arXiv subjects
Publications and source records attributed to J. E. Hirsch.
Herbert Fröhlich is generally credited with having predicted the fundamental role of electron-phonon interactions in superconductivity in 1950, and in particular the isotope effect, without any experimental input. Here we examine the facts on which this belief is based and point out that whether or not the generally accepted view is true depends on the meaning of the word {\it shortly}.
The theory of hole superconductivity proposes that superconductivity is driven by lowering of quantum kinetic energy and is associated with expansion of electronic orbits and expulsion of negative charge from the interior to the surface of superconductors and beyond. This physics provides a dynamical explanation of the Meissner effect. Here we propose that similar physics takes place in superfluid helium 4. Experimental manifestations of this physics in $^4He$ are the negative thermal expansion of $^4He$ below the $λ$ point and the "Onnes effect", the fact that superfluid helium will creep up the walls of the container and escape to the exterior. The Onnes effect and the Meissner effect are proposed to originate in macroscopic zero point rotational motion of the superfluids. It is proposed that this physics indicates a fundamental inadequacy of conventional quantum mechanics.
The Meissner effect and the Spin Meissner effect are the spontaneous generation of charge and spin current respectively near the surface of a metal making a transition to the superconducting state. The Meissner effect is well known but, I argue, not explained by the conventional theory, the Spin Meissner effect has yet to be detected. I propose that both effects take place in all superconductors, the first one in the presence of an applied magnetostatic field, the second one even in the absence of applied external fields. Both effects can be understood under the assumption that electrons expand their orbits and thereby lower their quantum kinetic energy in the transition to superconductivity. Associated with this process, the metal expels negative charge from the interior to the surface and an electric field is generated in the interior. The resulting charge current can be understood as arising from the magnetic Lorentz force on radially outgoing electrons, and the resulting spin current can be understood as arising from a spin Hall effect originating in the Rashba-like coupling of the electron magnetic moment to the internal electric field. The associated electrodynamics is qualitatively different from London electrodynamics, yet can be described by a small modification of the conventional London equations. The stability of the superconducting state and its macroscopic phase coherence hinge on the fact that the orbital angular momentum of the carriers of the spin current is found to be exactly $\hbar/2$, indicating a topological origin. The simplicity and universality of our theory argue for its validity, and the occurrence of superconductivity in many classes of materials can be understood within our theory.
Is superconductivity associated with a lowering or an increase of the kinetic energy of the charge carriers? Conventional BCS theory predicts that the kinetic energy of carriers increases in the transition from the normal to the superconducting state. However, substantial experimental evidence obtained in recent years indicates that in at least some superconductors the opposite occurs. Motivated in part by these experiments many novel mechanisms of superconductivity have recently been proposed where the transition to superconductivity is associated with a lowering of the kinetic energy of the carriers. However none of these proposed unconventional mechanisms explores the fundamental reason for kinetic energy lowering nor its wider implications. Here I propose that kinetic energy lowering is at the root of the Meissner effect, the most fundamental property of superconductors. The physics can be understood at the level of a single electron atom: kinetic energy lowering and enhanced diamagnetic susceptibility are intimately connected. According to the theory of hole superconductivity, superconductors expel negative charge from their interior driven by kinetic energy lowering and in the process expel any magnetic field lines present in their interior. Associated with this we predict the existence of a macroscopic electric field in the interior of superconductors and the existence of macroscopic quantum zero-point motion in the form of a spin current in the ground state of superconductors (spin Meissner effect). In turn, the understanding of the role of kinetic energy lowering in superconductivity suggests a new way to understand the fundamental origin of kinetic energy lowering in quantum mechanics quite generally.
The role of electron-electron interactions is analyzed for Rashba-like and spin-split systems within a tight-binding single-band Hubbard model with on-site and all nearest-neighbor matrix elements of the Coulomb interaction. By Rashba-like systems we refer to the Dresselhaus and Rashba spin-orbit coupled phases; spin-split systems have spin-up and spin-down Fermi surfaces shifted relative to each other. Both systems break parity but preserve time-reversal symmetry. They belong to a class of symmetry-breaking ground states that satisfy: (i) electron crystal momentum is a good quantum number (ii) these states have no net magnetic moment and (iii) their distribution of `polarized spin' in momentum space breaks the lattice symmetry. In this class, the relevant Coulomb matrix elements are found to be nearest-neighbor exchange $J$, pair-hopping $J'$ and nearest-neighbor repulsion $V$. These ground states lower their energy most effectively through $J$, hence we name them Class $J$ states. The competing effects of $V-J'$ on the direct and exchange energies determine the relative stability of Class $J$ states. We show that the spin-split and Rashba-like phases are the most favored ground states within Class $J$ because they have the minimum anisotropy in `polarized spin'. On a square lattice we find that the spin-split phase is always favored for near-empty bands; above a critical filling, we predict a transition from the paramagnetic to the Rashba-like phase at $ J_{c1}$ and a second transition to the spin-split state at $J_{c2}>J_{c1}$. An energetic comparison with ferromagnetism highlights the importance of the role of $V$ in the stability of Class $J$ states. We discuss the relevance of our results to (i) the $α$ and $β$ phases proposed by Wu and Zhang in the Fermi Liquid formalism and (ii) experimental observations of spin-orbit splitting in \emph{Au}(111) surface states.
At zero temperature, two-site dynamical mean field theory is applied to the Dynamic Hubbard model. The Dynamic Hubbard model describes the orbital relaxation that occurs when two electrons occupy the same site, by using a two-level boson field at each site. At finite boson frequency, the appearance of a Mott gap is found to be enhanced even though it shows a metallic phase with the same bare on-site interaction $U$ in the conventional Hubbard model. The lack of electron-hole symmetry is highlighted through the quasi-particle weight and the single particle density of states at different fillings, which qualitatively differentiates the dynamic Hubbard model from other conventional Hubbard-like models.
I propose that the phase of an electron's wave function changes by $π$ when the electron goes around a loop maintaining phase coherence. Equivalently, that the minimum orbital angular momentum of an electron in a ring is $\hbar/2$ rather than zero as generally assumed, hence that the electron in a ring has azimuthal zero point motion. This proposal provides a physical explanation for the origin of electronic `quantum pressure', it implies that a spin current exists in the ground state of aromatic ring molecules, and it suggests an explanation for the ubiquitousness of persistent currents observed in mesoscopic rings.
It is proposed that superconductors possess a hidden `hole core' buried deep in the Fermi sea. The proposed hole core is a small region of the Brillouin zone (usually at the center of the zone) where the lowest energy states in the normal state reside. We propose that in the superconducting state these energy states become {\it singly occupied} with electrons of a definite spin helicity. In other words, that holes of a definite spin helicity condense from the top to the bottom of the band in the transition to superconductivity, and electrons of that spin helicity `float' on top of the hole core, thus becoming highly mobile. The hole core has radius $q_0=1/2λ_L$, with $λ_L$ the London penetration depth, and the electrons expelled from the hole core give an excess negative charge density within a London penetration depth of the real space surface of the superconductor. The hole core explains the development of a spin current in the transition to superconductivity (Spin Meissner effect) and the associated negative charge expulsion from the interior of metals in the transition to superconductivity, effects we have proposed in earlier work to exist in all superconductors and to be at the root of the Meissner effect.
In paper III of this series (arXiv:0901.3612) we proposed a scenario of superconductivity driven by hole "undressing" that involved a complete redistribution of the occupation of single particle energy levels: the holes near the top of the band were proposed to all condense to the bottom of the band. Here we consider a less drastic redistribution involving electrons with a definite spin chirality and show that it is in fact energetically favored by the Coulomb exchange matrix element $J$ over the scenario proposed earlier. It is shown that spin splitting with chiral states reduces the Coulomb repulsion and hence that the Coulomb repulsion promotes spin splitting. Superconductors are proposed to possess a spin-split hole `core' at the bottom of the electronic conduction band in addition to a spin-split Fermi surface. The new scenario leads naturally to the existence of a spin current in the superconducting state and is consistent with the Spin Meissner effect and negative charge expulsion discussed earlier within the theory of hole superconductivity.
I propose the index $\hbar$ ("hbar"), defined as the number of papers of an individual that have citation count larger than or equal to the $\hbar$ of all coauthors of each paper, as a useful index to characterize the scientific output of a researcher that takes into account the effect of multiple coauthorship. The bar is higher for $\hbar$.
The symmetry properties of the Cooper pairing problem for multi-component ultra-cold dipolar molecular systems are investigated. The dipolar anisotropy provides a natural and robust mechanism for both triplet and singlet Cooper pairing to first order in the interaction strength. With a purely dipolar interaction, the triplet $p_z$-like polar pairing is the most dominant. A short-range attractive interaction can enhance the singlet pairing to be nearly degenerate with the triplet pairing. We point out that these two pairing channels can mix by developing a relative phase of $\pm\fracπ{2}$, thus spontaneously breaking time-reversal symmetry. We also suggest the possibility of such mixing of triplet and singlet pairing in other systems.
In the usual description of electrons in metals and superconductors, the single electron states are assumed to satisfy Bloch's theorem. This is because the electron-ion interaction is privileged over the electron-electron interaction. However the theory of hole superconductivity proposes that in the transition to superconductivity carriers `undress' from the electron-ion interaction. I propose here a new basis set to describe electrons in the superconducting state that does not satisfy Bloch's theorem but instead is designed to optimize the electron-electron interaction. The new basis set favors a superconducting state where a spin current exists and where states near the bottom of the band become partially occupied, as predicted by the theory of hole superconductivity.
In a voltaic cell, positive (negative) ions flow from the low (high) potential electrode to the high (low) potential electrode, driven by an `electromotive force' which points in opposite direction and overcomes the electric force. Similarly in a superconductor charge flows in direction opposite to that dictated by the Faraday electric field as the magnetic field is expelled in the Meissner effect. The puzzle is the same in both cases: what drives electric charges against electromagnetic forces? I propose that the answer is also the same in both cases: kinetic energy lowering, or `quantum pressure'.
We predict that simple metals and early transition metals that become superconducting under high pressures will show a change in sign of their Hall coefficient from negative to positive under pressure. If verified, this will strongly suggest that hole carriers play a fundamental role in `conventional' superconductivity, as predicted by the theory of hole superconductivity.
I argue that the conventional BCS-London theory of superconductivity does not explain the most fundamental property of superconductors, the Meissner effect: how is the Meissner current generated, and how is it able to defy Faraday's law? How is its mechanical angular momentum compensated? I propose that superconductivity is impossible unless the metal expels charge from its interior towards the surface in the transition to superconductivity. As a consequence, superconductors in their ground state are predicted to possess a macroscopic electric field in their interior, as well as excess negative charge and a macroscopic spin current near the surface. The system is driven normal when the applied magnetic field is strong enough to bring the spin current to a stop. High temperature superconductivity occurs in systems that have too much negative charge.
The time-tested BCS theory of superconductivity is generally accepted to be the correct theory of conventional superconductivity by physicists and, by extension, by the world at large. In a different realm of human activity, until very recently Bernard Madoff's time-tested investment operation was generally accepted as true and legitimate in the financial world. Madoff's Ponzi scheme, where old investors were being paid off by funds contributed by new investors, was fundamentally flawed, yet was able to thrive for decades because of many vested interests. `Red flags' suggesting its illegitimacy were ignored. Here I suggest that the same is true of BCS theory. There are an increasing number of `red flags' that strongly suggest the possibility that BCS theory may be fundamentally flawed. For example, an ever-growing number of superconductors are being classified as `unconventional', not described by the conventional BCS theory and each requiring a different physical mechanism. In addition, I argue that BCS theory is unable to explain the Meissner effect, $the$ most fundamental property of superconductors. There are several other phenomena in superconductors for which BCS theory provides no explanation, and BCS theory has proven unable to predict any new superconducting compounds. From one day to the next, Madoff's edifice came crashing down and a staggering 50 billion dollars evaporated, and I suggest that this may also be the fate of BCS theory. I outline an alternative theory to conventional BCS theory proposed to apply to all superconductors, `conventional' as well as `unconventional', that offers an explanation for the Meissner effect as well as for other puzzles and provides clear guidelines in the search for new high temperature superconductors.
In recent work, 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[1], and from a single particle point of view, originating in the electron-ion interaction[2]. We proposed that superconductivity in solids only occurs when the Fermi level is close to the top of a band (hole carriers), that it originates in `undressing' of carriers from $both$ the electron-electron and the electron-ion interaction, and that as a consequence holes in the normal state behave like electrons in the superconducting state[3]. However, the connection between both undressing effects was left unclear, as was left unclear how the transformation from hole behavior to electron behavior occurs. Here we clarify these questions by showing that the same electron-electron interaction physics that promotes pairing of hole carriers and undressing of carriers from the electron-electron interaction leads to undressing of carriers from the electron-ion interaction and transforms the behavior of carriers from hole-like to electron-like. Furthermore this phenomenon is connected with the expulsion of negative charge that we predict to occur in superconductors. These unexpected connections support the validity of our theoretical framework, the theory of hole superconductivity, to explain superconductivity in solids.
Superconductivity occurs in systems that have a lot of negative charge: the highly negatively charged $(CuO2)^{--}$ planes in the cuprates, negatively charged $(FeAs)^-$ planes in the iron arsenides, and negatively charged $B^-$ planes in magnesium diboride. And, in the nearly filled (with negative electrons) bands of almost all superconductors, as evidenced by their positive Hall coefficient in the normal state. According to the theory of hole superconductivity, metals become superconducting because they are driven to expel negative charge (electrons) from their interior. This is why NIS tunneling spectra are asymmetric, with larger current for negatively biased samples. It is also why there is a Meissner effect: as electrons are expelled towards the surface in the presence of a magnetic field, the Lorentz force imparts them with azimuthal velocity, thus generating the surface Meissner current that screens the interior magnetic field. In type II superconductors, the Lorentz force acting on expelled electrons that don't reach the surface gives rise to the azimuthal velocity of the vortex currents. In the absence of applied magnetic field, expelled electrons still acquire azimuthal velocity, due to the spin-orbit interaction, in opposite direction for spin-up and spin-down electrons: the "Spin Meissner effect". This results in a macroscopic spin current flowing near the surface of superconductors in the absence of applied fields. In strongly type II superconductors this physics should give rise to charge inhomogeneity and spin currents throughout the interior of the superconductor, to large sensitivity to (non-magnetic) disorder and to a strong tendency to phase separation.