Quantum Weirdness Part 6 Quantum Weirdness in Materials Quantum Cryptography Quantum Teleportation Quantum Snake Oil
Quantum Weirdness in Materials Why Materials Behave as they do
Combining Atoms Into Molecules • Molecular Orbital Theory The two 1s levels of two hydrogen atoms combine to form the 1 σ orbitals in H 2 Still producing discrete energy levels Gerhard Herzberg, Nobel prize 1971
Carbon Dioxide CO 2 • Triatomic molecule O=C=O • Shape depends on the shape of the orbitals, which depends on the wave equations
• Symmetric stretch does not absorb infra-red radiation • The three asymmetric stretches do absorb in the infra-red • This is what makes CO 2 a Greenhouse Gas
Electronic Orbitals in a Solid • Now we are combining ~10 23 atoms together. • The discrete energy levels are so close together, that they form a BAND Band Gap • Note this a gap in energy, not a distance
• The bands in the solid are filled up from the bottom with the electrons Part filled Like this multilevel fountain in Garda, Italy
• If a band is full, then the electrons can’t go anywhere and can’t be used for conducting electricity • If a band is partly full, then the electrons can slosh about, if a voltage is applied, and can move Metal Conduction Band partly filled with electrons
Insulator Valence band full Conduction band empty Large energy gap Conduction Band Δ𝐹 𝑏𝑞 Valence Band
Semiconductor Valence band full Conduction band empty Small energy gap Conduction Band Silicon 𝐹 𝑐𝑏𝑜𝑒 Valence Band
• A semiconductor has a Conduction Band filled band, but the gap 𝐹 𝑐𝑏𝑜𝑒 to the next level is small. Valence Band • At room temperature, a few electrons have sufficient energy to jump the gap, into the conducting band • Now we have a few electrons Conduction Band in the conduction band and a partly empty valance band Valence Band • Both can now conduct
Semiconductors and Doping • We can control the conductivity by adding impurities like Boron or Phosphorus to the semiconductor E gap E gap Conduction Band Conduction Band Donor level Acceptor level Valence Band Valence Band Doping with n-type Doping with p-type 12
Diodes: Very Useful In Circuits • Devices which only let current (charge) flow one way • They were invented in 1905 by Sir John Fleming (tubes/valves)
Semiconductor Diodes • A semiconductor device which does the same thing as the vacuum tube device • A p-type and an n-type semiconductor placed back- to-back p- type n- type Electron rich Electron deficient Current can flow
Inside the diode, electrons are moving between quantum states Conduction Band Conduction Band Donor level Acceptor level Valence Band Valence Band n-type p-type
Light Emitting Diodes • If the electrons drop between levels, they can give off visible light, if the energy difference is correct Running lights on an Audi
• Very efficient, as they only produce light in a very narrow set of wavelengths • Low power • Good replacements for incandescent lightbulbs, as they don’t emit in the infra-red • 2 Watts LED equivalent to a 15 W incandescent
• Some LEDs emit infra-red light, so invisible to the human eye • Most TV remote controllers use an IR-LED to send the signals
• Blue LEDs proved very difficult to make! Isamu Akasaki, Hiroshi Amano, and Shuji Nakamura: Nobel Prize in Physics 2014
Photodiodes • The diode can be used to detect photons. Increased current when light shines on the diode Conduction Band Conduction Band Valence Band Valence Band
• The TV has an infra-red photodiode receiver to pick up signals from the remote control • A solar cell, which makes energy from sunlight is an example of a photodiode
Diode Lasers • In the ordinary LED, the photons are emitted in random directions, because it is a spontaneous decay process • Careful design of the semiconductor layers can result in photons being produced by stimulated emission
Photodiodes • Some diodes are designed to be light sensors. • Light falling on them causes an electron to be excited into the conduction band, increasing the conductivity • These photodiodes can be made to detect many different frequencies of electromagnetic radiation (IR, visible UV being the most common) Circuit Symbol for Photodiode
• A solar cell, which makes energy from sunlight is an example of a photodiode • This type of operation is known as Photovoltaic Mode • The photon energy is used to create an electron-hole pair, which increases conductivity of the device.
Transistors • The transistor normally uses two p-n junctions back to back. It is a current amplification device n-p-n transistor 1955 GE transistor radio
Nanotechnology: Quantum Dots • These are small particles of semiconductors. Usually clusters of 100-10,000 atoms. • They do not show full band structures • By varying the size of the particle, the value of Δ E Δ E can be altered. Cluster of 5 atoms
• Cadmium Selenide
• Lead Selenide, stabilised with oleic acid • Form regular arrays when deposited on a surface
• Etch them on silicon or other semiconductors • Photo NIST, USA
• Quantum dots act as potential wells, to trap electrons • The electrons have quantized energy levels
• One application is to make the energy gap equivalent to visible wavelengths. • If the upper energy levels are occupied, then the quantum dot will fluoresce in the visible range as the electron drops back into the lower state hc E Δ E Cluster of 5 atoms
http://spectrum.mit.edu/articles/features/smarter-quantum-dots/ • Changing the size of the particle, changes the energy gap, and hence changes the colour of the emitted radiation
Crystals and Quantum Weirdness Yes, there is Crystal Energy
Crystal Lattices and Quantum Weirdness The regular nature of the atoms in a solid material leads to quantum effects and interactions Sodium Chloride Space Fill with the electrons
Sodium Chloride
Sapphire is an aluminium oxide, Al203 (corundum) with titanium and iron impurities
Sapphires • An electron bound to an iron impurity jumps to a nearby titanium impurity • Absorbs red and yellow light, white light passing through it emerges as blue http://scienceworld.wolfram.com/chemistry/IntervalenceChargeTransfer.html
Ruby • Ruby is also corundum • Different cause of colour – impurities of chromium. • Chromium is larger than aluminium, so it distorts the lattice out of shape, so the orbitals change energy http://www.webexhibits.org/causes ofcolor/6AA.html Natural ruby from Tanzania
Thermal Motion in Solids • Atoms oscillate around a fixed position • There are lots of possible oscillations! Vibrations of one of the structures of ice (crystalline water) http://www.crystal.unito.it/vibs/ICEXI/
Waves and Phonons • The vibrations inside the crystal are waves • Because of wave particle duality, we can also think of them as quasi-particles of energy called PHONONS • They carry energy through the material 𝐹 = ℎ𝑔 = ℎ𝑑 Phonon energy 𝜇 http://kino-ap.eng.hokudai.ac.jp/ripples.html We can watch the ripples of the waves at the surfaces of crystals using laser light
The idea of the phonon was introduced in 1932 by the Russian physicist Igor Tamm (Nobel Prize 1958) • Long wavelength phonons carry sound through materials • Short wavelength phonons carry heat energy through materials
Electrical Conductivity When Electrons Move Through a Conducting Material
+ + + + + + + + + + - + + + + + + + + + + • Electrons moving through the metal collide with the positive metal ions and lose energy • To push them through the metal lattice against resistance needs energy (from a battery)
• The moving electrons bump into lattice ions, and give energy to the lattice • The lattice ions have more energy (get hotter). • Metal heats up as electric current flows through it
Superconductors When the Phonons Become Important
Superconductivity • At extremely low temperatures, many metals (and other materials) become superconductors • No energy is lost as the electrons pass through the material • There are no heat losses
• At low temperature there is an interaction between the electrons and the phonons in the lattice • This results in the electrons forming pairs (Cooper pairs) • These can pass through the metal without interacting! • Very subtle quantum weirdness, involving interactions between quantum particles and quantum quasi-particle!
Quantum Computing Promising, but early days
Digital Computing: The Bit • The basic piece of digital data • Either 0 or 1 • Stored in a logic gate (a collection of a few transistors) 1 0 1 1 1 0 1 0 = 186 (1 × 2 8 ) + (0 × 2 7 ) + (1 × 2 6 ) + (1 × 2 5 ) + (1 × 2 5 ) + (0 × 2 3 ) + (1 × 2 2 ) + (0 × 2 1 )
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