Lattice Effects in Superconducting Cuprates

It is widely accepted that the remarkable properties of complex transition-metal oxides, such as colossal magnetoresistivity, are consequences of collaborative behaviors of many degrees of freedom, namely spin, charge, orbital moment and lattice. In stark contrast, most of the theories on the mechanism of the high-temperature superconductivity focus only on the spin degree of freedom. We suggest that the complex behaviors of the cuprates, including the electronic phase separation, involve charge as well as lattice degrees of freedom, and the interplay of the lattice and spin may be centrally important to the superconductivity of the cuprates. We speculate that an intermediate phase may appear when the Mott–Hubbard insulator is doped, and may support the two-component superconductivity involving spins and phonons.     

Pairing Fluctuations, the BCS–BEC Crossover and Strong Disorder in Superconductors

The mean field theory due to Bardeen, Cooper, and Schrieffer (BCS) provides the conceptual foundation of our understanding of superconductivity, but many examples over the last few decades have forced condensed matter physicists to extend the BCS framework. In particular, the extension to strong coupling, the BCS to Bose–Einstein condensation (BEC) crossover, requires the treatment of amplitude and phase fluctuations above the mean field state. Similarly, the presence of disorder can lead to strong inhomogeneity in the pairing amplitude, enhance phase fluctuations, and suppress the transition temperature. Finally, magnetic scattering quickly leads to a gapless superconducting state and then the loss of order. All of these involve physics beyond the BCS scenario. We employ a real space method that reduces to inhomogeneous mean field theory in the ground state, but fully retains the amplitude and phase fluctuations of the pairing field at finite temperature. This paper reviews some of our work in the weak to strong coupling (BCS–BEC) crossover, the disorder driven superconductor-insulator transition, and the role of magnetic impurities.     

Superconductivity in a quasi-one-dimensional metal with impurities

The influence of ordinary impurities on the superconducting transition is studied in a quasi-one-dimensional metal. Superconductivity is considered in a self-consistent field (BCS) approximation. It is shown that, depending on the properties of the electron-electron interaction, singlet or triplet superconductivity may appear. Impurities do not influence the critical temperature in the singlet case but destroy the triplet superconductivity. The concentration dependence of the critical temperature in the triplet case is in qualitative agreement with the experimental results for irradiated quasi-1d superconductors; therefore triplet superconductivity may be supposed in these systems. The superconducting current is calculated in the vicinity of the transition temperature and hence the longitudinal dielectric constant for not too high frequencies.     

Emergence of Pairing Interaction in the Hubbard Model in the Strong Coupling Limit

We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping t, which allows for the analytic study of the system in the low-energy limit. Both U(1) and SU(2) gauge transformations are used to factorize the charge and spin contribution to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy U-term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin quantization axis, providing a useful representation of strongly correlated systems. It is shown that these gauge fields play a similar role as phonons in the BCS theory: they act as the “glue” for fermion pairing. By tracing out gauge degrees of freedom the form of paired states is established and the strength of the pairing potential is determined. It is found that the attractive pairing potential in the effective low-energy fermionic action is non-zero in a rather narrow range of U/t.     

The Mechanism of d-Wave Superconductivity of Underdoped High-T c Cuprates

We have worked out the theory of d-wave superconductivity of the doped cuprate that is consistent with up-to-date data on the basis of the assumption of two-channel Kondo fixed point of the latter. Strong local Coulomb scattering between carriers combined with strong and weak involvement, respectively, of charge (spin) fluctuations and phonons in pairing justify the assumption of two-channel Kondo effect in the doped cuprate. This is true for diverse other data as well. The assumption explains not only the d-wave superconductivity but also all the relevant physics of this material.     

Current Pumping from Spin Dynamics

We show theoretically that charge and spin currents arise from spin dynamics in the presence of the spin–orbit interaction. The dominant calculation is the inverse spin Hall effect, namely the spin current pumped from precession of local spins is converted into the charge current by the spin–orbit interaction. The conversion mechanism is explained based on the conservation laws of charge and spin.     

Calculation of Entropy and Specific Heat in the Spin Polaron Formulation at Finite Temperature

Entropy and specific heat are calculated using the spin polaron formulation at finite temperature. Our theoretical approach makes use of the Matsubara Green's function method where the interaction term in the S-matrix is the spin polaron Hamiltonian, which is constructed in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. In the absence of this interaction term, the normal entropy and specific heat are obtained from the free holon thermodynamic potential and are found to resemble the BCS expressions in the low temperature regime. A second cumulant expansion of the thermodynamic potential with the spin polaron interaction yields an expression for the specific heat whose dominant term in the low temperature limit and small quasiparticle energy difference, resembles the superconducting-state electronic specific heat of the BCS theory.     

Solitonic lattice and Yukawa forces in the rare-earth orthoferrite TbFeO3

The random fluctuations of spins give rise to many interesting physical phenomena, such as the 'order-from-disorder' arising in frustrated magnets and unconventional Cooper pairing in magnetic superconductors. Here we show that the exchange of spin waves between extended topological defects, such as domain walls, can result in novel magnetic states. We report the discovery of an unusual incommensurate phase in the orthoferrite TbFeO(3) using neutron diffraction under an applied magnetic field. The magnetic modulation has a very long period of 340?? at 3?K and exhibits an anomalously large number of higher-order harmonics. These domain walls are formed by Ising-like Tb spins. They interact by exchanging magnons propagating through the Fe magnetic sublattice. The resulting force between the domain walls has a rather long range that determines the period of the incommensurate state and is analogous to the pion-mediated Yukawa interaction between protons and neutrons in nuclei.     

Superconductivity in a Correlated <Emphasis Type="Italic">E</Emphasis>⊗<Emphasis Type="Italic">e</Emphasis> Jahn–Teller System

By numerically solving the Eliashberg equation in the RPA as well as employing the Landau’s theory for phase transitions, we have investigated superconductivity, especially its pairing character, in a two-orbital Hubbard model coupled with E?e Jahn–Teller phonons on a two-dimensional square lattice at half filling. If the electron hopping between neighboring sites keeps the orbital character invariant in this E?e Jahn–Teller crystal, we find that a new superconducting phase characterized by the pairing of spin singlet, orbital singlet, and odd in momentum space, named a chiral p-wave pairing, is brought about by the collaboration of orbital fluctuations enhanced mainly by the electron–phonon interaction with spin fluctuations induced by the electron–electron one.     

Spin Dynamics and Spin Transport

Spin-orbit (SO) interaction critically influences electron spin dynamics and spin transport in bulk semiconductors and semiconductor microstructures. This interaction couples electron spin to dc and ac electric fields. Spin coupling to ac electric fields allows efficient spin manipulating by the electric component of electromagnetic field through the electric dipole spin resonance (EDSR) mechanism. Usually, it is much more efficient than the magnetic manipulation due to a larger coupling constant and the easier access to spins at a nanometer scale. The dependence of the EDSR intensity on the magnetic field direction allows measuring the relative strengths of the competing SO coupling mechanisms in quantum wells. Spin coupling to an in-plane electric field is much stronger than to a perpendicular field. Because electron bands in microstructures are spin split by SO interaction, electron spin is not conserved and spin transport in them is controlled by a number of competing parameters, hence, it is rather nontrivial. The relation between spin transport, spin currents, and spin populations is critically discussed. Importance of transients and sharp gradients for generating spin magnetization by electric fields and for ballistic spin transport is clarified.     

Plasmon–Phonon Pairing Mechanism and Superconducting State Parameters in Layered Mercury Cuprates

An effective two-dimensional dynamic interaction is developed which incorporates screening of holes by plasmons and by optical phonons to discuss the nature of the pairing mechanism leading to superconductivity in layered mercury cuprates. The system is treated as an ionic solid containing layers of charge carriers and a model dielectric function is set up which fulfils the appropriate sum rules on the electronic and ionic polarizabilities. The static limit of the model dielectric function is used to calculate the effective hole-hole coupling strength. The values of the electron-phonon coupling strength and of the Coulomb interaction parameter indicate that the superconductor is in the strong coupling regime with effective screening of the charge carriers. The superconducting transition temperature of optimally doped HgBa₂CuO₄₊ is estimated as 120 K from Kresin's strong coupling theory and the energy gap ratio is substantially larger than the BCS value. The value of the isotope exponent is severely reduced below the BCS value. The implications of the model and its analysis are discussed.     

Some Properties of a Spin-1 Fermi Superfluid: Application to Spin-Polarized 6Li

We discuss some of the unusual characteristics of a Fermi superfluid formed by Cooper pairing in a system, such as spin-polarized ⁶Li, which possesses triple nuclear spin degeneracy. In particular we show (a) that the “ naive” BCS expression for the transition temperature is (unlike in the usual spin-1/2 case) exact in the low-density limit, and (b) that there must always be a gapless branch of the excitation spectrum even for s-wave pairing, so that the normal density is nonzero at T = 0.     

Spin Dynamics and Spin Transport

Spin-orbit (SO) interaction critically influences electron spin dynamics and spin transport in bulk semiconductors and semiconductor microstructures. This interaction couples electron spin to dc and ac electric fields. Spin coupling to ac electric fields allows efficient spin manipulating by the electric component of electromagnetic field through the electric dipole spin resonance (EDSR) mechanism. Usually, it is much more efficient than the magnetic manipulation due to a larger coupling constant and the easier access to spins at a nanometer scale. The dependence of the EDSR intensity on the magnetic field direction allows measuring the relative strengths of the competing SO coupling mechanisms in quantum wells. Spin coupling to an in-plane electric field is much stronger than to a perpendicular field. Because electron bands in microstructures are spin split by SO interaction, electron spin is not conserved and spin transport in them is controlled by a number of competing parameters, hence, it is rather nontrivial. The relation between spin transport, spin currents, and spin populations is critically discussed. Importance of transients and sharp gradients for generating spin magnetization by electric fields and for ballistic spin transport is clarified.     

Charge Expulsion, Spin Meissner Effect, and Charge Inhomogeneity in Superconductors

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. No explanation for this charge asymmetry is provided by the conventional theory of superconductivity, within which the sign of electric charge plays no role. Instead, the sign of the charge carriers plays a key role in the theory of hole superconductivity, according to which 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. The theory also offers a compelling explanation of the 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 do not 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, of magnitude equal to the critical charge current (in appropriate units). Charge expulsion also gives rise to an interior outward-pointing electric field and to excess negative charge near the surface. 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.     

Meissner Effect, Spin Meissner Effect and Charge Expulsion in Superconductors

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 Lorenz 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 ?/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.     

A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor

One proposal for a solid-state-based quantum bit (qubit) is to control coupled electron spins on adjacent semiconductor quantum dots. Most experiments have focused on quantum dots made from III-V semiconductors; however, the coherence of electron spins in these materials is limited by hyperfine interactions with nuclear spins. Ge/Si core/shell nanowires seem ideally suited to overcome this limitation, because the most abundant nuclei in Ge and Si have spin zero and the nanowires can be chemically synthesized defect-free with tunable properties. Here, we present a double quantum dot based on Ge/Si nanowires in which we can completely control the coupling between the dots and to the leads. We also demonstrate that charge on the double dot can be detected by coupling it capacitively to an adjacent nanowire quantum dot. The double quantum dot and integrated charge sensor serve as an essential building block to form a solid-state qubit free of nuclear spin.     

Cooper-like Pairing and Energy Gap Induced by Ion Electronic Polarizability

We explore the possibility that the ionic electron polarizabilities of the oxygen ions in the cuprates and bismutates and the polarizabilities of As and Se ions in the iron pnictides contribute to charge carrier pairing leading to high Tc superconductivity. Using the fact that the ionic polarization responds to an abrupt change in the electric field is practically instantaneous, we find that charge carriers attract each other in limited regions in the two carrier position space. The attractive potential is used to calculate quantum mechanically the Cooper-like pairing energy and wave function and the gap energy showing they are consistent with pairing and gap energies of high Tc superconductors. Qualitative considerations show that this model may explain the large pairing energy observed in high Tc superconductors, the very short inter-carrier distance, the fact that Tc vanishes at very low and very high doping levels, and the dramatic increase in Tc of a one-unit cell thick FeSe film grown on SrTiO₃ substrate.     

Oscillator-Strength Sum Rule in the Cuprates

The oscillator-strength sum rule played an important role in the firstwork on the energy gap of superconductors by Tinkham. Recently, asmall but measurable depletion in the sum rule integral has beenobserved at optical frequencies in the cuprates. It has been suggestedthat this behavior contradicts what is expected of traditional modelsof superconductivity. We disagree with this conclusion. We show thatthis depletion is consistent with earlier Thermal DifferenceReflectance (TDR) measurements and their interpretation within thestrong coupling extension of the BCS theory, as evidence of anelectronic contribution to the pairing interaction at energies between1.0 and 2.0 eV for these materials. We show quantitative agreementwith the magnitude of the depletion and agreement with recent workwith ARPES on the dispersion and lifetime of quasiparticles from thesame model. We have located the two transitions responsible for theelectronic contribution from TDR measurements of the thermalderivative of the dielectric function.     

Spin caloritronics

Spintronics is about the coupled electron spin and charge transport in condensed-matter structures and devices. The recently invigorated field of spin caloritronics focuses on the interaction of spins with heat currents, motivated by newly discovered physical effects and strategies to improve existing thermoelectric devices. Here we give an overview of our understanding and the experimental state-of-the-art concerning the coupling of spin, charge and heat currents in magnetic thin films and nanostructures. Known phenomena are classified either as independent electron (such as spin-dependent Seebeck) effects in metals that can be understood by a model of two parallel spin-transport channels with different thermoelectric properties, or as collective (such as spin Seebeck) effects, caused by spin waves, that also exist in insulating ferromagnets. The search to find applications--for example heat sensors and waste heat recyclers--is on.