The University of Tokyo, The Institute For Solid State Physics

1
December, 2005 University Lecture Science of
Material
Lecture 6 What is Condensed Matter Physics?
Lecture 7 Quantum Mechanics and Artificial
Material -- High-tech and the
State-of-the-art Physics Lecture 8 Atom Control
and Quantum Control --Nano-science and
Quantum Information Lecture 9 Diverse Matter
and Physical Property

• The University of Tokyo, The Institute For Solid
  State Physics
• Yasuhiro Iye

2
Review of Lecture (1)

• Atom control and quantum control
• Observation and manipulation of atom
• Scanning probe microscope (STM and AFM)
• Nanoscience
• Macroscopic quantum phenomenon
• Quantum statistics
• Boson and fermion
• 4He and 3He
• Superfluidity of Liquid helium (4He).
• Bose-Einstein condensation of vapor atom.

3
Review of Lecture (2)

• Quantum information processing
• Measurement in quantum mechanics
• Stern-Gerlach experiment
• Loss of interference by observation (decoherence)
• EPR experiment and Bells iequality
• Cryptsystem
• The key and encryption
• Public key encryption and factorization in prime
  numbers
• Quantum computer
• Qubit
• Quantum gate
• Quantum cryptosystem (private key distribution)

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Todays Topics

• Property of electron in solid state (band
  structure)
• Metal, insulator, and semiconductor
• Magnetism
• Superconductivity

5
Property of Electron in Solid State (Band
Structure)
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Property of Electron in Solid Body

• Quantum mechanically, understand the behavior of
  electrons found in potential where atoms are
  arranged periodically.
• Two ways of understanding
• Place the atoms in a order? tight-binding
  electron model
• Start from free space to introduce the periodic
  potential ? nearly free electron model

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Arrangement of Atoms
Hydeogen moleculeH2
Periodic arrangement of hydrogen atoms
-e
e
e
-e
The superpositioning electron cloud in the
adjacent atoms may cause the electron to jump
between two orbitals the electrons travel around
in the whole crystal.
8
The Energy Spread by Electron Jumping
Each energy level of electron in atom may spread
and form the bands caused by the electron
jumping.
9
Scattering of Waves Obtained by Periodic Structure
The waves are lapping against the stakes that are
lined up in a pond.
The wavelength that are integral multiplication
of periodic arrangement in the scattering body is
reflected strongly (Bragg reflection) the
stationary waves are formed by incident waves and
reflected waves ? traveling waves cannot be
formed from particular wavelengths.
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Formation of Band and Gap via Bragg Reflection
Energy
Energy
Band
Gap
Band
0
k
p/a
-p/a
0
k
Wave number (momentum)
Wave number equivalent to the period.
The electrons existing energy range (band) and
absence range (gap) are formed.
The role of periodic potential ? change the
dispersion relation between energy and momentum
of the electron. (Bloch electron)
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Electron Band Structure
Electron in crystal (Bloch electron)
Near-free electron model
Tight-binding model
Localized electron
Itinerant electron
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Metal, Insulator, and Semiconductor
13
Metal and Insulator
The band filled halfway
Current flows
Electrify the field
The band filled completely
Current does not flow
Energy
Insulator (Band insulator)
Metal
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Behavior of Bloch Electrons
Zero velocity
Momentum space
e
Negative velocity
Zero velocity
Positive velocity
In real space
0
k
Electric field E
Insulator
Metal
Metal
In the real existing materials, the slightly
slipped off Fermi surface caused by the
scattering is the form of the stationary state.
Will electrons simply travel back and forth after
scattering completely disappears?
No change in occupying process of electron in the
electric field.
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Electron and Hole in Semiconductor
Electron
Hole
Thermal excitation
Light absorption
In semiconductors, very few carries (electron in
conduction band and hole in valence electron)
generated by thermal excitation or the optical
absorption are the responsible for electric
conduction.
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Temperature Change in Electric Resistance
Semiconductors (insulators) have low electric
resistance because many carrier electrons and
holes are generated by thermal excitation under
higher temperature.
Semiconductor
Electrical resistance
In metals, the number of existing electrons will
not be changed by the temperature. Under high
temperature, the lattice oscillation causes
scattering against electrons. Under low
temperature limit, electron scattering is
determined by the impurity and deficiency.
Metal
Temperature
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Doping
Donor (Electron donor)

Similar to hydrogen atom
Acceptor (Electron acceptor)
(Electron) donor impurity is added to feed the
electrons in conduction band is called n-type
semiconductor. (Electron) acceptor impurity is
added in order to form holes in valence band is
called p-type semiconductor.
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Light Emitting Diode
The color of the emitting light is determined by
the band gap of the semiconductor. 1eV 3eV
UV Blue
19
Metal-insulator Transition (Simple)
High Pressure
Energy
Metal (Half metal)
The band becomes wider as the lattice becomes
contracted via the application of high pressure.
Superposition between valence band and conduction
band occurs. ( The energy gaps are closed.)
Insulator (Band insulator)
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Mott Insulator
Children play on the bunk beds
The children who show up later have to go to the
upper bunk to play.
The state where there are two electrons occupied
the same orbit, the energy is increased by the
amount of interelectron Coulomb repulsion U .
When number of children is less than the number
of beds
When number of children is greater than the
number of beds
When the number of children and the number of
beds are equal
?cannot make any move
Mott insulator
In order to make a movement, the electrons have
to climb onto the upper bunk.
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Strongly Correlated Electron System

• The system in which the strong Coulomb
  interaction of electrons governs the behavior of
  electron, e.g., Mott insulator, is called
  strongly correlated electron system.
• Many dynamic phenomenon such as high-temperature
  superconductivity and giant magnetoresistance
  effect take place in the strongly correlated
  electron system.
• The behavior of strongly correlated electron
  system is intrinsically complicated many-body
  problem, which many physicists currently working
  to solve its physical nature.

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Magnetism
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Ferromagnetism
In order for a material to hold property of a
magnet (ferromagnet)
(1)Atom or molecule have magnetic moment
(micro-magnet).
(2)Those magnetic moments are aligned in the same
direction.
(3)Macroscopic sample possesses the entire
magnetization.
Magnetic domain
Domain wall
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Occupying Process of Electron Energy Levels
Many-electron atom
He
H
Transition metals
C
N
F
Ne
B
O
Li
Be
S
Cl
Ar
Al
Si
P
Mg
Na
Ca
Ti
V
Cr
K
Sc
Mn
Fe
Co
Ni
Cu
Se
Br
Zn
Ga
Ge
Kr
As
Rb
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Magnetic Moment of Atom (Ion and Molecule)
How the electrons are filled here?
To avoid the interelectron Coulomb repulsion as
possible, the electrons should be aligned in the
same spin direction.(Hunds rule)
Fe2(six d electrons example)
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Alignment of Magnetic Moment in Atom
What is the aligning force of the atoms magnetic
moment?
Is it the magnetic dipole interaction In
classical electromagnetism?
Too weak as the interaction (energylt1K)
Two spins are in parallel (spin-triplet term)

(
)/v2
Quantum-mechanical effect Exchange
interaction (difference of Coulomb interactions
due to spin direction)
Difference in Coulomb interaction energy
(exchange interaction)
Two spins are antiparallel (spin-singlet term)
Ferromagnetic J gt0
-
(
)/v2
Antiferromagnetic J lt0
Energy -J s1s2
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Varieties of Magnetic Body
Ferromagnetic (Includes macroscopic
Magnetization.)
Ferrimagnetic (Includes macroscopic
Magnetization.)
Antiferromagnetic (No macroscopic magnetization.)
Ordered state
Disordered state
Under high temperature
Paramagnetic (No macroscopic magnetization.)
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Magnetic Order (Corporative Phenomenon and Phase
Transition)
Magnetic field
Generate the magnetic field
Disordered state under high temperature
The spin aligning force of exchange interaction
represents a very large value when converted into
magnetic field 100 tesla.
The spins attract the adjacent spins to stay
parallel to each other.
Ferromagnetic ordered state
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Magnetic Domain and Domain Wall
Magnetizing process of ferromagnetic body
Magnetic hysteresis curve
Magnetization
Magnetic field
0
Magnetic field
Magnetic domain
Domain wall
Magnetic domain
30
Spintronics
Electronics takes advantage of the freedom in
the electron charges. Spintronics takes
advantage of both the freedom in electron charges
and the spins.
Spin transistor
Spin-valve device
The current flows smoothly when magnetization is
in the same direction.
Activation of domain wall by electric current
flow (spin polarization).
The current flows less smoothly when
magnetization is in the opposite direction.
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Superconductivity
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Superconductivity of Elements
Superconductivity of Elements
Elements that become superconductivity in normal
crystal phase.
Elements that become superconductivity under
particular conditions, e.g., high pressure and
amorphous.
No superconductivity phase have been found.
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Diagram of Superconducting Transition Temperature
(Under high pressure)
(Under high pressure)
Jun.
Apr.
Mar.
Jan.
Feb.
Liquid nitrogen
Mercury
Resistance
Liquid neon
Liquid hydrogen
Temperature (K)
Year
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Basic Property of Superconductivity
Perfect conductor (zero resistance)
Quantization of magnetic flux
F nF0
It is same as the quantization of circulation
(vortex) at superfluidity.
Electrical resistance
Superconductive transition temperature
Energy
Temperature
Perfect conductor
??
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Superconductor ? Perfect Conductor
Although the shielding current can flow when the
field is electrified in a Conductor (Lenzs
law), the damping occurs immediately due to the
resistance.
Perfect conductor allows the shielding current to
flow continually without damping.
In this case, the state depends on how the field
is being electrified.
Meissner effect (total diamagnetism) The magnetic
field is completely excluded in a
superconductor. Shielding current of
superconductor is the current under thermal
equilibrium state.
Superconductivity phase (Meissner state)
Normal phase
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Type I Superconductor and Type II Superconductor
Type I superconductor
Type II superconductor
Lower critical magnetic field
Critical magnetic field
Upper critical magnetic field
Mixed state
Normal state
Meissner state
Normal state
Type II superconductor is the most practically
used super conductivity in the materials.
Meissner state
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Quantum Magnetic Flux (Vortex Filament)
The mixed state of type II superconductors.
Quantum magnetic flux (vortex filament)
Repulsive force is acted on between the vortex
filaments.
Magnetic flux lattice (Abrikosov lattice)
Triangular lattice
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Observation of Magnetic Flux Lattice
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Lorentz Force and Pinning for Vortex Filament
Motion velocity of vortex filament v
Pinning of vortex filament
Lorentz force
Current
The energy dissipation do not occur if the vortex
filament is not pinned tightly.
Vortex filament
Electric field
Electric field occurs when the vortex filaments
start to move. Generation of the electric field
in the direction of current implies that there is
a non-zero electric resistance (energy
dissipation) being generated.
Lorentz force vs. pinning Electric current
density where vortex filament starts moving ?
Critical electric current density
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Hard Superconductivity
Strong pinning of vortex filament in a
superconductivity.
Magnetic hysteresis curve
Magnetization
Shielding current flows until it reaches the
critical current ?The gradient for magnetic flux
is being determined.
Magnetic field
Formation of a sand hill (Critical
self-organization state)
41
Josephson Junction
Y0 e iq1
Y0 e iq2
Y0 e iq1
Y0 e iq2
Tunnel junction
Weak bonding
Josephson current The phase difference between
junctions.
Superconducting quantum interference device
(SQUID)
Superconducting current in a circuit periodically
changes by unit magnetic flux quantum.
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Mechanism of Superconductivity
What about the origin of gravity? Electron-lattice
interaction
There should be a net attraction from the
interaction of electron lattice as long as the
interelectron attraction remains greater than the
Coulomb repulsion.
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Bardeen-Cooper-Schrieffer (BCS) Mechanism
Interelectron attraction is greater than the
interelectron Coulomb repulsion force.
Size of Cooper pair
Formation of Cooper pair
Coherence length
Bose-Einstein condensation of the Cooper pair ?
Superconductivity state
For ordinary molecules, the size of molecules are
smaller than the interparticle distances.
Cooper pairs are in the superposition state.
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Anisotropic Superconductor

Symmetric property of the Cooper pair.
s wave (l 0) (Spin-singlet term)
p wave (l 1) (Spin-triplet term)
d wave (l 2) (Spin-singlet term)
Ruthenium oxide UPt3 and superfluidity of 3He.
Most common superconductor.
E.g., Copper oxide high-tempereature
superconductor.
45
Exotic Superconductor

• Copper oxide superconductors (YBa2Cu3O7 and
  Bi2Sr2CaCu2O8)
• Sr2RuO4
• Heavy electron system (UPt3 and CeCu2 Si2 )
• Organic superconductors
• ((TMTSF)2PF6 and (BEDT-TTF)2Cu(NCS)4)
• MgB2
• Alkali-doped fullerene K3C60
• Boron-doped diamond

46
Is Room Temperature Superconductivity Possible?
Superconductivity transition temperature
(Under high pressure)
(Under high pressure)
Characteristic energy scale for the lattice
oscillation.
Jun.
Apr.
Intensity of electron-lattice interaction.
Mar.
Jan.
Is the limit around 30K?
Feb.
Liquid nitrogen
Critical temperature (K)
Liquid neon
Characteristic energy scale for elementary
excitation that mediates interelectron attraction.
Liquid hydrogen
Intensity of interaction.
Year
Room temperature superconductivity there is no
evidence to prove its impossibility.
47
Summary

• Property of electron in solid state (band
  structure)
• Band and Gap
• Metal, insulator, and semiconductor
• Conduction carriers
• Metal insulator transition, Mott insulator, and
  strongly correlated electron system.
• Magnetism
• Magnetic moment of atom ? exchange interaction
  ?magnetic domain structure.
• Spintronics
• Superconductivity
• Basic property of superconductor
• BCS mechanism
• Exotic superconductor

48
University Lecture Science of Material
Lecture 6 What is Condensed Matter Physics?
Lecture 7 Quantum Mechanics and Artificial
Material -- High-tech and the
State-of-the-art Physics Lecture 8 Atom Control
and Quantum Control --Nano-science and
Quantum Information Lecture 9 Diverse Matter
and Physical Property

• The University of Tokyo, The Institute For Solid
  State Physics
• Yasuhiro Iye

49
Condensed Matter Physics (Material Science)

• Study of the dynamic properties (physical
  properties) in dynamic matters based on the
  understanding of the fundamental principles in
  physics (quantum mechanics).
• The catch ball between experiment and theory.
• Experiments that can approach the very essence of
  quantum mechanics have been already performed.
• Basic study of the materials such as the electron
  devices and optical communications of the
  fundamental modern civilization .
• ? Covered in lectures by Dr. Komiyama.