Anos de Vitalidade

Transcription

Anos de Vitalidade

Supercondutividade
100 Anos de Vitalidade
J. Albino Aguiar
UFPE
Depto. de Física – UFPE, Recife, Brasil
Recife - BR
uperlab
RESUMO
Cem anos atrás, Heike Kamerlingh Onnes e
seus colaboradores descobriram a
supercondutividade. Esta descoberta
alimentou, desde o início, o sonho da obtenção
de altos campos magnéticos para aplicações
tecnológicas e instigou cientistas a procurarem
entender esta intrigante propriedade da
matéria.
Nesta palestra abordaremos o desenvolvimento
histórico dessa excitante área de pesquisa
desde o tempo de Heike, até os dias atuais.
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ROTEIRO
•O
COMEÇO
• AS PRELMINARES
• A DESCOBERTA
• O DESENVOLVIMENTO
• SUPERCONDUTIVIDADE NO
DF-UFPE
• AS PERSPECTIVAS
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O COMEÇO
O ELETROMAGNETISMO –
• A história do eletromagnetismo tem início na
Antiguidade.
• Thales de Mileto ao esfregar âmbar com
pele de carneiro, observou que pedaços de
palha eram atraídos pelo âmbar.
• Conhecia-se também as propriedades
magnéticas de certos materiais.
• Eléktron (ἤλεκτρον) = âmbar em grego
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O COMEÇO
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• Antigamente ligação entre eletricidade e magnetismo
era desconhecida. Somente no século XIX desenvolveuse uma relação entre os estudos desses fenômenos.
• O magnetismo na antiguidade = mineral magnetita.
Suas propriedades e seu uso eram envolvidos por muito
misticismo.
• Gerolamo Cardano (1550) - Em De Subtilitate discute
as diferenças entre forças elétricas e forças magnéticas.
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O COMEÇO
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• William Gilbert (século XVI) - trabalho metódico (De
Magnete) sobre as propriedades do magnetismo - Primeira
aplicação do método científico.
• Depois do trabalho de muita gente:
• Otto von Guericke (1660) – Elektrisiermaschine, a primeira
máquina eletrica.
• Robert Boyle (1675) - forças elétricas podem atuar no vácuo.
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O COMEÇO
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• Século XVIII:
• Luigi Aloisio Galvani realiza estudos em animais e, numa rã,
constata a presença do chamado "fluido de energia":
bioeletricidade.
• Charles François de Cisternay Du Fay - dois tipos de força
elétrica.
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O COMEÇO
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Benjamin Franklin - relâmpago é um fenômeno
elétrico.
• Joseph Priestley, Lord Henry Cavendish,
Charles Augustin de Coulomb e Siméon-Denis.
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O COMEÇO
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• Século XIX:
• 1820 - Hans Christian Ørsted - interação entre eletricidade e
magnetismo.
• André-Marie Ampère – explica a observação de Orsted.
•1827 - Georg Simon Ohm - Die galvanische Kette
mathematisch bearbeitet (O Circuito Galvânico Investigado
Matematicamente): teoria de circuitos: Lei de Ohm.
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O COMEÇO
• Século XIX:
• 1831 - Michael Faraday - indução magnética; formula o
princípio do transformador.
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O COMEÇO
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• Século XIX:
• 1864 - James Clerk Maxwell - A Treatise on Electricity and
Magnetism as quatro equações do eletromagnetismo. Previsão
da existência das ondas eletromagnéticas – luz como uma
forma de eletromagnetismo.
• FOTO DE MAXWELL !!!
• 1873 - Zénobe Gramme – transmissão de através de cabos
condutores aéreos.
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O COMEÇO
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• Século XIX:
• 1879 - Thomas Alva Edison inventa a lâmpada elétrica.
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O COMEÇO
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• Século XIX:
• Brasil - A eletricidade começa a ser utilizada no país, além da
Europa e dos Estados Unidos, logo após o invento do dínamo e
da lâmpada elétrica. No mesmo ano, D. Pedro II inaugura a
iluminação da estrada de ferro.
• 1880 - Edison patenteia o sistema de distribuição elétrica.
1881 - Brasil - A primeira iluminação externa pública do país é
inaugurada na atual Praça da República, em São Paulo.
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O COMEÇO
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• Século XIX:
• 1882- Edison implementa o primeiro sistema de distribuição
elétrica, em corrente contínua a 110 volts, em Manhattan.
• 1883 - Brasil - primeira usina hidrelétrica do país, em
Diamantina, Minas Gerais.
• 1883 - D. Pedro II inaugura, em Campos - RJ, o primeiro
serviço público municipal de iluminação elétrica do Brasil e da
América do Sul.
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O COMEÇO
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• Século XIX:
• 1888 - Heinrich Hertz comprova a existência das ondas
eletromagnéticas.
• 1890 (aproximadamente) - Disputa entre Nikola Tesla e Edison
na implementação dos sistemas de distribuição elétrica, a
chamada Guerra das Correntes. Vence Tesla, com a corrente
alternada. Transformadores elevadores de a tensão,
diminuindo as perdas na transmissão de energia.
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O COMEÇO
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• Século XIX:
• 1892 - Tesla publica a base do sistema de corrente alternada.
George Westinghouse patrocina os projetos de Tesla.
• 1893 - Charles Proteus Steinmetz desenvolve uma
formulação matemática para o estudo de circuitos em corrente
alternada.
• 1897 - Joseph John Thomson - O descobrimento do elétron.
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O COMEÇO
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• Século XIX:
• 1892 - Tesla realiza a primeira transmissão de rádio; porém,
esta invenção é creditada, embora sob controvérsias, a
Guglielmo Marconi em 1904. (Cristo Redentor (????)) !!!!
• A engenharia elétrica - profissão reconhecida.
• Grande desenvolvimento no campo da eletrônica - válvula,
transistores e circuitos integrados.
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O COMEÇO
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•O ELETROMAGNETISMO –
• Século XX:
• Diferenciação entre engenharia elétrica de potência e
eletrônica, e como consequência as telecomunicações e a
ciência da computação.
• A descoberta de materiais supercondutores causa grande
impacto no estudo da eletricidade, cujas inovações são
gradualmente implementadas.
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AS PRELIMINARES
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• 1906 - Heike Kamerlingh Onnes (1853-1926) Liquefação do
hidrogênio.
• Termometria a baixas temperaturas (Pt como termômetro
auxiliar).
• Resistividade (r) dos metais (Pt, Au, Hg) para T ~ 0 K :
• Lord Kelvin (1902) – r é infinita para T = 0 K.
• Menor temperatura atingida 14 K.
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AS PRELIMINARES
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• 1908 - Liquefação do hélio: 10 de julho de 1908 - Heike
Kamerlingh Onnes (1853-1926) – Abre-se um novo capítulo
na física das baixas temperaturas
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AS PRELIMINARES
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• 12 DE MARÇO DE 1910:
• Primeira tentativa de transferir hélio do liquefator para
um criostato: novo récorde de baixa temperatura, 1,1 K. –
novo experimento planejado para quatro meses após.
• 2 DE DEZEMBRO DE 1910: R(T) de Pt em temperaturas de
hélio líquido. R (Pt) ~ cte., para T = 4,25 K >> Kelvin dançou !!!
• 8 DE ABRIL DE 1911: transferir hélio para NOVO criostato termômetros a gás e de Au. Resistor de Pt (forma U em vidro)
para medida de R(T) x T instalado
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AS PRELIMINARES
O PRIMEIRO EXPERIMENTO COM Hg
• 8 DE ABRIL DE 1910:
• Bottom of the cryostat in which I-leike Kamerlingh
Onnes and coworkers carried out the 8 April 1911
experiment that first revealed superconductivity.
The original drawing is from reference 6, but colors
have been added to indicate various cryogenic
fluids within the intricate dewar alcohol (purpie),
liquid air (blue), liquid and gaseous hydrogen (dark
and light green), and liquid and gaseous helium
(dark and light red). Handwritten by Gerrit Flim are
labeis for the mercury and gold resistors (O Hg
and O Au), the gas thermometer (Th), conponents
at the end Çnia) of the transfer tube from the
heliun, liquefier, and parts of the liquidhelium stirrer
(Sb), which is also shown enlarged in several
cross sections at right.
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A DESCOBERTA
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• Os colaboradores:
• Jacob Clay - técnico chefe.
• Oscar Kesselring - hialotécnico.
• Cornelis Dorsman - pesquisador.
• Gilles Host - estudante: ficava em outra sala operando a
ponte de Wheatstone e o galvonômetro
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AS PRELIMINARES
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AS PRELIMINARES:
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• Início: 7:00 h; HKO chega às 11:20 h quando hélio começa a
circular (ele tinha outras coisas a fazer – HPK!)
• Termômetro de Au: T = 140 K em 30 min.
• Termômetro a gás: 5 K - “a válvula funcionou” - teste do
agitador e medida da taxa de evaporação do hélio.
• Holst: Medidas de R(4,3 K) de Au e Hg.
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AS PRELIMINARES:
uperlab
• Redução da pressão de vapor do hélio. Medida do calor
específico hélio. P = 197 mmHg (0,26 atm), T ~ 3 K
• Termômetro de Au: T = 140 K em 30 min.
• Termômetro a gás: 5 K - “a válvula funcionou” - teste do
agitador e medida da taxa de evaporação do hélio.
• 16:00 h (at 4 pm says notebook!) - nova medida da
resistência do Au e do Hg >>>>>>>>>>>>>>>>>>>>>>>>>>>
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AS PRELIMINARES:
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• 3 K – “Kwik nagenoeg null” !!!! (Resistência do mercúrio
praticamente zero @ 3 K.
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AS PRELIMINARES:
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• O experimento prosegue até mais tarde:
•HKO escreve: “Dorsman (who had controlled and measured
the temperatures) really had to hurry to make the observation.
The temperature had been surprisingly hard to control. Just
before the lowest temperature (about 1.8 K) was reached, the
boiling suddenly stoped and was replaced by evaporartion in
which the visible liquid shrank. So a remarkably strong
evaporation at the surface“. Sem perceber, o time de Leiden
observou também a transição superfluida do hélio. No
mesmo dia, pela primeira vez, duas transições quânticas
foram observadas em um mesmo laboratório!
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A DESCOBERTA
uperlab
Nova experiência com Hg
• As previsões de Heike (apresentadas três semanas após
na Real Academia Holandesa de Artes e Ciências RAHAC) para resistência de Hg ultra puro:
• 1) RPt(4,3 K) <<<< RPt(14 K), mas mensurável;
• 2) RPt(T) deveria ainda não ser indeendente da temperatura;
• 3) A temperaturas muito baixas RPt(T) deve ser nula!
• AGORA VAMOS AS MEDIDAS !!!
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A DESCOBERTA
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• 23 DE MAIO DE 1911 :
• Resolução da medida de resistividade ~ 30 nV !!!!!
• R(T)/Ro a 3 K menor que 10-7. Ro resistência Hg cristalino a 0
K (0 C???).
• Atingido 1.5 K para então explorar temperaturas entre 4,3 K e
3,0 K. Nenhuma resistência
• Meados da tarde 4.00 K nenhuma manifestação de aumento
de resistência. A 4.05 K ainda nada!
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A DESCOBERTA
• A 4.12 K resitência começa a “aparecer”!!!!
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A DESCOBERTA
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• Anotações contradizem a teoria os “rapazes azuis”!
• Relato de HKO na RAHAC: Para um pouco acima de 4.2 K
foi observado que RPt(T) ainda era menor que 10-5 Ro, no
entanto aumentando T somente 0,1 K RPt( 4,3 K) aumentou
por um fator de aproximadamente 400.
•Resultados comprovam expectativa de HKO!
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O DESENVOLVIMENTO
• 1914 EXPERIÊNCIA COM MODO PERSITENTE
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uperla
b
Perfect conductivity
Critical Current
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Diamagnetism
perfeito
Critical field
O DESENVOLVIMENTO
Leo V. Shubnikov (1901-1937)
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Dear Albino,
Thank you very much for the congratulations and
photos. Here are the answers to your questions.
2) Lev Vasilievich Shubnikov was arrested in 1937,
accused in the attempt to organize a
"counterrevolutionary“ strike and parished in gail.
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1) Nothing. I just wanted to study the magnetic properties of
bulk Type II superconductors, and vortices appeared as
a solution of the Ginzburg-Landau equations.
3) My great-grandfather was an owner of a large and
famous factory of sweets and candies, my grandfather
died joung, and my father was a famous physician and
never had higher titles than Vice-President of the
Academy of Medical Sciences and Director of the
Institute of Morphology.
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O fenômeno da
supercondutividade
uperla
b
Supercondutor tipo - I
Magnetização
Indução
Diagrama de fase
Supercondutor tipo - II
Magnetização
J.Indução
Albino Aguiar -
Diagrama de fase
O fenômeno da
supercondutividade:
vórtice
J. Albino Aguiar -
uperla
b
Vórtices em
supercondutoresDifração de neutrons
Rede de Abrikosov (volumétrico)
H
Baixa T
FL = 0 J 
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b
Alta T
Imagem do núcleo do vórtice (STM)
J
Rede de Abrikosov (filmes finos)
J. Albino Aguiar -
uperlab
5) This year I am too busy.
However, in general I feel pretty
reluctant to come to Brazil. The
reason is that I am rather old, and
…. Of course, I have nothing
against the Brazilian scientists.
Sincerely yours, Alex Abrikosov
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Vortex state in a mesoscopic
flat disk with rough surface
uperlab
Mesoscopic regime : Sample size becomes
comparable to superconducting penetration
depth, l, and/or coherence length, x.
Consequences: Vortex-surface interactions can
become comparable to the inter-vortex interaction
and the local flux density becomes intrinsically
dependent on sample geometry (shape and size).
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• Andre Geim -2003
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FROG MOVIE!
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O DESENVOLVIMENTO
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O DESENVOLVIMENTO
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HEIKE K A M E R L I N G H O N N E S
Investigations into the properties of substances at low temperatures, which have led, amongst other things,
to the preparation of liquid helium
Nobel Lecture, December 11, 1913
Since you have done me the honour of describing to you my investigations into the properties of substances
at low temperatures, which have also led me, amongst other things, to the preparation of liquid helium, I
must first of all express my deepest thanks to your old and famous Academy for distinguishing me in this
manner. This has happened at a time when the continuation of my work will make great demands upon me.
Nothing could make me more able than your good will does to meet new problems with the same hopeful
confidence with which, 30 years ago, I met difficulties now overcome.
The main aim in investigations at low temperatures has greatly changed since then. When I first turned to
this field of work the aim was still to liquefy statically the gases which up to then had not been mastered and
to pour into open containers those gases which it is most difficult to liquefy.
What has given a character of its own to the Leyden work from the very beginning is that I allowed myself to
be led by Van der Waals’ theories, particularly by the law of corresponding states which at that time had just
been deduced by Van der Waals.
This law had a particular attraction for me because I thought to find thebasis for it in the stationary
mechanical similarity of substances and from thispoint of view the study of deviations in substances of
simple chemical structurewith low critical temperatures seemed particularly important.
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O DESENVOLVIMENTO
Karl Walther Meißner
(1882-1974)
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Robert Ochsenfeld
(1901-1993)
O DESENVOLVIMENTO
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Heinz London (1907-1970) e Fritz Wolfgang London11 (1900-1954).
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O DESENVOLVIMENTO
Herbert Fröhlich (1905-1992)
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Lev D. Landau (1908-1968)
O DESENVOLVIMENTO
Vitaly L. Ginzburg (1916-2009)
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Alexei A. Abrikosov (1928- )
uperlab
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Vortex III, Crete (2003)
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Alexei Abrikosov
Alexander Andreev
Antonio Barone
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Alexei Abrikosov
Alexander Andreev
Antonio Barone
Albino Aguiar
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Stockholm, 10 December, 2003
Princess Madeleine
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Alexei Abrikosov
O DESENVOLVIMENTO
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Anthony James Leggett (1938- )
uperlab
O DESENVOLVIMENTO
uperlab
ON SUPERCONDUCTIVITY AND SUPERFLUIDITY
By
Vitaly L. Ginzburg
P. N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow, Russia.
INTRODUCTION
First of all I would like to express my heartfelt gratitude to the Royal Swedish Academy of Sciences and its Nobel
Committee for physics for awarding me the 2003 Nobel Prize in physics. I am well aware of how difficult it is to select
no more than three Laureates out of the far greater number of nominees. So all the more valuable is this award.
Personally, I have two additional motives for appreciating the award of the Prize. First, I am already 87, the Nobel
Prize is not awarded posthumously, and posthumous recognition is not all that significant to me since I am an atheist.
Second, the 1958 and 1962 Nobel Prizes were awarded respectively to Igor’ Evgen’evich Tamm and Lev Davidovich
Landau. Outside of high school, the notion of a teacher is very relative and is quite often applied by formal criteria: for
instance, it is applied to the supervisor in the preparation of a thesis. But I believe that the title real teacher can
appropriately be given only to those who have made the greatest impact on your work and whose example you have
followed. Tamm and Landau were precisely these kind of people for me. I feel particularly pleased, because in a sense I
have justified their good attitude toward me. Of course, the reason lies not with the Prize itself, but with the fact that
my receiving the award after them signifies following their path.
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O DESENVOLVIMENTO
uperlab
TYPE II SUPERCONDUCTORS AND THE VORTEX LATTICE
By
Alexei A. Abrikosov
Materials Science Division, Argonne National Laboratory, 9700 South Cass
Ave., Argonne, IL 60439, USA.
In 1950, Vitalii Ginzburg and Lev Landau published their famous paper on the theory of superconductivity [1]. The
approach was based on the general theory of the second order phase transitions proposed by Landau in 1937 [2]. There
Landau introduced the main variable, the so called “order parameter”which was finite below the transition and zero
above it. Different phase transitions had different order parameters, and whereas it was evident for, e. g., the
ferromagnetic transition, namely, the spontaneous magnetization, it was far less evident for the superconducting
transition. Ginzburg and Landau had a stroke of genius, when they chose, as the order parameter some sort of wave
function. At that time nobody knew about Cooper pairs, and about their Bose condensate, where all particles become
coherent, i. e. described by the same wave function. This assumption was the basis of the new theory, which managed
to solve the main contradiction of the old theory by Fritz and Heinz London [3], namely, the positive surface energy.
Besides it made many useful predictions, such as the critical magnetic field of thin films, the critical current in thin
wires etc.
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O DESENVOLVIMENTO
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SUPERFLUID 3-He:THE EARLY DAYS AS SEEN BY A THEORIST
By
Anthony J. Leggett
University of Illinois, Department of Physics, 1110 West Green Street, Urbana, Ijl 61801-3080, USA.
It is needless to say that I feel it a great honor and privilege to have been selected for the 2003 Nobel prize
in physics for my theoretical work on superfluid 3He; I am particularly pleased to be sharing the award with
Professors Ginzburg and Abrikosov, whom I have always looked up to as giants of the closely related fleld of
superconductivity. The story of how, in roughly the twelve-month period July 1972–July 1973, we came to a
theoretical understanding of the experimental data on what we now know as superfluid 3He is a sort of
complex detective tale, involving many actors besides me; for reasons of time I will concentrate in this
lecture on my own involvement, and will have to omit several important developments in which I had no
direct role.
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O DESENVOLVIMENTO
Newton Bernardes (1931-2007)
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O DESENVOLVIMENTO
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O DESENVOLVIMENTO
John Bardeen
John Bardeen
John Bardeen
(1908-1991)
(1908-1991)
(1908-1991)
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Leon Neil Cooper
John Robert Schrieffer
Leon Neil
Cooper
John Robert
Schrieffer
Leon
Neil Cooper
John Robert
Schrieffer
(1930- )
(1931- )
(1930- )(1930- )
(1931- )(1931- )
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2 PAGES !!!
Phys. Rev. 106, 162 - 164 (1957)
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02 PAGES !!!
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30 PAGES !!!
O DESENVOLVIMENTO
Brian David Josephson (1940- )
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O DESENVOLVIMENTO
B. D. Josephson, Phys. Lett. 1, 251 (1962)
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O DESENVOLVIMENTO
Bernd Theodor Matthias
(1918-1980).
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O DESENVOLVIMENTO
Johannes Georg Bednorz
(1950- )
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Karl Alexander Müller
(1927- )
O DESENVOLVIMENTO
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O DESENVOLVIMENTO
Paul Ching-Wu Chu (1941- )
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Robert J. Cava
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O DESENVOLVIMENTO
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O DESENVOLVIMENTO
Philip Warren Anderson (1923- )
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SUPERCONDUTIVIDADE
NO DF-UFPE
• Projeto CNPq – 1972
•Marcílio Ferreira – San Diego (1986)
• Albino Aguiar – Leiden (1986)
• Sérgio Rezende
• Maurício Coutinho-Filho
• Ernesto Raposo
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SUPERCONDUTIVIDADE
NO DF-UFPE
• Erivaldo Montarroyos
•Clécio C. De Souza Silva
• Leonardo R. E. Cabral
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Mesoscopic regime : Sample size becomes
comparable to superconducting penetration
depth, l, and/or coherence length, x.
Consequences: Vortex-surface interactions can
become comparable to the inter-vortex interaction
and the local flux density becomes intrinsically
dependent on sample geometry (shape and size).
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Magnetization in mesoscopic
Al disks (Geim et al. 97).
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Andre Konstantin Gein
uperlab
Vortex configurations, calculated by using either
the Ginzburg-Landau theory or the London
approach for triangles, squares, rectangles, disks
and slabs, reveal that:
• Vortex configurations obey the superconductor
geometry for low total vorticity, and,
• An hexagonal arrangement appears close to the
center of the superconductor, for large systems
and higher vorticity.
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L. R. E. Cabral and J. Albino Aguiar,
PRB, 80 (2009), 214533.
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Nb/Al Multilayers:
Nb layers
d = 50 nm
C. C. de Souza Silva,
and J. Albino Aguiar,
Physica B 284 (2000)
634.
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Al layers
d = 20 nm
Glass
Vortices in mesoscopic
superconductors
Nb/Al Multilayers - Longitudinal field
C. C. de Souza
Silva, and J. Albino
Aguiar, Physica B
284 (2000) 634.
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Nb/Al Multilayers - Transverse field
C. C. de Souza
Aguiar, Physica B
284 (2000) 634.
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30
20
10
0
-4
m (10 emu)
C. C. de Souza
Aguiar, Physica B
284 (2000) 634.
T = 4,22 K
-10
-20
-30
0,0
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0,5
1,0
Ha (kOe)
1,5
2,0
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2,0
1,5
B (kG)
C. C. de Souza
Aguiar, Physica B
284 (2000) 634.
T = 4,22 K
1,0
0,5
0,0
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0,0
0,5
1,0
Ha (kOe)
1,5
2,0
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800
T=5K
600
400
200
4
M (10 emu)
C. C. de Souza
Aguiar, Physica B
284 (2000) 634.
0
-200
-400
-600
0,0
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0,5
1,0
1,5
Ha (kOe)
2,0
2,5
3,0
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14
12
Number of events
M
 1,66
10
8
6
4
2
5
10
15
20
25
3
M (10 emu)
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30
35
40
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Theoretical formalism
•
Mesoscopic flat disk with rough surface.
TDGL solved using link variable method. Leading
order in ϵ:
η(∂ψ/∂t) = (−1/g)[(−i∇− A)・g (−i∇− A)ψ] + ψ(1 − |ψ|2),
in Ω0.
Boundary conditions:
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
e* 
 i
nˆ. i  A  

c 
b

, on ∂ Ω0.
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Example of a surface
z = g(x, y) generated
randomly, which was
used in the
simulations for 20%
roughness.
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Magnetic field Hs in which the first vortex entrance takes
place for three different radii R = 4.5 x(T), R = 5.5 x (T),
R = 6.5 x (T)) and for 0%, 5%, 10%, 15%, 20% roughness.
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Magnetization curve as a function of the external applied magnetic field H 0 for
different values of the de Gennes extrapolation length b = 1, 2.5, 1.25, 0.88.
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Topology of the current density streamlines for R = 4.5 x(T), H0 = 1.013 Hc2 (T)
and rugosity of 20%. Notice that we have five vortices at the center.
For a flat disk of equivalent size, there should be a giant vortex state.
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flat disk with surface deffects
Disk with R = 6.5 x
Number of deffects varies from 1 to 5
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Vortices states in two
band superconductors
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Crystal structure of MgB2.
Boron atoms form stacks
of honeycomb layers and
magnesium atoms are in
between the boron layers
at the center of the
hexagons.
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The Fermi surface of MgB2
from band structure
calculation. Green and blue
cylinders (hole-like) are the
σ bands,
and the blue (hole-like) and
the red (electron-like)
tubular networks
are the π bands. (Reprinted
with permission from
Kortus et al [9].
Copyright 2001 by the
American Physical Society.
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Vortices states two
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1 - Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent
superconductors
“Traditionally, superconductors are categorized as type I or type II. Type-I superconductors support only
Meissner and normal states, while type-II superconductors form magnetic vortices in sufficiently strong
applied magnetic fields. Recently there has been much interest in superconducting systems with several
species of condensates, in fields ranging from condensed matter to high energy physics. Here we show
that the classification into types I and II is insufficient for such multicomponent superconductors. We obtain
solutions representing thermodynamically stable vortices with properties falling outside the usual type-I/typeII dichotomy, in that they have the following features: i) Pippard electrodynamics, ii) interaction potential
with long-range attractive and short-range repulsive parts, iii) for an n-quantum vortex, a nonmonotonic ratio
E(n) /n where E(n) is the energy per unit length, iv) energetic preference for nonaxisymmetric vortex states,
“vortex molecules.” Consequently, these superconductors exhibit an emerging first order transition into a
“semi-Meissner” state, an inhomogeneous state comprising a mixture of domains of two-component
Meissner state and vortex clusters”.
Egor Babaev and Martin Speight - PHYSICAL REVIEW B 72, 180502_R_ 2005
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2 -Type-1.5 Superconductivity
”We demonstrate the existence of a novel superconducting state in high quality twocomponent MgB2 single crystalline superconductors where a unique combination of both
type-1 (l1/x1 < 2-1/2 = 0.71) and type-2 (l2/x2 > 2-1/2= 0.71) super-conductor conditions is
realized for the two components of the order parameter. This condition leads to a vortexvortex interaction attractive at long distances and repulsive at short distances, which
stabilizes unconventional stripe- and gossamerlike vortex patterns that we have
visualized in this type-1.5 superconductor using Bitter decoration and also reproduced in
numerical simulations”.
Victor Moshchalkov, Mariela Menghini, T. Nishio, Q. H, Chen, A.V. Silhanek, V. H. Dao,
L. F. Chibotaru, N. D. Zhigadlo, and J. Karpinski, PRL 102, 117001 (2009)
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Magnetic decoration images of the vortex structure at T = 4.2 K and H = 1
Oe in (a) MgB2 and (b) NbSe2 single crystals. The scale bars in the images
correspond to 10 _m. Notice that the density of vortices in the decoration
experiments represents the internal field B rather than the applied field H.
This leads to a different number of decorated vortices for NbSe2 and MgB2,
even at the same applied field.
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(a) Experimental vortex locations in a selected part of the image shown
in Fig. 1(a). The vortex configuration resulting from the numerical
simulations in a two-component superconductor at low density is shown
in (b) evidencing an inhomogeneous spatial distribution of vortices. In
both cases, the regions enclosed by the dashed white line indicate voids
of vortices caused by the inhomogeneous distribution. In (c) the vortex
pattern obtained by a magnetic decoration of the NbSe2 crystal at 1 Oe is
shown and (d) corresponds to the vortex pattern obtained by a numerical
simulation of a type-2 superconductor. The white scale bars correspond
to 10 _m. (e) and (f ) display the distribution of first neighbor distance,
Pa, of the experimental and theoretical vortex structures, respectively. In
the case of MgB2, Pa shows additional peaks at distances shorter and
longer than the most probable separation (see the red and green
arrows). The pair of vortices separated at the distances where the
additional peaks are located are highlighted in (a) and (b) by red and
green circles. The light blue circles correspond to pair of vortices
separated by the most probable distance.
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(a) Magnetic decoration image in the MgB2 single crystal at H = 5 Oe. (b) Disordered
Abrikosov lattice obtained at H= 5 Oe in the NbSe2 sample. The formation of vortex stripes is
also reproduced in numerical simulations of a two-component type- 1.5 superconductor (c) in
contrast to a homogeneous vortex distribution in a type-2 superconductor at the same vortex
density (d). The scale bars in the images correspond to 10 microm. Inset of (b): Vortex density
along lines parallel to the vortex stripe direction [yellow dashed lines in (a)] for MgB2 and
NbSe2 vortex structures. The variation of the vortex density is calculated as a function of the
distance measured along the direction perpendicular to the stripes [yellow arrows in (a) and
(b)]. The curves are normalized by their respective average density. The results of a similar
calculation performed on the simulated vortex structures are shown in the inset of (d).
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3 - Attractive vortices
Ernst Helmut Brandt and Shi-Ping Zhou - Physics 2, 22 (2009) Published March 16, 2009.
Victor Moshchalkov et al.[1] argue that in the recently discovered two-band superconductor
MgB2, the presence of two nearly independent order parameters yp and ys, corresponding to
the two electronic bands that carry the superconductivity, may lead to novel effects related to
the attraction of vortices. They showed that from the two-band GL functional follows a vortex–
vortex interaction that is short-range repulsive and weakly long-range attractive, as was also
found by Babaev [10]. Particularly fascinating effects should occur when the GL parameters of
the p and s bands, and of the two corresponding superfluids, are kp  lp/xp = 0.66 < 0.71 and
ks  ls/xs = 3.68 > 0.71, as they find from measured energy gaps, Fermi velocities, and
plasma frequencies. MgB2 should thus have properties of both type-I and type-II
superconductors simultaneously. The authors of Ref. [1] name this type-1.5
suPerconductivity. Figure 1 shows the suggested spatial profiles of y and B for vortices in
type-I, II, and 1.5 superconductors; for the latter they suggest the existence of two different
core widths, corresponding to the p and s components, as it is expected for complete absence
of interband coupling.
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The predicted vortex attraction and potential minimum should occur in a wide range of materials parameters, in
contrast to the very particular case of k ~ 1 / 2-1/2 mentioned above. This minimum stabilizes unconventional
stripe- and gossamer-like vortex patterns, as observed also in magnetic films, colloids, polymers, gels, etc., see
Ref. [11] for a short review.
To check their prediction of type 1.5 behavior, Moshchalkov et al.[1] show images of vortex arrangements obtained
by decoration experiments on field cooled MgB2 and, for comparison, NbSe2, and of computer simulations at very
low inductions. Field cooling r0  (1 - T/Tc) 1/2, decreases from r0 =  at T = Tc when the vortices nucleate, to a
value several times l(0). For MgB2, Fig. 2(a) (experiment at H = 1 Oe) and ig. 2(b) (simulation) in Ref. [1] show
chains of nearly equidistant vortices, and Fig. 3(a) and Fig. 3(c) show condensation of vortices into clusters. All
these features are absent in the corresponding images for NbSe2 and thus indicate that in MgB2, vortices indeed
have a potential with attractive tail and minimum.
In conclusion, the ideas and results of Ref. [1] are highly interesting and will certainly stimulate further
investigation into the fascinating field of two component superconductivity. One should advance the theories [12]
and the measurement of their input parameters, and account for the coupling terms in their solution. One should
investigate the singlet-triplet mixtures of pairing states near a halfmetal–superconductor interface, and a two-band
BCS-type Hamiltonian to capture the essential features in hole-doped iron-based superconductors [13]. Note that
during the decoration experiments in Ref. [1] the applied field is much less than the vortex penetration field (1􀀀
N)Hc1, where Hc1 is the lower critical field, and the vortices would thus mostly leave the specimen if they were
not pinned. The main challenge will be finding experimental ways to separate the
effects of pinning and vortex attraction.
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Intermediate state of a type-I
superconductor. The normal
domains are dark. Coexistence
of triangular lattice of flux
tubes and of laminar domains.
Tantalum disk of ticknessd =
33 μm, diameter D = 5 mm, T
= 1.2 K , Ba = 34 mT.
(Courtesy U. Essmann).
Optical microscope.
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In conclusion, the ideas and results of Ref. [1] are highly interesting and will
certainly stimulate further investigation into the fascinating field of two component
superconductivity. One should advance the theories [12] and the measurement of
their input parameters, and account for the coupling terms in their solution. One
should investigate the singlet-triplet mixtures of pairing states near a halfmetal–
superconductor interface, and a two-band BCS-type Hamiltonian to capture the
essential features in hole-doped iron-based superconductors [13]. Note that during
the decoration experiments in Ref. [1] the applied field is much less than the vortex
penetration field (1􀀀 N)Hc1, where Hc1 is the lower critical field, and the vortices
would thus mostly leave the specimen if they were not pinned. The main challenge
will be finding experimental ways to separate the effects of pinning and vortex
attraction.
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Type-1.5 superconductors : Multicomponent superconductor
which simultaneously has several magnetic properties of a type-I
and a type-II superconductors.
In a type-1.5 superconductor, the vortices repel each other (as in
type-II superconductors) over short distances while they attract
each other (as in type-I superconductors) over long distances.
(V. V. Moshchalkov, et al, PRL 102, 17001(2009).
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Schematic of the spatial
distribution of the
superconducting order
parameter jy(x)j and the field
profile B(x) for two neighboring
fluxons in (top) type-I, (middle)
type-II, and (bottom) type-1.5
superconductors. The bottom
sketch in each panel shows
|y(x)| in a color plot with darker
regions indicating the smaller
order parameter, and the stray
field emanating from the sample
surface. (Illustration: Courtesy of
V. V. Moshchalkov)
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SERIOUS CRITICISM FROM:
E. H. Brandt.
A.Gurevich.
V. G. Kogan.
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Two band superconductor - Theoretical formalism:
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Previous Results:
Superconducting disks
- One band superc-
(1,8)-state
ductor
H0 /Hc2 = 0.7
B. J. Baelus
L. R. E. Cabral,
and F. M. Peeters,
PRB, 69 (2004) 0654506.
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Cooper pair density for a two band superconductor in a
mesoscopic disk, R=5ξ10 and γ=0.0; 0.02 and 0.04 respectively.
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Jofre Gutierrez, et al., unpublished
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Vortices states in
states in two band
superconductors
N = 40
N = 60
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N = 50
N = 100
J. Albino Aguiar, et al., to be published (2012).
uperlab
Iemanjá
Iemanjá – Iyemanjá, Yemanjá, Yemaya,
uperlab
Iemoja "Iemanjá" ou Yemoja, é um orixá
africano, cujo nome deriva da expressão
Iorubá "Yèyé omo ejá" ("Mãe cujos filhos
são peixes”) identificada no jogo do
merindilogum pelos odu ejibe e ossá,
representado materialmente e imaterial pelo
camdoblé, através do assentamento
sagrado denominado Igbá yemanja.
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Iemanjá
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Em Cuba, Yemayá também possui as cores azul e branca,
é uma rainha do mar negra, assume o nome cristão de
La Virgen de la Regla e faz parte da Santeria como Santa
padroeira dos portos de Havana.
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Chico Science
Francisco de Assis França, mais conhecido pela alcunha de
Chico Science (Olinda, 13 de março de 1966 – Recife,
2 de fevereiro de 1997) foi um cantor e compositor olindense, um
dos principais colaboradores do movimento manguebeat em
meados da década de 1990. Líder da banda
Chico Science & Nação Zumbi, deixou dois discos gravados:
Da Lama ao Caos e Afrociberdelia, tendo sua carreira
precocemente encerradapor um acidente de carro numa das vias
Que ligam Olinda e Recife. Seus dois álbuns foram incluídos na
lista dos 100 melhores discos da música brasileira da revista
Rolling Stone, elaborada a partir de uma votação com 60
UFPE jornalistas, produtores e estudiosos de música
Recife - BR
Laboratory of Superconductivity
and Advanced Materials
Post-doctoral position available !
Contact: Prof. J. Albino. Aguiar
[email protected]
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VII Brazilian School of Superconductivity and
Workshop on Frontiers of Superconductivity and
Magnetism – Materials, Mechanisms and Applications
Muro Alto-PE, Brazil, 08 to 12 December 2008
X Brazilian School of Superconductivity and
Workshop on Frontiers of Superconductivity and
Magnetism – Materials, Mechanisms and
Applications
10 -15 December, 2012
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Porto de Galinhas – PE – Brazil
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AXÉ
IEMANJÁ!
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PLAY - A PRAIEIRA!!!
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Uma cerveja antes do almoço é muito bom, p´ra
gente ficar pensando melhor!
A beer just before lunch is excellent
to make you think better!
Chico Science –
Olinda, March 13, 1966.
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Recife, February 2, 1977.
Financial Support
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FACA
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Thank you
for your
attention!
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AS PERSPECTIVAS
• NOVOS MATERIAIS
• FLUXÔNICA
• ELETRÔNICA SUPERCONDUTORA
• SUPERCONDUTIVIDADE TIPO - 1,5
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AS PERSPECTIVAS
IX Brazilian School of Superconductivity and
Workshop on Frontiers of Superconductivity
and Magnetism – Materials, Mechanisms and
Applications
10 -14 December, 2012
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Porto de Galinhas – PE – Brazil
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100 Anos de
Supercondutividade
OBRIGADO!
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Anos de Vitalidade

Transcription

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