1.25V (mV)
B (T
)
In general, copper is a little more complicated than aluminum.
Effects of Spin-Orbit Scattering (perturbative picture)
1) g< 2perturbation theory:
nth level
Due to fluctuations in matrix elements and level spacing, gn variesfrom level to level.
2) Avoided crossings
gn = 2 1− 2ψm↓ Hso ψn↑
2
En − Em( )2m≠n
ℜ
�ℜ�ℜ�ℜ
ℜ
ℜ
�ℜ�ℜ�ℜ
H =
ε1(B) HsoHso
* ε2 (B)ℜ�ℜ
ℜ
ℜ�ℜ
Random Matrix Theories: In the presence of spin-orbit interactions, the random fluctuations in orbital electron-in-a-box wavefunctions will affect the spin part of the wavefunction.
Brouwer, Waintal, Halperin PRL 85, 369 (2000).Matveev, Glazman, Larkin PRL 85, 2789 (2000).
The g factor for each energy level should be a tensor -- should vary depending on the direction of magnetic field.
The theories provide quantitative predictions for the distributions of g-factors.
δε µµ2
2
12
12
22
22
32
32
4= + +B g B g B g B( ) , where B1, B2, and B3 are along the principal axes.
A
B
A700
0
B (m
T)
0.25 0.75V (mV)
C
D
B
C
D
Anisotropy of g-factors
Variations from Quantum State to Quantum State
Red: Cu#1
Blue: Cu#2
gmax gmiddle gmin
Orientations of principal axes for the g-factor ellipsoids:
The ellipsoids seem to be oriented randomly, as expected for coupling ofthe spin to random orbital wavefunctions.
Excellent quantitative agreement with theory for g-factor statistics.sample s-o strength gmax exp gmax th gmid exp gmid th gmin exp gmin th
• On breaking the wires, a fraction of them have the two thiol groups of the molecule bridging the gap between the electrodes - the signature of this is Coulomb blockade.
•Control experiments on gold wires, and gold wires with only the tpy-SH molecules attached to them do not exhibit Coulomb blockade.
• Unbroken wires are immersed in Co-(tpySH) solution for 1-3 days
• Wires are broken at low temperatures (4.2 Kelvin and below) - this is essential to create small gaps when the electrodes are broken, and to reduce diffusion.
Source Drain
GateV
Vg
I
I-V traces at different gate voltages - Coulomb blockade
• In resonant tunneling, we get a step in current each time the voltage on the source sweeps past an energy level on the molecule
• Tunneling can be assisted by phonons. When the difference between the source energy and the energy level on the molecule matches a vibrational mode’s energy, there is a step in current.
• In support of vibrational modes is the fact that the structure of the levels is similar for both charged states.
ResonantTunneling
Inelastic tunneling
7 meV normal mode
Visualizing low-energy molecular vibrations
Zeeman Splitting in a Magnetic Field
0 2 4 60.0
0.5
Peak
spl
ittin
g (m
eV)
Magnetic field (T)-0.50
6
3
0
-3
-6-0.40
V(m
V)
Vg (V)
Co3+ Co2+
-0.45
g = 2.1±0.21.0
magnetic field = 6 Tesla
S=1/2 for Co2+, S=0 for Co3+.
Higher-energy excitations.
E ~ 25 meV
Co
SH
HS
N NN
N NN
Shorter Linker Molecules -- Increased Coupling to Electrodes
Kondo-Assisted Tunneling via the Cobalt Atom
0T4T5T6T7T8T9T10T
0
1.0
1.2
dI/d
V(e
2 /h)
V (mV)-5 5 0-5 5
1.5K
18K0.8
1.4
1 10
1.4
1.2
1.0
0.8
T (K)
dI/d
V(e
2 /h)
0 3 6 9
-2.0
-1.0
0.0
1.0
2.0
Magnetic field (T)
V (m
V)
12 21 30Differential conductance (µS)
Zeeman Splitting of Kondo Resonance
ConclusionsMeasurements of electron-in-a-box energy levels provide a way to study in detail the forces acting on electrons
• Spin-orbit coupling
• Superconducting interactions
• Fluctuations in e-e interactions
• Ferromagnetism
Can make single-molecule transistors using designer molecules
• These molecules exhibit quantized electronic and vibrational states.
• Changing the length of the molecule changes the transistor characteristics.