Classical physics and
Johannes van der Waals with the
helium liquefactor at Leiden in 1908 One of the first studies of condensed states of matter was by
English chemist Humphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty
chemical elements known at the time, twenty-six had
metallic properties such as
lustre,
ductility and high electrical and thermal conductivity. This indicated that the atoms in
John Dalton's
atomic theory were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were then believed to be gases, such as
nitrogen and
hydrogen could be liquefied under the right conditions and would then behave as metals. In 1823,
Michael Faraday, then an assistant in Davy's lab, successfully liquefied
chlorine and went on to liquefy all known gaseous elements, except for nitrogen, hydrogen, and
oxygen. and
Dutch physicist
Johannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures. By 1908,
James Dewar and
Heike Kamerlingh Onnes were successfully able to liquefy hydrogen and the then newly discovered
helium respectively. However, despite the success of
Drude's model, it had one notable problem: it was unable to correctly explain the electronic contribution to the
specific heat and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures. In 1911, three years after helium was first liquefied, Onnes working at
University of Leiden discovered
superconductivity in
mercury, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value. The phenomenon completely surprised the best theoretical physicists of the time, and it remained unexplained for several decades.
Albert Einstein, in 1922, said regarding contemporary theories of superconductivity that "with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas."
Advent of quantum mechanics Drude's classical model was augmented by
Wolfgang Pauli,
Arnold Sommerfeld,
Felix Bloch and other physicists. Pauli realized that the free electrons in metal must obey the
Fermi–Dirac statistics. Using this idea, he developed the theory of
paramagnetism in 1926. Shortly after, Sommerfeld incorporated the
Fermi–Dirac statistics into the
free electron model and made it better to explain the heat capacity. Two years later, Bloch used
quantum mechanics to describe the motion of an electron in a periodic lattice.
Band structure calculations were first used in 1930 to predict the properties of new materials, and in 1947
John Bardeen,
Walter Brattain and
William Shockley developed the first
semiconductor-based
transistor, heralding a revolution in electronics. This phenomenon, arising due to the nature of charge carriers in the conductor, came to be termed the
Hall effect, but it was not properly explained at the time because the electron was not experimentally discovered until 18 years later. After the advent of quantum mechanics,
Lev Landau in 1930 developed the theory of
Landau quantization and laid the foundation for a theoretical explanation of the
quantum Hall effect which was discovered half a century later. Magnetism as a property of matter has been known in China since 4000 BC. However, the first modern studies of magnetism only started with the development of
electrodynamics by Faraday,
Maxwell and others in the nineteenth century, which included classifying materials as
ferromagnetic,
paramagnetic and
diamagnetic based on their response to magnetization.
Pierre Curie studied the dependence of magnetization on temperature and discovered the
Curie point phase transition in ferromagnetic materials. The first attempt at a microscopic description of magnetism was by
Wilhelm Lenz and
Ernst Ising through the
Ising model that described magnetic materials as consisting of a periodic lattice of
spins that collectively acquired magnetization. The Sommerfeld model and spin models for ferromagnetism illustrated the successful application of quantum mechanics to condensed matter problems in the 1930s. However, there still were several unsolved problems, most notably the description of
superconductivity and the
Kondo effect. After
World War II, several ideas from quantum field theory were applied to condensed matter problems. These included recognition of
collective excitation modes of solids and the important notion of a quasiparticle. Soviet physicist
Lev Landau used the idea for the
Fermi liquid theory wherein low energy properties of interacting fermion systems were given in terms of what are now termed Landau-quasiparticles. Eventually in 1956,
John Bardeen,
Leon Cooper and
Robert Schrieffer developed the so-called
BCS theory of superconductivity, based on the discovery that arbitrarily small attraction between two electrons of opposite spin mediated by
phonons in the lattice can give rise to a bound state called a
Cooper pair.
Leo Kadanoff,
Benjamin Widom and
Michael Fisher developed the ideas of
critical exponents and
widom scaling. These ideas were unified by
Kenneth G. Wilson in 1972, under the formalism of the
renormalization group in the context of quantum field theory. In 1981, theorist
Robert Laughlin proposed a theory explaining the unanticipated precision of the integral plateau. It also implied that the Hall conductance is proportional to a topological invariant, called
Chern number, whose relevance for the band structure of solids was formulated by
David J. Thouless and collaborators. Shortly after, in 1982,
Horst Störmer and
Daniel Tsui observed the
fractional quantum Hall effect where the conductance was now a rational multiple of the constant e^2/h. Laughlin, in 1983, realized that this was a consequence of quasiparticle interaction in the Hall states and formulated a
variational method solution, named the
Laughlin wavefunction. The study of topological properties of the fractional Hall effect remains an active field of research. Decades later, the aforementioned topological band theory advanced by
David J. Thouless and collaborators was further expanded leading to the discovery of
topological insulators. In 1986,
Karl Müller and
Johannes Bednorz discovered the first
high temperature superconductor, La2-xBaxCuO4, which is superconducting at temperatures as high as 39
kelvin. It was realized that the high temperature superconductors are examples of strongly correlated materials where the electron–electron interactions play an important role. A satisfactory theoretical description of high-temperature superconductors is still not known and the field of
strongly correlated materials continues to be an active research topic.