research projects on mesoscopic physics
TRANSCRIPT
Introduction 1
Nanophysics: MENA5010/9010
The course is organized by Department of Physics, UiO
Lecturer: Pavlo Mikheenko, University of Oslo
Spring 2018
Lectures on physics of nanostructures
Student presentations (will be graded and form a part of exam)
Introduction 2
Pavlo Mikheenko
E-mail: [email protected]
http://www.mn.uio.no/fysikk/english/people/aca/pavlom/index.html
Physics building, Room FV404
Direct/Voice Mail: 22 8(5 7471)
Lecture plan and lectures:
Introduction
MENA5010/9010
Spring 2018
Introduction 3
http://folk.uio.no/pavlom/MEF5010-general.html
http://folk.uio.no/pavlom/MENA5010-2018.html
http://www.uio.no/studier/emner/matnat/fys/MENA5010/
Richard Feynman 29th December 1959 on APS Meeting at
Caltech: „There is plenty of room at the bottom“
Syllabus
Introduction 4
‘The purpose of the present book isto introduce the reader to thistopic from an experimental point ofview. “The reader” is herebyassumed to be a student of physicsor a related field, who has justfinished introductory courses, inparticular those on solid statephysics and quantum mechanics, andplans to study nanoscience moreclosely. The reader is picked up atthe knowledge he/she is likely tohave, and a ride is given to ongoingresearch activities in the field ofmesoscopic transport. Along theway, the elementary concepts andnanostructures are introduced.’
Introduction 5
Broad definition - Nanoscience and nanotechnology are all about relating and exploiting phenomena for materials having one, two or three dimensions reduced to the nanoscale.
What is nanoscience and nanotechnology?
Very broad area of science and
technology having many branches.
Beginning of this course
Introduction 6
The course aims at an introduction to basic principlesof nanophysics allowing working in research and development in nanotechnology.
You will learn principle of physics of nanometer-size systems with a focus on basic physical phenomena.
In addition to main theoretical concepts, the applications of nanophysics to existing and future electronics, will be discussed.
Introduction 7
Structure of the course
The course will offer lectures on basic principles behind nanoscience and nanotechnology and presentations of some topics by students.
These presentations are compulsory, they will be graded and the grading will be taken into account at the final examination.
There will also be few problems solving.
Midterm and end term evaluations will be carried out.
Introducing elements of Students Active Learning: reading chapter before lecture.
MSHRL: Met, Seen, Heard, Respected and Loved
Exam: 40% + 30% + 30% (10% + 10%).
Introduction 8
Nanoscience is referred to as a research area devoted to studies of various phenomena in small-size devices.
It is a cross-disciplinary field including physics, chemistry, and biology.
The key for understanding of nanoscience is mesoscopic physics.
The word ``meso'' reflects the fact that the size of the systems under consideration is located between microscopic (atoms) and macroscopic scales.
Nanomechanics
Nano-Electromechanics Nano-Optomechanics
Nano-OptoelectronicsNanophysics:Main trends and
crossroads
9Introduction
Introduction to Nanophysics 10
What is Nano?
1 nm =10-9 m= 10-7 cm
Nano means Small !
Introduction to Nanophysics 11
Many atoms, electrons, etc., are involved
Number of degrees of freedom is large
Nanoscale objects do not fully belong to the microcosm
Nano means Big !
Size
MicroNuclei
Atoms
Small molecules
MacroFluids
Crystals
Glasses
MesoNano-objects
Characteristic scales in nanoscience
Nanometer scale
Atoms Molecules &
Clusters
Electron
mean free
path
Bulk
materials
Length scale
MesoMicro Macro
Modern electronic devices belong to mesoscopic scale
12Introduction
Introduction 13
Nanophysics and Edvard Munch
Edvard Munch, 1863-1944
Press Release: The Nobel Prize in Chemistry 20174 October 2017The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Chemistry 2017 toJacques DubochetUniversity of Lausanne, SwitzerlandJoachim FrankColumbia University, New York, USA andRichard HendersonMRC Laboratory of Molecular Biology, Cambridge, UK"for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution"
Jacques Dubochet Joachim Frank2017
https://www.nobelprize.org/nobel_prizes/chemistry/
Richard Henderson
Press release
The Nobel Prize in Chemistry 2017
‘…in 1990, Richard Henderson succeeded in using an electronmicroscope to generate a three-dimensional image of a protein atatomic resolution. This breakthrough proved the technology’s potential.Joachim Frank made the technology generally applicable. Between 1975and 1986 he developed an image processing method in which theelectron microscope’s fuzzy twodimensional images are analysed andmerged to reveal a sharp three-dimensional structure.Jacques Dubochet added water to electron microscopy. Liquid waterevaporates in the electron microscope’s vacuum, which makes thebiomolecules collapse. In the early 1980s, Dubochet succeeded invitrifying water – he cooled water so rapidly that it solidified in its liquidform around a biological sample, allowing the biomolecules to retaintheir natural shape even in a vacuum.’
https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2017/press.html
The Nobel Prize in Chemistry 2017
https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2017/
The Nobel Prize in Chemistry 2017
https://www.nobelprize.org/nobel_prizes/chemistry/laureates/2017/
Introduction 18
Chemistry Nobel Prize 2016 for molecular nanomachines
Jean-Pierre Sauvage, Sir J Fraser Stoddart and Bernard L Feringa
Introduction 19
Physics Nobel Prize 2016 for topological phase transitions and topological phases of matter
David Thouless, Duncan Haldane and Michael Kosterlitz
Introduction 20
2016: 30 years of the Nobel Prize for scanning tunnelling microscopy (STM) and the first report of atomic force
microscopy (AFM).
Introduction 21
Nobel Prize for scanning tunnelling microscopy (STM)
The Nobel Prize in Physics 1986 was divided, one half awarded to Ernst Ruska "for his fundamental work in electron optics, and for the design of the first electron microscope", the other half jointly to Gerd Binnig and Heinrich Rohrer "for their design of the scanning tunneling microscope".
Superconductivity in Nanosystems 22
Tunneling effect
Ivar Giaever
1973
The Nobel Prize in Physics 1973Leo Esaki, Ivar Giaever, Brian D. Josephson
Prize motivation: "for their experimental discoveries regarding tunnelling phenomena in semiconductors and superconductors, respectively"Field: condensed matter physics, semiconductors
Beginning of nanophysics: in 1951, Gorter suggested that experiments by van Itterbeek andcoworkers, who measured the current through metal grains embedded in an isolated matrix, couldbe explained by single-electron charging.
Electron phase coherence
Quantum tunneling: Ivar Giaver
Following on Esaki's discovery of electron tunnelling insemiconductors in 1958, Giaever showed that tunnellingalso took place in superconductors (1960).
Giaever's demonstration of tunnelling in superconductors stimulated BrianJosephson to work on the phenomenon, leading to his prediction of theJosephson effect in 1962. Esaki and Giaever shared half of the 1973 NobelPrize, and Josephson received the other half.
May 2012, Lofoten
Official opening on 7 September 2016http://www.mn.uio.no/geo/om/aktuelt/aktuelle-saker/2016/geomagnetisme.html
http://www.iggl.no/
Lake Shore PMC MicroMag 3900 Vibrating Sample Magnetometer (VSM)
Instruments for Paleomagnetic Measurements and Rock Magnetic Analyses
AGICO JR-6A Spinner Magnetometer
Introduction 25
2016: Memristor behaves like a synapse
Researchers led by Qiangfei Xia and Joshua Yang at the University of Massachusetts at Amherst in the US have made a "diffusive" memristor that emulates how a real synapse works. The device could be used as a key element in integrated circuits and next-generation computers that mimic how the human brain works.
The new device is made from a memory resistor or memristor (a resistor that “remembers” how much current has flowed through it). Unlike other modern-day electronics memories like those made from CMOS devices, memristors are able to remember their state (that is the information stored in them) even if you lose power. They also use much less energy and, importantly, so-called diffusive memristors can realistically mimic how ions, such as
Ca2+, diffuse through synapses.http://nanotechweb.org/cws/article/tech/66462
Introduction 26
2016: Other highlights
• Graphene patch detects glucose in sweat
• Quantum-dot barcodes for diagnosing disease
• Polymeric nanoparticles deliver anti-inflammatory proteins
• Nanotube array transistor breaks new record
• Graphene composite enables metre-sized flexible displays
• 2D perovskite solar cells break new efficiency record
• Self-powered textile could be woven into smart clothes
• Nanostructured supercapacitors empower sustainable storage
Lenovo folding displaySamsung Galaxy S8 with 10-nm design Qualcomm Snapdragon 830 microprocessor
Flexible LG display
http://nanotechweb.org/cws/article/tech/67338
t19. What applications of nanophysics do
you know?
Introduction 27
2017 highlights
• World's Smallest Christmas Card Offers Season's Tiniest Greetings
• Practical Quantum Computers
• Self-Driving Trucks
• Brain implants to restore the freedom of movement
• Amazing Artificial Intelligence Achievements
• Samsung: Pushing the boundaries in OLEDs
• Samsung Galaxy S8 with 10 nm design released
• 4K and Ultra HD screens: the hot new resolution
Quantum ComputerWorld's Smallest Christmas Card
http://nanotechweb.org/cws/article/tech/70720
t19. What applications of nanophysics do
you know?
Introduction 28
2017 highlights
• Graphene composite provides wireless power
• Designing highly reversible aluminum-ion
batteries with graphene
• Graphene-oxide membranes filter organic solutions
• Brain-penetrating nanoparticles restore neuron function
• Nanotechnology takes on microbial drug resistance
• Nanoparticles resurrect antibacterial drugs
• High conductance detected in a human integrin protein
• Nano-patterning technique records structural color at low cost
Nano-cone arrays produce structural color by diffraction.
Fixed-junction device for protein measurementNanomaterials help fight infectious disease
http://nanotechweb.org/cws/article/tech/70720
t19. What applications of nanophysics do
you know?
Introduction 29
January 3, 2018
Cornell University
‘Robotics experts have made a robot exoskeleton that can rapidly change its shape upon sensing chemical or thermal changes in its environment. And, they claim, these microscale machines equipped with electronic, photonic and chemical payloads could become a powerful platform for robotics at the size scale of biological microorganisms.’
https://www.sciencedaily.com/releases/2018/01/180103160115.htm
Physicists build muscle for shape-changing, cell-sized robots
Introduction to Nanophysics 30
What number of electrons can weexpect in mesoscopic objects?
C – 6 el./atom
(5 nm)3 ~ 125 x 30 = 3750 atoms
1 nm3 ~ 30 atoms
Ga – 31 el./atom
As – 33 el./atomGe – 32 el./atom
https://www.chem.wisc.edu
Hund's rules
Introduction to Nanophysics 31
Electron orbitals and shells in atoms
http://chemistry.stackexchange.com/questions/8598/maximum-number-of-electrons-each-shell
In atoms number of electrons per shell is 2n2: 2, 8, 18, 32
In atoms number of electrons per orbit is 2(2l+1): 2,6,10,14,18,22,26
Introduction to Nanophysics 32
Role of surface effects in mesoscopic objects
https://www.chem.wisc.edu
A / V = 6a2 / a3 = 6 / a = 6 V-1/3
V = a3 (2a)3 = 8 a3 (5a)3 = 125 a3 (10a)3 = 1000 a3
Percentage of „surface atoms“:100% 100% 78,4% 48,8%
Macroscopic: V = (108a)3 = 1024 a3 A = 6 (108a)2 = 6 1016 a2
Percentage of surface atoms: 6 10-6 % !!! (negligible)
t2. What happens to the laws of physics
on a mesoscopic scale? Give an
example.
Introduction 33
Classical vs. Quantum Physics for mesoscopic objects
Classical MechanicsElectrodynamicsThermodynamics
Quantum MechanicsQuantum ElectrodynamicsQuantum Statistics
Mesoscopic phenomena (quasiclassical regime)
t2. What happens to the laws of physics
on a mesoscopic scale? Give an
example.
Moor’s law and necessity for mesoscopics
Introduction 34
http://en.wikipedia.org/wiki/Moore's_law
t1. What is Moore’s law? Why do we
need Nanophysics?
35
CMOS TECHNOLOGY
Intel’s Prescott processor
(released March 2004):
• 150 million transistors
• 90 nm design rules
• 3.4 GHz clock frequency
DRAM chips:
4 Gb chips demonstrated
(~ 109 transistors/cm2)
Intel’s Norwood (Pentium 4 - 130 nm) processor
In 2010 chips were based on the design rule of 22 nm.
Introduction20 years back we were already well inside nanotechnology!
complementary metal-oxide semiconductor technology
Dynamic random-access memory
Progress in miniaturisation
Introduction 36
By Cmglee - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=16991155 t1. What is Moore’s law? Why do we
need Nanophysics?
Introduction 37
Main ingredients of nanoelectronics
• Two-dimensional electron gas (2DEG)
• Quantum wires and point contacts
• Quantum dots
• Nano-electro-mechanical systems
• Vibrating carbon and non-carbon nanotubes and other
molecular devices
• Devices using superconductivity and magnetism at nanoscale
– Devices for quantum computation
• Spintronics – manipulation of electron spin
Novel devices
Introduction 38
Samples, materials, and experimental techniques
Semiconductor devices: GaAlAs heterostructures(optoelectronics, high mobility under modulation doping)
Si-MOSFET(silicon has a natural oxide, that is very important)
New systems: Carbon nanotubes, etcStructure of a carbon nanotube. The circles denote carbon atoms in a graphite sheet, which is rolled up and forms a tube with a diameter of a few nanometers. The ends aresupposedly capped by a carbon hemisphere.
t18. What semiconducting materials are
usually used in the nano-industry and
nanophysics experiments? What are
reasons for that?
Introduction 39
Self-assembled quantum dots are periodic arrays of “artificial atoms”.
They are considered to be promising systems for heterostructure lasers.
t18. What semiconducting materials are
usually used in the nano-industry and
nanophysics experiments? What are
reasons for that?
Ga[Al]As
Si
Materials for nano-industry
Introduction 40
SINGLE-ELECTRON
SINGLE-MOLECULE TRANSISTORS
J. Park et al. (2002)
-2 -1 0 1 2-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Vt (for Q
0 = 0)
Qe = 0
Qe = e/2
C1 = C
2 = C/2
R1 = R
2 = R/2
kBT = 0.01 e
2/C
-2 -1 0 1 2-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-2 -1 0 1 2-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-2 -1 0 1 2-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-2 -1 0 1 2-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Cu
rre
nt I
(e/R
C)
-2 -1 0 1 2-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Source-drain Voltage V (e/C)
(b)
see also:
- E. S. Soldatov et al. (1996)
- H. Park et al. (2000)
- N. Zhitenev et al. (2002)
- S. Kubatkin et al. (2003)
SET within the “Orthodox” theory:
t18. What semiconducting materials are
usually used in the nano-industry and
nanophysics experiments? What are
reasons for that?
Introduction 41
Growth
MBE
Fabrication
EBL Quantum corralls
Characterization
STM
Instrumentation for nanoscience and nanotechnology
Introduction 42
New laws of Nature at nanoscale?
In a classical resistor, the resistance is due to electron scattering.
Otherwise electrons are just accelerated by the electric field.
QM: Particle or wave?
2
Quantum modes in the wire
1
2
t2. What happens to the laws of physics
on a mesoscopic scale? Give an
example. t5. What length scale is important for a
double slit experiment in the solid state?
Please explain.
Electron diffraction is controlled by phase coherence length
Introduction 43
Classical versus quantum physics
t2. What happens to the laws of physics
on a mesoscopic scale? Give an
example.
Introduction 44
Basic problems
• Features of nanoscale systems:– Quantum transport– Specific electron-electron interaction, which is more
pronounced in low-dimensional systems– Stronger role of disorder– Enhanced role of contacts and electromagnetic environment
• Nano-devices are usually out of equilibrium, which requires special understanding
All these issues are far from being fully understood
It is new research area with rich physics and chemistry!
t2. What happens to the laws of physics
on a mesoscopic scale? Give an
example.
Introduction 45
Quantum Mechanics of Interacting Particles
Condensation Wigner crystal
Self-assembly systems
Scheme for molecular
manufacturing
Encapsulated 4 nm Au
particles self-assembled into
a 2D array supported by a
thin film, Anders et al., 1995
Nanomaterials
46Introduction
Introduction 47
In nanomaterials electrical and mechanical energies are comparable
Electrical and mechanical modes are strongly coupled
Nano-electro-mechanics
Electron “shuttles” Molecular motors Carbon nanotubes
Examples of the systems
Introduction 48
“Shuttle” transfer of electrons
A movable cluster “conveys” electron one by one
In some cases electro-mechanic instabilities can take place
“Shuttle” transport has been observed in several concrete systems
Introduction 49
Solar cells with nanoparticles: Nanoplasmonics
Metallic nanoparticles embedded in the host system close to the
active layer
Main principle: Plasmon resonances due to nanoparticles strongly enhance the time, which photons spend close to the active layer
Simulation of increased light
intensity beneath a metal nanoparticle
on a silicon cell
Key players: Centre for Sustainable Energy Systems at the Australian NationalUniversity (ANU) ; Caltech, US; FOM-Institute, AMOLF,the Netherlands.
Introduction 50
Mesoscopic Superconductivity
Studies of individual magnetic vortices by magneto-optical (MO) imaging
Tom Henning Johansen et al., Univ. Oslo
B dA = 0Fluks kvantum:
x
l
JB(r)
2003
Introduction 51
Example: Edge effects
prøvekant
MOI single vortices allows to study and influence mesoscopic structure
of vortex matter
One can take snapshots at different times, and in this way observe vortex dynamics
10 m
Introduction 52
More about physical scales
Classical length – electron mean free path,
Quantum length – de Broglie wavelength of an electron having the Fermi energy:
This scale is relevant to the size quantization –quantum films, wires, and dots
t4. What is de Broglie wavelength of
electrons and size quantization?
Introduction 53
Another important scale – phase coherence length,
Scale introduced by Coulomb interaction and depending on the device capacitance, C
- relevant to single-electron tunneling
Interplay between different scales leads to a rich picture of transport through nanosystems.
The specific properties of different regimes can be used for various applications.
t6. What is the role of charging effects on
nano-scale?
Introduction 54
Basic classification of transport regimes
mean free path
phase coherence length
Fermi wavelength
t3. What are characteristic length scales
and specific parameters that define
transition to mesoscopic regime?
2DEG is a generic object for new physics
Nobel Prizes 1985, 1998, 2000
It serves as a building block for electronic
devices
Two-dimensional Electron Gas (2DEG)
Metal-Oxide-Semiconductor (MOS) structures
2DEG is formed at the semiconductor-insulator
interface
Semiconductor heterostructure
2DEG is formed at the interface between two semiconductors
Band gap engineering
We will come back to these structures later
55Introduction
Introduction 56
Quantum Wires and Point Contacts
Split-gate structures
Cleaved structures
Carbon nanotubesPoint contacts
Introduction 57
Ballistic transport, , quantum point contact
The measurement to the right shows the conductance of the wire as a function of the gate voltage.
At low temperatures, a conductance quantization in units of 2e2/h is visible, which vanishes around 20 K.
To the left, the surface topography of a GaAs microchip is shown. The picture has been taken with an atomic force microscope.
The chip hosts a quantum film about 30 nm below its surface, which is removed underneath the bright lines. A small and short wire of length 140 nm and width 80 nm connects source and drain.
t7. What length scale is important for
ballistic transport? How is it influenced
by temperature?
t10. What is the quantum point contact
(QPC), and at what temperatures and
lengths does it usually operate? What
length scale is important for QPC?
Introduction 58
Quantization of conductance vs. gate voltage!
New universal unit of resistance – h/e2
Absent in classical theoryt8. Does a ballistic wire have infinite
conductance?
25.812 KOhm
Conductance quantum: 7.748 10-5 S
t9. What is the quantum of conductance?
Where does it appear? What is the
value of quantum resistance in Ohm?
Introduction 59
The quantum Hall effects and Shubnikov-de Haas oscillations
Shubnikov-de Haas oscillations and the quantum Hall effect. We look at a measurement of the longitudinal and the Hall resistance (Rxx and Ryy, respectively), of a two dimensional electron gas, as a function of a magnetic field applied perpendicular to the plane of the quantum film. The experiment has been performed at a temperature of 100 mK.
The Hall resistance is quantized in units of h/2e2.
Classical
Hall effect
t11. What is the quantum Hall effect and
Shubnikov–de Haas oscillations? Are these
effects linked? In what systems do they take
place? In what units is resistance quantized?
What temperatures and magnetic fields are
essential for these effects?
Introduction 60
Phase coherence
The resistance of a small ring with a diameter of about 1 micron (the light gray areas in the inset) as a function of a magnetic field applied perpendicular to the ring plane shows periodic oscillations, known as Aharonov-Bohm oscillations. They indicate that a significant fraction of the electrons traverse the ring phase coherently. Dephasing is caused by inelastic (e-ph, e-e) scattering. Diffusive coherent systems are possible. E-e scattering does not contribute to resistance.
At low temperatures
t13. What is the Aharonov–Bohm effect?
What is typical geometry of the device
showing this effect? What length scale
is important for this effect, and by what
kind of scattering is it influenced? Is
resistance a local property in this effect?
Is high magnetic field and low
temperatures necessary for it?
Introduction 61
Single-electron tunneling and quantum dots
The main figure shows the conductance through the island as a functionof the gate voltage VI applied to region I. VI tunes the potential of the island. The conductance peaks indicate that only for a particular island potential, electrons can be transferred betweenthe island and the leads. The left inset shows a fit to a function one would expect for peaks thatare governed by thermal smearing of the Fermi function.
The right inset shows again the surface topography of a semi-conductor with a two dimensional electron gas underneath. The bright lines enclose a small island. It is coupled to source and drain via two quantum point contacts, forming tunnel barriers for the electrons. The barriers are tuned by adjusting the voltages at the gates Ql and Q2.
t15. What is a quantum dot and what is
its relation to single electron quantum
transistor?
Introduction 62
Quantum Dots
Lateral quantum dots
Vertical Artificial atoms – new periodic table
Coulomb blockage!
t15. What is a quantum dot and what is
its relation to single electron quantum
transistor?
Ivar Giæver
In atoms number of electrons per shell is 2n2: 2, 8, 18, 32
In artificial atoms number of electrons per shell is : 2, 6, 12, 20
Introduction 63
Gate
DotElectron
Attraction to the gate
Repulsion at the dot
Cost
At
the energy cost vanishes !
Coulomb blockade
Single-electron transistor (SET)
t14. What is single-electron tunneling
and the role of capacitance in this
effect? What is the characteristic energy
that plays a major role in this effect?
Fermi wavelength
Introduction 64
21. Why does Fermi wavelength
decrease with the electron density?
What is the relation between Fermi
wavelength and electron density in
different dimensions? Can you derive
this? Can you find mistakes in TH p.
158 (pdf)?
Update of solid state physics 65
Electron density of states in the effective mass approximation as a function of energy, in one, two, and three dimensions
12. What is the role of Fermi wavelength
in changing the dimensionality of
mesoscopic systems? Is it related to de
Broglie wavelength? What are the
implications of changing dimensionality?
What is the density of states as function
of energy per unit volume in systems of
different dimensions? Can you derive
this?
Density of states
Update of solid state physics 66
Density of states
Two dimensional system , periodic boundary conditions
Momentum is quantized in units of
A quadratic lattice in k-space, each of them is g-folddegenerate (spin, valleys).
Assume that , the limit of continuous spectrum.
Number of states between k and k+dk:
Update of solid state physics 67
Number of states per volume per the region k,k+dk
Density of states -Number of states per volume per the
region E,E+dE. Since
3
68
Electron spin
• Was first introduced in 1925 by Uhlenbeck and Goudsmit to explain the hyperfine structure of the atomic spectrum.
• A theoretical foundation has been provided in 1928 by Dirac by making a relativistic correction to the wave equation.
Spintronics
16. What is the role of electron spin in
solid-state physics? What characteristic
length scale is important in nano-
spintronics? Do you know any
commercial devices that use spin of
electrons?
Giant magnetoresistance 69
In GMR, resistance depends on the relative orientation of the electron spin-defined magnetizations of the ferromagnetic layers.
Giant magnetoresistance
16. What is the role of electron spin in
solid-state physics? What characteristic
length scale is important in nano-
spintronics? Do you know any
commercial devices that use spin of
electrons?
70
Electronics applications
Spintronics
16. What is the role of electron spin in
solid-state physics? What characteristic
length scale is important in nano-
spintronics? Do you know any
commercial devices that use spin of
electrons?
t19. What applications of nanophysics do
you know?
Update of solid state physics 71
Mesoscopic effects: role of temperature
17. What energies and temperatures are
typical for mesoscopic electronic
devices? What is the relation between
temperature and electron energy? What
is typical length scale at which the
mesoscopic regime takes place at
different temperatures?
The typical length scale at which the mesoscopic regime is reached depends on
the temperature. The numbers below give an order of magnitude.
Temperature (K) L (nm)
4.2 (liquid helium) <5000
77 (liquid nitrogen) <100
300 (room temperature) <10
t20. What determines the temperature at
which a mesoscopic effect vanishes?
How is it in contrast with
superconductivity?
Quantum scattering length
Introduction 72
22. What is quantum scattering length and quantum scattering time? Is it the same as Drude scattering time τ?
t22. What is quantum scattering length
and quantum scattering time? Is it the
same as Drude scattering time τ?
Update of solid state physics 73
Diffusive transport
Between scattering events electrons move like free particles with a given effective mass.
In 1D case the relation between the final velocity and the
effective free path, l, is then
Assuming where is the drift velocitywhile is the typical velocity and introducing the collision time as we obtain in the linear approximation:
Mobility
Dephasing time
Introduction 74
t23. How does dephasing time of
electrons depend on T at low and high
temperatures?
τ