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№1 слайд![Long-Range Order and](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img0.jpg)
Содержание слайда: Long-Range Order and Superconductivity
Alexander Gabovich, KPI,
Lecture 1
№2 слайд![Density matrix in quantum](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img1.jpg)
Содержание слайда: Density matrix in quantum mechanics
If one has a large closed quantum-mechanical system with co-ordinates q and a subsystem with co-ordinates x, its wave function Ψ(q,x) generally speaking does not decompose into two ones, each dependent on q and x.
If f is a physical quantity, its mean value is given by
№3 слайд![Density matrix in quantum](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img2.jpg)
Содержание слайда: Density matrix in quantum mechanics
In the pure case, when the system concerned is described by the wave function one has
№4 слайд![Density matrix in quantum](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img3.jpg)
Содержание слайда: Density matrix in quantum mechanics
Another kind of the long-range order is the following:
№5 слайд![Off-diagonal long-range order](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img4.jpg)
Содержание слайда: Off-diagonal long-range order
№6 слайд![Long-range orders below](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img5.jpg)
Содержание слайда: Long-range orders below critical lines of phase transitions (4He)
№7 слайд![Phase transitions](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img6.jpg)
Содержание слайда: Phase transitions
№8 слайд![MICHAEL FARADAY, THE](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img7.jpg)
Содержание слайда: MICHAEL FARADAY, THE PRECURSOR OF LIQUEFACTION
Michael Faraday, 1791-1867
He liquefied all gases known to him except O2, N2, CO, NO, CH4, H2. Permanent gases? – NO!
COLD WAR OF LIQUEFACTION: O2 – Louis-Paul Cailletet (France) and Raoul-Pierre Pictet (Switzerland) [1877]; N2, Ar – Zygmund Wróblewski and Karol Olszewski (Poland) [1883]
№9 слайд![JAMES DEWAR, THE COMPETITOR A](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img8.jpg)
Содержание слайда: JAMES DEWAR, THE COMPETITOR – A MAN, WHO LIQUEFIED HYDROGEN IN 1898
A Dewar flask in the hands of the inventor. James Dewar’s laboratory in the basement of the Royal Institution in London appears as the background.
№10 слайд![KAMERLINGH-ONNES, THE WINNER](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img9.jpg)
Содержание слайда: KAMERLINGH-ONNES, THE WINNER – PHYSICIST AND ENGINEER (Nobel Prize in Physics, 1913)
Heike Kamerlingh Onnes (right) in his Cryogenic Laboratory at Leiden University, with his assistant Gerrit Jan Flim, around the time of the discovery of superconductivity: 1911
№11 слайд![LOW TEMPERATURE STUDIES USING](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img10.jpg)
Содержание слайда: LOW TEMPERATURE STUDIES USING LIQUID HELIUM LED TO NEW DISCOVERIES: NOT ONLY SUPERCONDUCTIVITY!
№12 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img11.jpg)
Содержание слайда: Superconducting phenomenology
№13 слайд![SUPERCONDUCTIVITY AMONG](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img12.jpg)
Содержание слайда: SUPERCONDUCTIVITY AMONG ELEMENTS
№14 слайд![SUPERCONDUCTIVITY, A MIRACLE](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img13.jpg)
Содержание слайда: SUPERCONDUCTIVITY, A MIRACLE FOUND BY KAMERLINGH-ONNES
№15 слайд![ANNIVERSARIES OF key](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img14.jpg)
Содержание слайда: ANNIVERSARIES OF key discoveries
1908-2008 (100) Helium liquefying
1911-2011 (100) Superconductivity
1933-2013 (70) Meissner-Ochsenfeld effect
1956-2011 (55) Cooper pairing concept
1962-2012 (50) Josephson effect
1971-2011 (40) Superfluidity of 3He
1986-2011 (25) High-Tc oxide superconductivity
2001-2011 (10) MgB2 with Tc = 39 K
2008-2013 (5) Iron-based superconductors with Tc = 75 K (in single layers of FeSe)
№16 слайд![PHENOMENOLOGY. NORMAL METALS](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img15.jpg)
Содержание слайда: PHENOMENOLOGY. NORMAL METALS
№17 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img16.jpg)
Содержание слайда: Superconducting phenomenology
№18 слайд![Magnetic field, magnetic](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img17.jpg)
Содержание слайда: Magnetic field, magnetic induction, and magnetization
№19 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img18.jpg)
Содержание слайда: Superconducting phenomenology
№20 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img19.jpg)
Содержание слайда: Superconducting phenomenology
№21 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img20.jpg)
Содержание слайда: Superconducting phenomenology
№22 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img21.jpg)
Содержание слайда: Superconducting phenomenology
№23 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img22.jpg)
Содержание слайда: Superconducting phenomenology
№24 слайд![Creators of the type II](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img23.jpg)
Содержание слайда: Creators of the type II superconductors
№25 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img24.jpg)
Содержание слайда: Superconducting phenomenology
№26 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img25.jpg)
Содержание слайда: Superconducting phenomenology
№27 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img26.jpg)
Содержание слайда: Superconducting phenomenology: London equation
№28 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img27.jpg)
Содержание слайда: Superconducting phenomenology: London equation
№29 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img28.jpg)
Содержание слайда: Superconducting phenomenology: London equation
Let us consider the second Newton law mdv/dt = eE. This equations means that there is no resistance! (The main point! – infinite conductivity).
The current density j = nsev.
Then d(Λj)/dt = E (*),
where
Λ=m/(nse2).
One knows that the full and partial time derivative are connected by the equation
d/dt = / t + v.
Since real current velocities v in metals are small in comparison with the Fermi velocity vF, one can replace the full derivative by the partial one. Then
(Λj)/t = E (i).
We have the Maxwell equation (Faraday electromagnetic induction equation):
rot E = − c-1H/t (**).
Let us apply a rotor operation to the equation (i). Then
(Λ rot j)/t = rot E (***).
№30 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img29.jpg)
Содержание слайда: Superconducting phenomenology: London equation
From (**) and (***) one obtains
(Λ rot j)/t = − c-1H/t (***). Or
/t(rot Λj + c-1H ) =0 (****).
It means that the quantity in the parentheses of Eq. (****) is conserved in time.
Now, it is another main step, that takes into account the superconductivity itself! Specifically, in the bulk of the superconductor both
j = 0
And
H = 0.
It simply reflects the Meissner effect!
Then
rot Λj + c-1H = 0 (*****).
Equations (*****) and (i) constitute the basis of the London theory.
№31 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img30.jpg)
Содержание слайда: Superconducting phenomenology: London equation
Equation (*****) and the Maxwell equation
rot H = 4πj/c
leads to the characteristic result of London electrodynamics. Below, we shall write relevant equations in the SI unit system.
№32 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img31.jpg)
Содержание слайда: Superconducting phenomenology: London equation
№33 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img32.jpg)
Содержание слайда: Superconducting phenomenology: London equation
№34 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img33.jpg)
Содержание слайда: Superconducting phenomenology: London equation
Eq. (3.46) can be transformed and solved to obtain Eq. (3.52). Namely, one knows the vector identity
rot rot B = div B – Δ B, where B is an arbitrary vector. However, div B = 0, because there are no magnetic charges. Therefore, Δ B = B/2. Now, for the special geometry of Fig. 3.12 one has
№35 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img34.jpg)
Содержание слайда: Superconducting phenomenology: London equation
№36 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img35.jpg)
Содержание слайда: Superconducting phenomenology: London-Pippard equation
№37 слайд![Brian Pippard -](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img36.jpg)
Содержание слайда: Brian Pippard (1920-2008)
№38 слайд![Superconducting phenomenology](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img37.jpg)
Содержание слайда: Superconducting phenomenology: London-Pippard equation
№39 слайд![Superconductors of the first](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img38.jpg)
Содержание слайда: Superconductors of the first and second kind
№40 слайд![Superconductors of the first](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img39.jpg)
Содержание слайда: Superconductors of the first and second kind
№41 слайд![The London vortex](/documents_6/2fe2e2c193712ed8389edf8f53e9a61c/img40.jpg)
Содержание слайда: The London vortex