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John Bardeen

Other affiliations: Harvard University, Bell Labs
Bio: John Bardeen is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Superconductivity & Quantum tunnelling. The author has an hindex of 47, co-authored 127 publications receiving 26243 citations. Previous affiliations of John Bardeen include Harvard University & Bell Labs.


Papers
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TL;DR: In this article, a theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, and it is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction.
Abstract: A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, $\ensuremath{\hbar}\ensuremath{\omega}$. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor, formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum, is lower in energy than the normal state by amount proportional to an average ${(\ensuremath{\hbar}\ensuremath{\omega})}^{2}$, consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about $3.5k{T}_{c}$ at $T=0\ifmmode^\circ\else\textdegree\fi{}$K to zero at ${T}_{c}$. Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions, useful for perturbation expansions and calculations of transition probabilities, are given.

9,619 citations

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TL;DR: In this article, the authors used the method of effective mass, extended to apply to gradual shifts in energy bands resulting from deformations of the crystal lattice, to estimate the interaction between electrons of thermal energy and the acoustical modes of vibration.
Abstract: The method of effective mass, extended to apply to gradual shifts in energy bands resulting from deformations of the crystal lattice, is used to estimate the interaction between electrons of thermal energy and the acoustical modes of vibration. The mobilities of electrons and holes are thus related to the shifts of the conduction and valence-bond (filled) bands, respectively, associated with dilations of longitudinal waves. The theory is checked by comparison of the sum of the shifts of the conduction and valence-bond bands, as derived from the mobilities, with the shift of the energy gap with dilation. The latter is obtained independently for silicon, germanium and tellurium from one or more of the following: (1) the change in intrinsic conductivity with pressure, (2) the change in resistance of an $n\ensuremath{-}p$ junction with pressure, and (3) the variation of intrinsic concentration with temperature and the thermal expansion coefficient. Higher mobilities of electrons and holes in germanium as compared with silicon are correlated with a smaller shift of energy gap with dilation.

2,530 citations

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TL;DR: In this paper, the key steps in the development of the microscopic understanding of superconductivity are discussed, and a detailed review of the main steps in this process is presented. But,
Abstract: Key steps in the development of the microscopic understanding of superconductivity are discussed.

1,969 citations

Journal ArticleDOI
John Bardeen1
TL;DR: In this article, it was shown that if contact is made with a metal, the difference in work function between metal semi-conductor is compensated by surface states charge, rather than by a space charge as is independent of the metal.
Abstract: Localized states (Tamm levels), having energies distributed in the “forbidden” range between the filled band and the conduction band, may exist at the surface of a semi-conductor. A condition of no net charge on the surface atoms may correspond to a partial filling of these states. If the density of surface levels is sufficiently high, there will be an appreciable double layer at the free surface of a semi-conductor formed from a net charge from electrons in surface states and a space charge of opposite sign, similar to that at a rectifying junction, extending into the semi-conductor. This double layer tends to make the work function independent of the height of the level in the interior (which in turn depends on impurity content). If contact is made with a metal, the difference in work function between metal semi-conductor is compensated by surface states charge, rather than by a space charge as is independent of the metal. Rectification characteristics are then independent of the metal. These ideas are used to explain results of Meyerhof and others on the relation between contact potential differences and rectification.

1,716 citations


Cited by
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TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
Abstract: It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc , and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.

8,720 citations

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TL;DR: In this article, a relation for the variation of the energy gap (E g ) with temperature (T ) in semiconductors is proposed. And the equation satisfactorily represents the experimental data for diamond, Si, Ge, 6H-SiC, GaAs, InP and InAs.

4,451 citations

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TL;DR: In this paper, a superconductive solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian, and the pions of finite mass are found as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangians which otherwise possesses a certain type of the ∆-ensuremath{gamma{5}$ invariance.
Abstract: Continuing the program developed in a previous paper, a "superconductive" solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian. We find the pions of finite mass as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangian which otherwise possesses a certain type of the ${\ensuremath{\gamma}}_{5}$ invariance. In addition, heavier mesons and two-nucleon bound states are obtained in the same approximation. On the basis of numerical mass relations, it is suggested that the bare nucleon field is similar to the electron-neutrino field, and further speculations are made concerning the complete description of the baryons and leptons.

3,923 citations

Journal ArticleDOI
W. L. McMillan1
TL;DR: In this paper, the superconducting transition temperature is calculated as a function of the electron-phonon and electron-electron coupling constants within the framework of strong coupling theory.
Abstract: The superconducting transition temperature is calculated as a function of the electron-phonon and electron-electron coupling constants within the framework of the strong-coupling theory. Using this theoretical result, we find empirical values of the coupling constants and the "band-structure" density of states for a number of metals and alloys. It is noted that the electron-phonon coupling constant depends primarily on the phonon frequencies rather than on the electronic properties of the metal. Finally, using these results, one can predict a maximum superconducting transition temperature.

3,895 citations

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Jingsi Qiao1, Xianghua Kong1, Zhixin Hu1, Feng Yang1, Wei Ji1 
TL;DR: A detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) is presented to predict its electrical and optical properties, finding that the mobilities are hole-dominated, rather high and highly anisotropic.
Abstract: Two-dimensional crystals are emerging materials for nanoelectronics. Development of the field requires candidate systems with both a high carrier mobility and, in contrast to graphene, a sufficiently large electronic bandgap. Here we present a detailed theoretical investigation of the atomic and electronic structure of few-layer black phosphorus (BP) to predict its electrical and optical properties. This system has a direct bandgap, tunable from 1.51 eV for a monolayer to 0.59 eV for a five-layer sample. We predict that the mobilities are hole-dominated, rather high and highly anisotropic. The monolayer is exceptional in having an extremely high hole mobility (of order 10,000 cm(2) V(-1) s(-1)) and anomalous elastic properties which reverse the anisotropy. Light absorption spectra indicate linear dichroism between perpendicular in-plane directions, which allows optical determination of the crystalline orientation and optical activation of the anisotropic transport properties. These results make few-layer BP a promising candidate for future electronics.

3,622 citations