Gu,4 and jiandong guo1 1beijing national laboratory for condensedmatter physics and institute of physics, chinese academy of sciences, beijing. In metals, where the relaxation processes depend on both electrons and phonons, all thermodynamic and transport properties are dictated by electron phonon ep interaction. Competition of electronphonon mediated superconductivity and. Gu,4 and jiandong guo1 1beijing national laboratory for condensedmatter physics and institute of physics, chinese academy of sciences, beijing 100190, china 2international center for quantum. Direct determination of the electron phonon coupling matrix element in a correlated system huajun qin,1 junren shi,2,1 yanwei cao,1 kehui wu,1 jiandi zhang,3 e. Here the theory of electrons interacting with harmonic phonons, initially pioneered by.
The gatekeepers of bcs theory are those relatively few physicists who have performed detailed eliashberg calculations of. Bcs theory of superconductivity the properties of type i superconductors were modeled successfully by the efforts of john bardeen, leon cooper, and robert schrieffer in what is commonly called the bcs theory. The effective attractive interaction between electrons, mediated by electronphonon coupling, is a wellestablished mechanism of conventional superconductivity. In metals, where the relaxation processes depend on both electrons and phonons, all thermodynamic and transport. The theory describes superconductivity as a microscopic effect caused by a condensation of cooper pairs. Electronphonon interaction in conventional and unconventional superconductors pegor aynajian auth.
Electron phonon in general, electron ion interaction is an important and ubiquitous process in solids, affecting almost all physical properties. The main point of the bcs theory is that the attractive electronelectron interaction mediated by the phonons gives rise to cooper pairs, i. The theory is also used in nuclear physics to describe the pairing. If one now includes the electron phonon coupling, however, the electronic medium screens the longrange coulomb interaction, leading to a nite interaction length and the. Scrutiny shows that the outcomewasaconsistentmismatch. Electron phonon interactions are crucial for conventional superconductors. Lecture notes on superconductivity a work in progress.
Electronphonon interactions so far, we considered the motion of electrons in the static periodic potential that would arise if. Bcs theory fails to explain high temperature superconductivity because electronphonon coupling cannot be made strong enough and more importantly because the hightc superconductors lack a fermi surface just above tc. A recently developed renormalization approach is used to study the electron phonon coupling in many electron systems. Related evidence for strong electronphonon interaction. The factors, which determine superconducting behavior, are electron phonon interaction, the effect of electron electron coulomb interaction on pairing, averaged phonon frequency square, 2, and debye temperature d. In the meantime a second electron seen below in a is attracted to the po larized region, which has remained polarized long after the first electron has left the region. A primary reason for this is the instantaneous nature of the bcs interaction which does not incorporate enough of the physics of the electronphonon system.
T, which derives from the same electronphonon interaction in the normal state. A recently developed renormalization approach is used to study the electronphonon coupling in manyelectron systems. Superconductivity in diamond, electron phonon interaction and. Coulomb interaction between electrons is shielded by the other electrons and the electrons also shield the ions involved in the vibrational motion. This lecture addresses the consequences of electronphonon coupling.
Bcs theory or bardeencooperschrieffer theory named after john bardeen, leon cooper, and john robert schrieffer is the first microscopic theory of superconductivity since heike kamerlingh onness 1911 discovery. Lecture notes on superconductivity a work in progress daniel arovas congjun wu department of physics university of california, san diego june 23, 2019. We use the standard bcs theory and assume an swave pairing interaction. Electron phonon interactions an overview sciencedirect topics. Bcs theory electrons acting as pairs via lattice interaction. Superconductivity in diamond, electron phonon interaction. Bcs theory of superconductivity hyperphysics concepts. Bcs theory of driven superconductivity european physical journal.
In conventional superconductors, this attraction is due to the electronphonon interaction. Bcs theory fails to explain high temperature superconductivity because electron phonon coupling cannot be made strong enough and more importantly because the hightc superconductors lack a fermi surface just above tc. The fundamental difference between the superconducting and normal ground state wave functions is produced when the large degeneracy of singleparticle electron levels in the normal state is removed. However, bcs theory predicted a theoretical maximum to t c of around 3040k, as above this, thermal energy would cause electronphonon interactions of an energy too high to allow formation of or sustain cooper pairs. Pines and i derived an effective electron electron interaction starting from a hamiltonian in which phonon and coulomb terms are included from the start. Electronphonon interaction in strongly correlated systems article pdf available in advances in condensed matter physics 201012 march 2010 with 241 reads how we measure reads. Pdf electronphonon interaction in strongly correlated systems. The cooper pair state is responsible for superconductivity, as described in the bcs theory developed by john bardeen, leon cooper, and john schrieffer for which they shared the 1972 nobel prize.
We are now ready to show that interaction with phonons leads to atraction. Recallthattheionsinametalhave two basic e ects on the electronic states. By that virtue, two electrons couple to form socalled cooper pairs, which act in a fundamentally different way from single electrons. This is surprising, because the electronphonon problem is well studied, especially in the weak coupling limit. For a formal derivation, expand the evolution operator with respect to the electronphonon interaction. Empirical rule to reconcile bardeencooperschrieffer theory.
Phonon mediated attractive interaction and the cooper pairs. At this point we are seriously worried that we dont understand how acoustic phonons ever exist in charged systems. Nonadiabatic interaction between the valence electrons and the ion motion in a solid reveals the break down of the bornoppenheimer approximation electrons are not in nitely fast plasmon. A key conceptual element in this theory is the pairing of electrons close to the fermi level into cooper pairs through interaction with the crystal lattice. The salient point of the socalled bcs theory is the attractive electron interaction mediated by phonons. Electronphonon in general, electronion interaction is an important and ubiquitous process in solids, affecting almost all physical properties. The electron phonon interaction plays an important role in imparting superconductivity in the material. The problem of conventional, lowtemperature superconductivity has been regarded as solved since the seminal work of bardeen, cooper, and schrieffer bcs more than 50 years ago. Coulomb interaction between electrons modify the electronphonon interaction that gives rise to the apparently weak attractive phononinduced interaction between electrons that frohlich 4 had conjectured in 1952 might be the way phonons make possible a transition to the superconducting state, and what is the net interaction that results when.
The first conclusion are based on the isotopic effect in conventional. Electronphonon interaction in nanostructures at subkelvin. D is a typical debye phonon frequency after averaging for. Bcs theory electron pairing vih hia phonon exchange main ingredient. Pdf electronphonon interaction in strongly correlated. Electronphonon coupling in metallic solids from density. By starting from an hamiltonian which includes a small gauge symmetry breaking field, we directly derive a bcs like equation for the energy gap from the renormalization approach. The factors, which determine superconducting behavior, are electronphonon interaction, the effect of electronelectron coulomb interaction on pairing, averaged phonon frequency square, 2, and debye temperature d. The second term is the extra part describing the electronphonon interaction. Electron phonon interactions a rigorous treatment on electronphonon interactions requires quantum field theory. The evidence for a small band gap at the fermi level was a key piece in the puzzle. This indicates that a mechanism qualitatively beyond the standard bcs theory determines the magnitude and anisotropy of the superconducting gap. Superconductivity in diamond, electronphonon interaction.
In conventional superconductors, this attraction is due to the electron phonon interaction. Why does bcs theory fail to explain superconductivity at. The superconductivity observed in borondoped diamond is discussed from the point of view of the phonondriven bcs theory. But the effects of anharmonicity on the electronphonon problem, and more speci. These fermion pairs are known as cooper pairs, and this theory of superconductivity is known as the bcs theory for bardeen, cooper and schrieffer. Othersemiconductors possibly exhibiting superconductivity are broughtto the fore. Concepts of fermi liquid theory and instability of the normal state. This attraction appears in the second order of the perturbation theory as the phonon line in the diagram, see fig. Electronphonon interaction in nanostructures at sub. Evidence for strong electronphonon coupling in mgcni3. Bcs theory relates the value of the critical field at zero temperature to the value of the transition temperature and the density of states at the fermi level.
How the electronphonon coupling mechanism work in metal. The effective attractive interaction between electrons, mediated by electron phonon coupling, is a wellestablished mechanism of conventional superconductivity. Electronic band structure, electronphonon interaction. Bcs theory showed that the basic interaction responsible for superconductivity appears to be that of a pair of electrons by means of an interchange of virtual phonons. Competition of electronphonon mediated superconductivity.
Introduction to electronphonon interactions youtube. Due to timelimitation here are just describe the physical picture without rigorous proof. Bcs theory \bcsbardeencooperschrie ertheoryisessentiallyjusthartreefocktheorylec. We will then calculate and study interesting quantities of the superconducting system, and nally describe how the results predicted by the bcs theory fare against experimental evidence obtained about superconductors.
First, we need to write this in the second quantization, to be similar to the electronic and phonon parts. Within the bcs theory, the electronphonon interaction is the source of the attraction that binds two electrons into a paired state, generally referred to as cooper. The vast majority of physicists that use bcs theory do so with model. The treatment of a metal as containing a gas of electrons completely free to move within it. Electronphonon interactions induce an effective attractive interactions between electrons. Other semiconductors possibly exhibiting superconductivity are brought to the fore. Electronphonon interaction in nanostructures at subkelvin temperatures 2 nd international conference and exhibition on mesoscopic and condensed matter physics october 2628, 2016 chicago, usa. Upon evaluating the drivinginduced vertex corrections of the phonon mediated electronelectron interaction. Bcs theory \ bcs bardeencooperschrie ertheoryisessentiallyjusthartreefocktheorylec. Meanwhile,apparentlyasacheck,attempts were made to calculate electrical resistivity against temperature. Electronic band structure, electronphonon interaction, and. F density of states per spin at fermi level g kk eltlectronphhtiltonon matrix element. Q, gives only a small renormalization of the phonon frequencies. It is shown that electronphonon interaction is particularly strong in diamond.
The theory was originally proposed in 1900 to describe and correlate the electrical and thermal properties of metals. Direct determination of the electronphonon coupling matrix. The hubbardholstein model is a simple model including both electron phonon interaction and electron electron correlations. How did they come up with that idea for the bcs theory of superconductivity. Why does bcs theory fail to explain superconductivity at high.
Electron phonon interactions a rigorous treatment on electron phonon interactions requires quantum field theory. Last but not least, there is also a sizable variety on the magnitude of the electronphonon. Empirical rule to reconcile bardeencooperschrieffer. Thus the bcs theory focuses on the consequences of an attractive twobody interaction without enquiring too much further about its origin. As to the electrons, migdal noted that we are interested in states k very close to kf. Electronphonon interaction in conventional and unconventional superconductors. The formation of cooper pairs is supported by the fact that bcs and the ginzburglandau theories predict the charge and mass of the supercurrent. However, the theory does not allow accurate predictions of some of the most fundamental properties of a superconductor. In its simplest form, bcs gives the superconducting transition temperature t c in terms of the electron phonon coupling potential v and the debye cutoff energy e d. The electronphonon interaction plays an important role in imparting superconductivity in the material. By starting from an hamiltonian which includes a small gauge symmetry breaking field, we directly derive a bcslike equation for the.
Electron phonon interaction in conventional and unconventional superconductors pegor aynajian auth. In this work, using the extended attractive hubbard model and greens function method, we calculate the superconducting critical temperature, tc, as a function of electron band. Direct determination of the electronphonon coupling matrix element in a correlated system huajun qin,1 junren shi,2,1 yanwei cao,1 kehui wu,1 jiandi zhang,3 e. Bcs theory finite temperatures formation of pairs origin of attractive interaction outline 1 cooperpairs formation of pairs origin of attractive interaction 2 bcs theory the model hamiltonian bogoliubovvalatintransformation calculation of the condensation energy 3 finite temperatures excitation energies and the energy gap determination of t c. Introduction superconductivity discovered in 1911 by onnes 9, is the. Originally this idea sounds like crazy, because electrons the same charge so they have repulsive interactions. In metals exhibiting a fermi surface, the critical temperature of superconductivity is exponentially smaller than the characteristic phonon energy. Bcs theory revisited pdf isospin representation of the bcs hamiltonian. Suppose an electron approaches a positive ion core.