# SUPERCONDUCTIVITY FROM UNDRESSING

Why does 'undressing' give rise to superconductivity? The qualitative explanation is as follows: electrons in metals are 'dressed' by a cloud of other electrons with which they interact. The dressing causes an increase in the electron's effective mass, and when the dressing is large the metal can't conduct electricity well. If however the electrons manage to 'undress' when the temperature is lowered, their effective mass will be reduced and electricity will flow easily. According to the papers listed below, this is how superconductivity arises. This process can only occur if the carriers in the metal in the normal state are 'holes' rather than electrons, and 'undressing' occurs (not surprisingly) when two hole carriers (of opposite spin of course!) form a pair. A hole is the absence of an electron, and it carries a positive rather than a negative charge. When holes undress, they turn into electrons, which then behave as electrons in giant atoms . BCS theory does not differentiate between electrons and holes, and consequently BCS theory cannot predict which materials will become superconducting at low temperatures.

Electrons in metals are also 'dressed' by the electron-ion interaction, and this interaction also impairs the electrical conductivity in the normal state, increasingly so as more electrons occupy the band. When there are too many electrons in a band (more than half as many as fit in), some of them 'anticontribute' rather than contribute to the electrical conductivity, i.e. they move in the wrong direction due to electron-ion scattering (this is the regime where conduction is carried by 'holes'). 'Undressing' also occurs from the electron-ion interaction, so that all electrons can contribute to the conduction of electricity in the superconducting state. Note added (2015) : the second part of the previous sentence, written several years ago, is certainly not correct.

### Superconductors that change color when they become superconducting,

Physica C 201, 347 (1992)

We consider models of superconductivity where pairing originates in gain of kinetic rather than potential energy of the carriers. In such systems, a change in the frequency dependent conductivity occurs at frequencies much higher than the scale set by the superconducting energy gap. This property follows from a general sum-rule argument. To clarify the physical origin of this spectral weight transfer we consider several microscopic Hamiltonians that give rise to an effective Hamiltonian with a kinetic pairing interaction. These models describe small polarons with a non-linear interaction with a background degree of freedom, that gives rise to an effective mass enhancement that depends on the local charge occupation. Superconductivity in these models can be understood as arising from the partial 'undressing' of carriers that occurs upon pairing. The same 'undressing' occurs in these systems upon doping in the normal state, which causes superconductivity to disappear at high doping. Optical conductivity is calculated for one of the model Hamiltonians to illustrate the effect. It is suggested that some of the observed phenomenology of high T_c oxide superconductors resembles the behavior of the class of superconductors discussed here.
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### Color change and other unusual spectroscopic features predicted by the model of hole superconductivity,

J. Phys. Chem. Solids 54 1101 (1993)

The model of hole superconductivity postulates that the mobility of a hole carrier increases with the hole concentration in the system. From this single assumption follows the existence of superconductivity in the system in the regime of low hole concentration, and a number of unusual spectroscopic features. (1) Spectral weight in the frequency dependent conductivity should be transfered from high to low frequencies in the normal state as the system is doped; (2) A similar spectral weight transfer in the frequency dependent conductivity should occur for fixed carrier concentration as the temperature is lowered and the system becomes superconducting; (3) In the single particle density of states, spectral weight transfer between positive and negative energies should occur when the system is cooled below T_c, leading to an asymmetry in tunneling and photoemission experiments: an enhanced spectral weight in photoemission and a corresponding decreased spectral weight in inverse photoemission, and a larger tunneling current for a negatively compared to a positively biased sample should be seen; (4) In angle resolved photoemission the sharpest peaks in the normal and superconducting states should occur for different k-values, and in a range of k-values the peak should move $towards$ the Fermi energy in the superconducting state while it is moving $away$ from it in the normal state.
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### Electron-hole asymmetric polarons

in "Polarons and Bipolarons in high Tc Superconductors and Related Materials", ed. by E.K.H. Salje, A.S. Alexandrov and W.Y. Liang, Cambridge University Press, Cambridge, 1995, p. 234

In small polaron models the hopping amplitude for a carrier from a site to a neighboring site is reduced due to dressing'' by a background degree of freedom. Electron-hole symmetry is broken if this reduction is different for a carrier in a singly occupied site and one in a doubly occupied site. Assuming that the reduction is smaller in the latter case, the implication is that a gradual 'undressing' of the carriers takes place as the system is doped and the carrier concentration increases. A similar 'undressing' will occur at fixed (low) carrier concentration as the temperature is lowered, if the carriers pair below a critical temperature and as a result the local'' carrier concentration increases (and the system becomes a superconductor). In both cases the 'undressing' can be seen in a transfer of spectral weight in the frequency-dependent conductivity from high frequencies (corresponding to non-diagonal transitions) to low frequencies (corresponding to diagonal transitions), as the carrier concentration increases or the temperature is lowered respectively. This experimental signature of electron-hole asymmetric polaronic superconductors as well as several others have been seen in high temperature superconducting oxides. Other experimental signatures predicted by electron-hole asymmetric polaron models remain to be tested.
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### Superconductivity from Undressing

Phys.Rev. B62, 14487 (2000) , cond-mat/0007115 (Los Alamos)

Photoemission experiments in high $T_c$ cuprates indicate that quasiparticles are heavily 'dressed' in the normal state, particularly in the low doping regime. Furthermore these experiments show that a gradual undressing occurs both in the normal state as the system is doped and the carrier concentration increases, as well as at fixed carrier concentration as the temperature is lowered and the system becomes superconducting. A similar picture can be inferred from optical experiments. It is argued that these experiments can be simply understood with the single assumption that the quasiparticle dressing is a function of the local carrier concentration. Microscopic Hamiltonians describing this physics are discussed. The undressing process manifests itself in both the one-particle and two-particle Green's functions, hence leads to observable consequences in photoemission and optical experiments respectively. An essential consequence of this phenomenology is that the microscopic Hamiltonians describing it break electron-hole symmetry: these Hamiltonians predict that superconductivity will only occur for carriers with hole-like character, as proposed in the theory of hole superconductivity.
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### Superconductivity from Undressing .II. Single Particle Green's Function and Photoemission in Cuprates

Phys.Rev. B62, 14498 (2000) , cond-mat/0007328 (Los Alamos)

Experimental evidence indicates that the superconducting transition in high $T_c$ cuprates is an 'undressing' transition. Microscopic mechanisms giving rise to this physics were discussed in the first paper of this series. Here we discuss the calculation of the single particle Green's function and spectral function for Hamiltonians describing undressing transitions in the normal and superconducting states. A single parameter, $\Upsilon$, describes the strength of the undressing process and drives the transition to superconductivity. In the normal state, the spectral function evolves from predominantly incoherent to partly coherent as the hole concentration increases. In the superconducting state, the 'normal' Green's function acquires a contribution from the anomalous Green's function when $\Upsilon$ is non-zero; the resulting contribution to the spectral function is $positive$ for hole extraction and $negative$ for hole injection. It is proposed that these results explain the observation of sharp quasiparticle states in the superconducting state of cuprates along the $(\pi,0)$ direction and their absence along the $(\pi,\pi)$ direction.
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### Superconductivity from Hole Undressing

cond-mat/0102136 (Los Alamos) , Physica C 364-365, 37 (2001)

Photoemission and optical experiments indicate that the transition to superconductivity in cuprates is an 'undressing' transition . In photoemission this is seen as a coherent quasiparticle peak emerging from an incoherent background, in optics as violation of the Ferrell-Glover-Tinkham sum rule indicating effective mass reduction of superconducting carriers. We propose that this is a manifestation of the fundamental electron-hole asymmetry of condensed matter described by the theory of hole superconductivity. The theory asserts that electrons in nearly empty bands and holes in nearly full bands are fundamentally different : the former yield high conductivity and normal metals, the latter yield low normal state conductivity and high temperature superconductivity. This is because the normal state transport of electrons is coherent and that of holes is incoherent. We explain how this asymmetry arises from the Coulomb interaction between electrons in atoms and the nature of atomic orbitals, and propose a simple Hamiltonian to describe it. A $universal$ mechanism for superconductivity follows from this physics, whereby dressed hole carriers undress by pairing, turning (partially) into electrons and becoming more mobile in the superconducting state.
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### Quasiparticle undressing in a dynamic Hubbard model: exact diagonalization study

cond-mat/0205006 (Los Alamos) , Phys.Rev. B66, 064507 (2002)

Dynamic Hubbard models have been proposed as extensions of the conventional Hubbard model to describe the orbital relaxation that occurs upon double occupancy of an atomic orbital. These models give rise to pairing of holes and superconductivity in certain parameter ranges. Here we explore the changes in carrier effective mass and quasiparticle weight and in one- and two-particle spectral functions that occur in a dynamic Hubbard model upon pairing, by exact diagonalization of small systems. It is found that pairing is associated with lowering of effective mass and increase of quasiparticle weight, manifested in transfer of spectral weight from high to low frequencies in one- and two-particle spectral functions. This 'undressing' phenomenology resembles observations in transport, photoemission and optical experiments in high $T_c$ cuprates. This behavior is contrasted with that of a conventional electron-hole symmetric Holstein-like model with attractive on-site interaction, where pairing is associated with 'dressing' instead of 'undressing'.

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### Electronic dynamic Hubbard model: exact diagonalization study

cond-mat/0207369 (Los Alamos) ,

A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wavefunction for two electrons occupying the same Wannier orbital is different from the product of single electron wavefunctions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transfered from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more 'dressed' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases, and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to 'undress' , hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.

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### Quasiparticle undressing: a new route to collective effects in solids

cond-mat/0211642 (Los Alamos) , in "Concepts in Electron Correlation", ed. by A.C. Hewson and V. Zlatic, Kluwer Academic Publishers, Dordrecht, 2003, p. 371.

The carriers of electric current in a metal are quasiparticles dressed by electron-electron interactions, which have a larger effective mass $m^*$ and a smaller quasiparticle weight $z$ than non-interacting carriers. If the momentum dependence of the self-energy can be neglected, the effective mass enhancement and quasiparticle weight of quasiparticles at the Fermi energy are simply related by $z=m/m^*$ ($m$=bare mass). We propose that both superconductivity and ferromagnetism in metals are driven by quasiparticle 'undressing', i.e., that the correlations between quasiparticles that give rise to the collective state are associated with an increase in $z$ and a corresponding decrease in $m^*$ of the carriers. Undressing gives rise to lowering of kinetic energy, which provides the condensation energy for the collective state. In contrast, in conventional descriptions of superconductivity and ferromagnetism the transitions to these collective states result in $increase$ in kinetic energy of the carriers and are driven by lowering of potential energy and exchange energy respectively.

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### Electron-hole asymmetry is the key to superconductivity

cond-mat/0301610 (Los Alamos) , New3SC-4 meeting, San Diego, Jan. 16-21 2003; Int. J. Mod. Phys. B 17, 3236 (2003).

In a solid, transport of electricity can occur via negative electrons or via positive holes. In the normal state of superconducting materials experiments show that transport is usually dominated by dressed positive hole carriers. Instead, in the superconducting state experiments show that the supercurrent is always carried by undressed negative electron carriers. These experimental facts indicate that electron-hole asymmetry plays a fundamental role in superconductivity, as proposed by the theory of hole superconductivity.
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### Why holes are not like electrons. II. The role of the electron-ion interaction.

cond-mat/0504013(Los Alamos) , Phys.Rev.B 71, 104522 (2005).

In recent work ( Phys.Rev. B 65, 184502 (2002) ), we discussed the difference between electrons and holes in energy band in solids from a many-particle point of view, originating in the electron-electron interaction, and argued that it has fundamental consequences for superconductivity. Here we discuss the fact that there is also a fundamental difference between electrons and holes already at the single particle level, arising from the electron-ion interaction. The difference between electrons and holes due to this effect parallels the difference due to electron-electron interactions: holes are more dressed than electrons . We propose that superconductivity originates in 'undressing' of carriers from $both$ electron-electron and electron-ion interactions, and that both aspects of undressing have observable consequences. -----------------------------------------------------------------------------------------------------------------------------

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