How fast is fast? (Intel Museum, Santa Clara, CA) We may ask similar and even more follow-up questions, such as High-energy particle physics How high is high? How high can we go? How high do we have to go? Nanotechnology How small is small? How small can we go? How small do we have to go? Environmental issues How green is green? How green can we go? How green do we have to go?

Low temperature physics How low is low. How low can we go Low temperature physics How low is low? How low can we go? How low do we have to go? James C. Ho October 26, 2016

Nobel prizes related to low temperature physics/chemistry 1913 Kamerlingh-Onnes (liquid helium and superconductivity) 1920C Nernst (3rd law of thermodynamics) 1949C Giauque (low temperature property measurements) Landau (condensed matter, liquid helium) 1972 Bardeen, Cooper and Schrieffer (theory of superconductivity) 1973 Esaki and Giaever (tunneling phenomena) 1978 Kapitsa (low temperature physics) 1985 Klitzing (quantum Hall effect) 1987 Bednorz and Müller (high-Tc superconductivity) Lee, Osheroff and Richardson (superfluidity in 3He) 1998 Laughlin, Störmer and Tsui (fractional quantum Hall effect) 1997 Chu, Cohen-Tannoudji and Phillips (cooled and trapped atoms) 2001 Cornell, Ketterle and Wieman (Bose-Einstein condensation) 2003 Abrikosov, Ginzburg and Leggett (theory of superconductors and superfluids) 2007 Fert and Grünberg (giant magnetoresistance) 2016 Thouless, Haldane and Kosterlitz (topological phases and phase transitions) __________________ 2003 Nobel Prize in Physiology or Medicine -- Lauterbur and Mansfield (MRI)

How low is low? Record coldest temperatures The record coldest temperature in Wichita was -22°F (-30°C) on February 12, 1899. The record coldest temperature on earth was −128.6 °F (-89°C) at Vostok in Antarctica on July 21, 1983. Temperature scales Fahrenheit (oF) Celsius (oC) Kelvin (K)

How low can we go? Coolant at normal or reduced pressure Liquid H2 (20 - 14 K) Dewar (1898) Liquid N2 (77 - 63 K) Linde (1905) [Liquid O2 (90 K)] Liquid 4He (4.2 - 1 K) Onnes (1908) Liquid 3He (3.2 - 0.3 K) Closed-cycle cooler (down to near 4 K) Adiabatic demagnetization of paramagnetic salt (down to mK) 3He-4He dilution refrigerator (down to mK) Pomeranchuk (compressional) cooling (only 3He to below 1 mK) Nuclear adiabatic demagnetization (down to 10-9 K)

How low can we go? Coolant at normal or reduced pressure Liquid H2 (20 - 14 K) Dewar (1898) Liquid N2 (77 - 63 K) Linde (1905) [Liquid O2 (90 K)] Liquid 4He (4.2 - 1 K) Onnes (1908) Liquid 3He (3.2 - 0.3 K) Closed-cycle cooler (down to near 4 K) Adiabatic demagnetization of paramagnetic salt (down to mK) 3He-4He dilution refrigerator (down to mK) Pomeranchuk (compressional) cooling (only 3He to below 1 mK) Nuclear adiabatic demagnetization (down to 10-9 K)

Helium supply The US is currently the largest helium producer, providing 40% of world supply (approx. 1.5 billion ft3) from natural gas wells in parts of Kansas, Oklahoma and Texas. Other major helium producers are Algeria and Qatar. The US federal government has also been selling large quantities of helium from underground stockpiles, mostly in Texas. The reserve is quickly being depleted, and may not last long. But most recently, researchers in U.K. and Norway have used geochemistry and seismic imaging to locate 54 billion ft3 of helium in Tanzania.

One of the world’s largest helium production facility in Otis, Kansas

How low can we go? Coolant at normal or reduced pressure Liquid H2 (20 - 14 K) Dewar (1898) Liquid N2 (77 - 63 K) Linde (1905) [Liquid O2 (90 K)] Liquid 4He (4.2 - 1 K) Onnes (1908) Liquid 3He (3.2 - 0.3 K) Closed-cycle cooler (down to near 4 K) Adiabatic demagnetization of paramagnetic salt (down to mK) 3He-4He dilution refrigerator (down to mK) Pomeranchuk (compressional) cooling (only 3He to below 1 mK) Nuclear adiabatic demagnetization (down to 10-9 K)

Adiabatic demagnetization of a paramagnetic salt Adiabatic demagnetization of a paramagnetic salt For example: Ce2Mg3(NO3)12.24H2O, S = 1/2 for Ce3+ (4f1)

Spin-lattice relaxation

Specific heat of manganese. C = CPh + Cel +CN. = 0. 055T3 + 9. 20T + 0 Specific heat of manganese C = CPh + Cel +CN = 0.055T3 + 9.20T + 0.264/T2 CN = Nk[(I+1)/3I](μHe/kT)2 - [(I+1)(2I2+2I+1)/30I3](μHe/kT)4 + …. = A/T2 – A’/T4 + …. where I = 5/2 and μ = 3.4532μN, With A = 0.264, He = 65 kOe

How low can we go? Coolant at normal or reduced pressure Liquid H2 (20 - 14 K) Dewar (1898) Liquid N2 (77 - 63 K) Linde (1905) [Liquid O2 (90 K)] Liquid 4He (4.2 - 1 K) Onnes (1908) Liquid 3He (3.2 - 0.3 K) Closed-cycle cooler (down to near 4 K) Adiabatic demagnetization of paramagnetic salt (down to mK) 3He-4He dilution refrigerator (down to mK) Pomeranchuk (compressional) cooling (only 3He to below 1 mK) Nuclear adiabatic demagnetization (down to 10-9 K)

3He-4He dilution refrigerator In a 3He–4He mixing chamber below 1 K, a concentrated (practically 100% 3He) and a dilute phase (about 6.6% 3He) are in equilibrium and separated by a phase boundary. As the 3He in the dilute phase is pumped out through the still, where the lower vapor-pressure 4He is at rest, more 3He from the concentrated phase flows through the phase boundary into the dilute phase. This endothermic dilution process removes heat from the mixing chamber environment.

3He-4He dilution refrigerator

LOW TEMPERATURE THERMOMETRY Temperature range, K Temperature range, K Thermocouples Magnetic thermometers 300-700 ppm Fe in Au / Ag+ 0.37 at. % Au 1–25 Gadolinium metaphosphate, Gd(PO3)3 2–100 Chromel / 300-700 ppm Fe in Au 1–300 Ce2Mg3(NO3)12.24H2O single crystal 0.003–4 Chromel / Constantan 20–1100 CMN powder sphere or cylinder 0.002–4 Resistance thermometers Copper (and other nuclear paramagnets) 0.001–0.01 Platinum (capsule) 4–500 Gamma-ray anisotropy thermometers Rhodium + 0.5 at. % Fe 0.5–300 60Co in hexagonal close-packed cobalt single crystal 0.002–0.04 Carbon 0.01–300 54Mn in iron 0.003–0.03 Germanium 0.01–30 54Mn in nickel 0.004–0.045 Saturation vapor pressure thermometers Hydrogen 14–21 Helium-4 1.0–5.2 Helium-3 0.5–3.3

Thermistors are semiconductor-based thermometers

Magnetic thermometers based on the Curie’s law of paramagnetic materials [e.g., Ce2Mg3(NO3)12.24H2O)] χ = M/B = Nμ2/kT = C/T, where the Curie constant C = Nμ2/k M/μN = μB/kT For Ce+3 (2.54 μB) at 10 G, μB/k ≈ 2 x 10-4 (K)

Science and technology How low do we have to go? Science and technology

Space shuttle external tank (ET-94) shipped from New Orleans to Los Angeles (April-May, 2016), via the Gulf of Mexico and the Panama Canal. When filled in full capacity: 0.23-million lb of liquid H2 and 1.39-million lb of liquid O2

Scientific discovery Technological development Low temperature technology Liquefying helium (1908) Heike Kamerlingh Onnes (with Ehrenfest, Lorentz and Bohr)

Scientific discovery Technological development Low temperature technology Superconductivity (1911) Liquefying helium (1908) Nobel prize (1913) Heike Kamerlingh Onnes (with Ehrenfest, Lorentz and Bohr)

Type I (Walther Meissner effect, 1933) and Type-II superconductors (frozen flux Φ0)

Scientific discovery. Technological development. Superconductivity Scientific discovery Technological development Superconductivity Superconducting technology Type-II fine wires and cables Niobium-tin Nb3Sn (Tc = 18 K, Hc2 = 30 T) multifilaments embedded in bronze with high-purity copper (tantalum shielding) for thermal stability and molybdenum for structural support.

Scientific discovery. Technological development. Superconductivity Scientific discovery Technological development Superconductivity Superconducting technology High-field magnets MRI (Nobel prize 2003) Medical technology Neuroimaging Cancer diagnosis

Scientific discovery Technological development. Superconductivity Scientific discovery Technological development Superconductivity High-field magnets Particle physics The LHC at CERN has 1,232 (15 m long) dipole, 392 (3 m long) quadrupole, and about 6000 corrector superconducting magnets.

Superconducting transmission lines in power system, with superconducting magnets as energy storage Testing site at Bonneville Power

Superconducting magnets being used in transportation

Materials evaluation by low temperature calorimetry Electronic density of states at Fermi level from electronic specific heat coefficient electronic specific heat at T << TF ≈ 105 K Ce = (π2/3)D(EF)k2T ≡ γT, and phonon (lattice) specific heat at T << ϴD ≈ 102 K Cph = Nk(12π4/5)(T/ϴD)3 ≡ βT3 __________________ C = Ce + Cph = γT + βT3 or C/T = γ+ βT2 Two different stainless steels (For the National Bureau of Standards)

High temperature, high-strength Ti-Al alloys become brittle at near 25 at.% Al. Why? In collaboration with Edward Collings and John Enderby

Ordering effect (directional bonding) on the electronic structure Ordering effect (directional bonding) on the electronic structure and subsequently the mechanical behavior (stronger but brittle).

Professor Sir John Enderby, University of Bristol Professor Sir John Enderby, University of Bristol CBE (1997), Kt (2004) Vice President of Royal Society, 1999-2004 President of Institute of Physics, 2004-2006

(Traditional) phase transitions Question: Being seemingly unnatural but actually natural phenomena, do they prevail to all or only limited types of materials? Melting/ Solidification , Vaporization /Condensation (practically all materials) Ferromagnetism / Antiferromagnetism (only materials carrying magnetic moments) Ferroelectricity / Antiferroelectricity (only materials carrying electric dipoles) Superconductivity (?)

Superconductivity has been observed in more than half of Superconductivity has been observed in more than half of elements in the periodic table. How about the others? (Red: ambient pressure, Blue: high pressure, Green: thin film)

Are the “good” conductors, Cu, Ag and Au, non-superconducting? Or, superconductivity at much lower temperatures? Unsettled argument between Bernd Matthias (experimentally discovering most of the important superconductors) and Phillip Anderson (condensed matter theorist, 1977 Nobel prize in Physics).

Nobel prizes related to low temperature physics/chemistry 1913 Kamerlingh-Onnes (liquid helium and superconductivity) 1920C Nernst (3rd law of thermodynamics) 1949C Giauque (low temperature property measurements) Landau (condensed matter, liquid helium) 1972 Bardeen, Cooper and Schrieffer (theory of superconductivity) 1973 Esaki and Giaever (tunneling phenomena) 1978 Kapitsa (low temperature physics, superfluidity in 4He) 1985 Klitzing (quantum Hall effect) 1987 Bednorz and Müller (high-Tc superconductivity) Lee, Osheroff and Richardson (superfluidity in 3He) 1998 Laughlin, Störmer and Tsui (fractional quantum Hall effect) 1997 Chu, Cohen-Tannoudji and Phillips (cooled and trapped atoms) 2001 Cornell, Ketterle and Wieman (Bose-Einstein condensation) 2003 Abrikosov, Ginzburg and Leggett (theory of superconductors and superfluids) 2007 Fert and Grünberg (giant magnetoresistance) 2016 Thouless, Haldane and Kosterlitz (topological phases and phase transitions) __________________ 2003 Nobel Prize in Physiology or Medicine -- Lauterbur and Mansfield (MRI)

Superfluidity in 4He – zero viscosity

Superfluidity in 4He – zero thermal resistance The LHC at CERN uses 120 tonnes of helium at 1.9 K for cooling its 1,232 (15 m long) dipole, 392 (3 m long) quadrupole, and about 6000 corrector superconducting magnets.

While superfluid phase transition prevails above 2 K in 4He (bosons), none was observed in 3He (fermions), even with extensive research to well below 1 K over a long period of time. Would 3He ever undergo a superfluid transition? Lower temperature region needs to be probed!

How low can we go? Coolant at normal or reduced pressure Liquid H2 (20 - 14 K) Dewar (1898) Liquid N2 (77 - 63 K) Linde (1905) [Liquid O2 (90 K)] Liquid 4He (4.2 - 1 K) Onnes (1908) Liquid 3He (3.2 - 0.3 K) Closed-cycle cooler (down to near 4 K) Adiabatic demagnetization of paramagnetic salt (down to mK) 3He-4He dilution refrigerator (down to mK) Pomeranchuk (compressional) cooling (only 3He to below 1 mK) Nuclear adiabatic demagnetization (down to 10-9 K)

Pomeranchuk (compressional) cooling of 3He The conversion of liquid to solid 3He below 0.32 K will lead to an absorption of heat, due to a higher spin-disorder entropy in the solid phase. When pressure was applied to a cell containing liquid 3He at its freezing pressure, the liquid would start converting to solid 3He, gradually yielding a cooler mixture of solid and liquid present in the cell. One can reach below 1 mK by this technique.

3He remains liquid at less than 3 3He remains liquid at less than 3.4 Mpa, and enters the superfluid phase below 2.5 mK. 1996 Nobel prize in Physics : David Lee, Douglas Osheroff, and Robert Richardson.

Nobel prizes related to low temperature physics/chemistry 1913 Kamerlingh-Onnes (liquid helium and superconductivity) 1920C Nernst (3rd law of thermodynamics) 1949C Giauque (low temperature property measurements) Landau (condensed matter, liquid helium) 1972 Bardeen, Cooper and Schrieffer (theory of superconductivity) 1973 Esaki and Giaever (tunneling phenomena) 1978 Kapitsa (low temperature physics) 1985 Klitzing (quantum Hall effect) 1987 Bednorz and Müller (high-Tc superconductivity) Lee, Osheroff and Richardson (superfluidity in 3He) 1998 Laughlin, Störmer and Tsui (fractional quantum Hall effect) 1997 Chu, Cohen-Tannoudji and Phillips (cooled and trapped atoms) 2001 Cornell, Ketterle and Wieman (Bose-Einstein condensation) 2003 Abrikosov, Ginzburg and Leggett (theory of superconductors and superfluids) 2007 Fert and Grünberg (giant magnetoresistance) 2016 Thouless, Haldane and Kosterlitz (topological phases and phase transitions) __________________ 2003 Nobel Prize in Physiology or Medicine -- Lauterbur and Mansfield (MRI)

2007 Nobel prize in physics -- Giant magnetoresisitivity (GMR) Albert Fert (4.2 K) and Peter Grünberg (300 K) Spin valve An effect observed in thin-film structures composed of alternating ferromagnetic and non-magnetic conductive layers (e.g., Fe-Cr). A significant change in the spin-dependent electron scattering, thus the electrical resistance, depending on whether the magnetization of adjacent ferromagnetic layers are in a parallel or an antiparallel alignment. Main application of GMR is magnetic field sensors, which are used to read data in hard disk drives, biosensors, microelectromechanical systems.

Nobel prizes related to low temperature physics/chemistry 1913 Kamerlingh-Onnes (liquid helium and superconductivity) 1920C Nernst (3rd law of thermodynamics) 1949C Giauque (low temperature property measurements) Landau (condensed matter, liquid helium) 1972 Bardeen, Cooper and Schrieffer (theory of superconductivity) 1973 Esaki and Giaever (tunneling phenomena) 1978 Kapitsa (low temperature physics) 1985 Klitzing (quantum Hall effect) 1987 Bednorz and Müller (high-Tc superconductivity) Lee, Osheroff and Richardson (superfluidity in 3He) 1998 Laughlin, Störmer and Tsui (fractional quantum Hall effect) 1997 Chu, Cohen-Tannoudji and Phillips (cooled and trapped atoms) 2001 Cornell, Ketterle and Wieman (Bose-Einstein condensation) 2003 Abrikosov, Ginzburg and Leggett (theory of superconductors and superfluids) 2007 Fert and Grünberg (giant magnetoresistance) 2016 Thouless, Haldane and Kosterlitz (topological phases and phase transitions) __________________ 2003 Nobel Prize in Physiology or Medicine -- Lauterbur and Mansfield (MRI)

Hall effect (1879): RH = VH/I = - 1/ne at room temperature and with moderate magnetic fields. ______________________ Klaus von Klitzing (1985 Nobel prize) -- Quantum Hall effect In 2-D electron systems subjected to low temperatures and strong magnetic fields, the Hall resistance RH varies stepwise with B. Step height is given by the physical constant h/e2 (≈ 25 kΩ) divided by an integer i. The figure shows steps for i =2,3,4,5,6, 8 and 10. This is caused by the fact that the electrons move only in certain circular paths, the basic sizes of which are determined by the magnetic field. The various steps turn out to show how many of the smallest paths are entirely full of electrons. __________________ The integers that appear in the Hall effect are examples of topological quantum numbers. “Quantized Hall conductance as a topological invariant”, Qian Niu, D. J. Thouless, and Yong-Shi Wu., PRB 31, 3372 (1985). A new international standard for resistance: 1 Klitzing defined as the Hall resistance at the fourth step (h/4e2).

Robert Laughlin, Horst Störmer and Daniel Tsui (1998 Nobel prize) Fractional quantum Hall effect. More new steps at lower temperatures and more powerful magnetic fields, both above and between the integers. All the new step heights can be expressed with the same constant h/e2 but now divided by different fractions. The low temperature and the powerful magnetic field compel the electron gas to condense to form a new type of quantum fluid. Since electrons are fermions, they first, in a sense, combine with the "flux quanta" of the magnetic field, thus forming boson-type composite particles.

No definite answer to either of the three questions: Conclusions No definite answer to either of the three questions: How low is low? How low can we go? How low do we have to go? Work goes on ….

More and more intriguing phenomena are being discovered at low temperatures, sometimes complemented with high magnetic fields and low material dimensions. Actual discoveries by surprise or experimental verifications of theoretical prediction are often results of certain technological developments. These new discoveries either have contributed, or provide potential to technological advancements. _______________________ Without scientific discovery, technological development tends to be limited. Without technological development, scientific discovery tends to be hindered.

Thank you.