Based on the real-space Mott insulator model, we establish a unifiedpairing, coherent and condensate mechanism of superconductivity. Motivatedby Dirac's magnetic monopole and Maxwell's displacement current hypothesis,we demonstrate that electric and magnetic fields are intrinsicallyrelevant. An isolated proton or electron creates an electric field,whereas a quantized proton-electron pair creates a magnetic field.The electric dipole vector of the proton-electron pair is the Ginzburg-Landauorder parameter in the superconducting phase transition. The Pierce-likedimerization pairing transition of the electron-proton electric dipolelattice leads to the symmetry breaking of the Mott insulating stateand the emergence of superconducting and magnetic states. This theoreticalframework can comprehensively explain all superconducting phenomena.Our research sheds new light on electron spin, magnetic monopoles,and the symmetry of Maxwell's equations.
Based on the real-space Mott insulator model, we establish a unifiedpairing, coherent and condensate mechanism of superconductivity. Motivatedby Dirac's magnetic monopole and Maxwell's displacement current hypothesis,we demonstrate that electric and magnetic fields are intrinsicallyrelevant. An isolated proton or electron creates an electric field,whereas a quantized proton-electron pair creates a magnetic field.The electric dipole vector of the proton-electron pair is the Ginzburg-Landauorder parameter in the superconducting phase transition. The Pierce-likedimerization pairing transition of the electron-proton electric dipolelattice leads to the symmetry breaking of the Mott insulating stateand the emergence of superconducting and magnetic states. This theoreticalframework can comprehensively explain all superconducting phenomena.Our research sheds new light on electron spin, magnetic monopoles,and the symmetry of Maxwell's equations.
We improve a previous theory of doped Mott insulators with duality between pairing and magnetism by a further duality transform. As the result we obtained a quantum Ginzburg-Landau theory describing the Cooper pair condensate and the dual of spin condensate. We address the superconductivity by doping a Mott insulator, which we call the Mott superconductivity. Some fingerprints of such novelty in cuprates are the scaling between neutron resonance energy and superfluid density, and the induced quantized spin moment by vortices or Zn impurity (together with circulating charge super-current to be checked by experiments).
We address the question of real space pairing induced by exchange interaction, customarily associated with the presence of the broken-symmetry magnetism. For such mechanism of pairing, the appearance of superconductivity (or superfluidity) without magnetism presents itself still as a highly nontrivial problem and it seems, it can be practically realized only when the kinetic energy of individual-particle motion is comparable or even smaller than the magnitude of exchange interaction that takes place among strongly correlated fermions , where the kinetic exchange and/or the Hund's rule coupling can become relatively strong in the vicinity of the onset of the Mott insulating state. In that situation, the pairing arises from a coherent correlated pair motion rather than from a free motion of a tightly bound pair. We elaborate on this question in general terms, as well as provide selected results in the mean-field approximation in concrete situations.
In this brief overview, I address some of the fundamental topics related to the physics of strongly correlated fermions, which have been also the subject of my research. After addressing the question why the field has a fundamental meaning, we next turn to the specific problems with their simple theoretical description. Those topics are: (i) the concept of spindependent masses of heavy particles and its subsequent experimental verification; (ii) the correlated metal–insulator transitions of the Mott–Hubbardtype; (iii) real space pairing and its subsequent experimental verification for high-temperature superconducting cuprates. I mention also the persistence of quantum spin and charge excitations in the superconducting phase. All those phenomena confirm the view that the strongly correlated fermionic \nsystems represent a new class of quantum liquids, with some properties quantitatively different than those of the Landau Fermi liquids. Namely, they can be classified as those that fall in between those of the anomalous Landau Fermi liquid and localized-magnetic-moment system.
In this thesis, we investigate several topics pertaining to emergent collective quantum phenomena in the domain of correlated fermions, using the quantum Monte Carlo method. They display exotic low temperature phases as well as phase transitions which are beyond the Landau–Ginzburg theory. The interplay between three key points is crucial for us: fermion statistics, many body effects and topology. We highlight the following several achievements: 1. Successful modeling of continuum field theories with lattice Hamiltonians, 2. their sign-problem-free Monte Carlo simulations of these models, 3. and numerical results beyond mean field descriptions. First, we consider a model of Dirac fermions with a spin rotational invariant inter- action term that dynamically generates a quantum spin Hall insulator. Surprisingly, an s-wave superconducting phase emerges due to the condensation of topological de- fects of the spin Hall order parameter. When particle-hole symmetry is present, the phase transition between the topological insulator and the superconducting phase is an example of a deconfined quantum critical point(DQCP). Although its low energy effec- tive field theory is purely bosonic, the exact conservation law of the skyrmion number operator rules out the possibility of realizing this critical point in lattice boson models. This work is published in Ref. [1]. Second, we dope the dynamically generated quantum spin Hall insulator mentioned above. Hence it is described by a field theory without Lorentz invariance due to the lack of particle-hole symmetry. This sheds light on the extremely hot topic of twisted bilayergraphene: Why is superconductivity generated when the repulsive Coulomb interaction is much stronger than the electron-phonon coupling energy scale? In our case, Cooper pairs come from the topological skyrmion defects of the spin current order parameter, which are charged. Remarkably, the nature of the phase transition is highly non-mean-field-like: one is not allowed to simply view pairs of electrons as single bosons in a superfluid-Mott insulator transition, since the spin-current order parameter can not be ignored. Again, due to the aforementioned skyrmions, the two order parameters are intertwined: One phase transition occurs between the two symmetry breaking states. This work is summarized in Ref. [2]. Third, we investigate the 2 + 1 dimensional O(5) nonlinear sigma model with a topological Wess-Zumino-Witten term. Remarkably, we are able to perform Monte Carlo calculations with a UV cutoff given by the Dirac Landau level quantization. It is a successful example of simulating a continuous field theory without lattice regularization which leads to an additional symmetry breaking. The Dirac background and the five anti-commuting Dirac mass terms naturally introduce the picture of a non-trivial Berry phase contribution in the parameter space of the five component order parameter. Using the finite size scaling method given by the flux quantization, we find a stable critical phase in the low stiffness region of the sigma model. This is a candidate ground state of DQCP when the O(5) symmetry breaking terms are irrelevant at the critical point. Again, it has a bosonic low energy field theory which is seemingly unable to be realized in pure boson Hamiltonians. This work is summarized in Ref. [3].
Good order is the foundation of all good things. E. Burke, Reflections on the Revolution in France , 1790 Josephson effect Superconductivity: A crash course The transition from the theoretical description of hypothetical building blocks of a quantum coherent device to something which can be actually fabricated and controlled is made much easier by the existence of superconductivity . This phenomenon, roughly speaking, allows a macroscopic quantum coherent flow of electrons in a sufficiently cold piece of an appropriate material by establishing a specific long-range order among them. Due to this one can, for example, use macroscopically different states of a superconductor as quantum states of a qubit, with the obvious advantage over “microscopically quantum” systems (like actual atoms) from the point of view of control, measurement and, last but not least, fabrication of structures with the desired parameters and on the desired scale. The phenomenon of superconductivity – the history of its discovery, experimental manifestations, theoretical explanation, open questions, relevance to other branches of physics, and technological applications – requires a thorough treatment, which can be found in any number of books. For our purposes Tinkham (2004) will provide more than sufficient background. We will not wander into the field of exotic/high-temperature superconductors for two simple reasons: the quantum coherent behaviour of the kind we need to realize qubits or other quantum coherent devices has not yet been properly and/or routinely achieved in these systems; and the fabrication of such devices is not yet reliable enough or even feasible.
We theoretically demonstrate that a pair of Dirac monopoles with opposite synthetic charges can be created within a single spin-1 Bose-Einstein condensate by steering the spin degrees of freedom by external magnetic fields. Although the net synthetic magnetic charge of this configuration vanishes, both the monopole and the antimonopole are accompanied by vortex filaments carrying opposite angular momenta. Such a Dirac dipole can be realized experimentally by imprinting a spin texture with a nonlinear magnetic field generated by a pair of coils in a modified Helmholtz configuration. We also investigate the case where the initial state for the dipole-creation procedure is pierced by a quantized vortex line with a winding number $\ensuremath{\kappa}$. It is shown that if $\ensuremath{\kappa}=\ensuremath{-}1$, the resulting monopole and antimonopole lie along the core of a singly quantized vortex whose sign is reversed at the locations of the monopoles. For $\ensuremath{\kappa}=\ensuremath{-}2$, the monopole and antimonopole are connected by a vortex line segment carrying two quanta of angular momentum, and hence the dipole as a whole is an isolated configuration. In addition, we simulate the long-time evolution of the dipoles in the magnetic field used to create them. For $\ensuremath{\kappa}=0$, each of the semi-infinite doubly quantized vortices splits into two singly quantized vortices, as in the case of a single Dirac monopole. For $\ensuremath{\kappa}=\ensuremath{-}1$ and $\ensuremath{\kappa}=\ensuremath{-}2$, the initial vortices deform into a vortex with a kink and a vortex ring, respectively.