79 research outputs found
Theory of Unconventional Superconductivity in Strongly Correlated Systems: Real Space Pairing and Statistically Consistent Mean-Field Theory - in Perspective
In this brief overview we discuss the principal features of real space
pairing as expressed via corresponding low-energy (t-J or periodic
Anderson-Kondo) effective Hamiltonian, as well as consider concrete properties
of those unconventional superconductors. We also rise the basic question of
statistical consistency within the so-called renormalized mean-field theory. In
particular, we provide the phase diagrams encompassing the stable magnetic and
superconducting states. We interpret real space pairing as correlated motion of
fermion pair coupled by short-range exchange interaction of magnitude J
comparable to the particle renormalized band energy , where is the
carrier number per site. We also discuss briefly the difference between the
real-space and the paramagnon - mediated sources of superconductivity. The
paper concentrates both on recent novel results obtained in our research group,
as well as puts the theoretical concepts in a conceptual as well as historical
perspective. No slave-bosons are required to formulate the present approach
Fifty years of Hubbard and Anderson lattice models: from magnetism to unconventional superconductivity - A brief overview
We briefly overview the importance of Hubbard and Anderson-lattice models as
applied to explanation of high-temperature and heavy-fermion superconductivity.
Application of the models during the last two decades provided an explanation
of the paired states in correlated fermion systems and thus extended
essentially their earlier usage to the description of itinerant magnetism,
fluctuating valence, and the metal-insulator transition. In second part, we
also present some of the new results concerning the unconventional
superconductivity and obtained very recently in our group. A comparison with
experiment is also discussed, but the main emphasis is put on rationalization
of the superconducting properties of those materials within the real-space
pairing mechanism based on either kinetic exchange and/or Kondo-type
interaction combined with the electron correlation effects.Comment: 22 pages, 7 figures, sent to Philosophical Magazin
Stability of the coexistent superconducting-nematic phase under the presence of intersite interactions
We analyze the effect of intersite-interaction terms on the stability of the
coexisting superconucting-nematic phase (SC+N) within the extended Hubbard and
-- models on the square lattice. In order to take into account the
correlation effects with a proper precision, we use the approach based on the
\textit{diagrammatic expansion of the Gutzwiller wave function} (DE-GWF), which
goes beyond the renormalized mean field theory (RMFT) in a systematic manner.
As a starting point of our analysis we discuss the stability region of the SC+N
phase on the intrasite Coulomb repulsion-hole doping plane for the case of the
Hubbard model. Next, we show that the exchange interaction term enhances
superconductivity while suppresses the nematicity, whereas the intersite
Coulomb repulsion term acts in the opposite manner. The competing character of
the SC and N phases interplay is clearly visible throughout the analysis. A
universal conclusion is that the nematic phase does not survive within the
-- model with the value of integral typical for the high-T
cuprates (eV). For the sake of completeness, the effect of the
correlated hopping term is also analyzed. Thus the present discussion contains
all relevant two-site interaction terms which appear in the parametrized
one-band model within the second quantization scheme. At the end, the influence
of the higher-order terms of the diagrammatic expansion on the rotational
symmetry breaking is also shown by comparing the DE-GWF results with those
corresponding to the RMFT
A brief perspective of high temperature superconductivity in the cuprates: Strong correlations combined with superexchange match experiment
High temperature superconductivity encompasses the cuprates, nickelates, iron
pnictides, and LaH compounds. The first three groups of compounds involve
in the pairing electrons, which are strongly to moderately correlated, whereas
in the last class of systems specific phonon excitations. In this overview we
concentrate first on the (semi)quantitative theory of high T
superconductivity in the cuprates based on our original vibrational approach
beyond the renormalized mean field theory. The model we explore mainly is
-- model containing both the superexchange (kinetic energy) combined
with strong interelectronic correlations. Selected equilibrium and
dynamic-excitation properties are analyzed briefly. General questions regarding
the pseudogap and two--dimensional character of those systems are raised
Statystyka Bosego-Einsteina: Uwagi na temat wkładu P. Debye’a, W. Natansona i P. Ehrenfesta oraz wyłonienie się zasady nierozróżnialności cząstek kwantowych
The principal mathematical idea behind the statistical properties of black-body radiation (photons) was introduced already by L. Boltzmann (1877/2015) and used by M. Planck (1900; 1906) to derive the frequency distribution of radiation (Planck’s law) when its discrete (quantum) structure was additionally added to the reasoning.
The fundamental physical idea – the principle of indistinguishability of the quanta (photons) – had been somewhat hidden behind the formalism and evolved slowly.
Here the role of P. Debye (1910), H. Kamerlingh Onnes and P. Ehrenfest (1914) is briefly elaborated and the crucial role of W. Natanson (1911a; 1911b; 1913) is emphasized.
The reintroduction of this Natanson’s statistics by S. N. Bose (1924/2009) for light quanta (called photons since the late 1920s), and its subsequent generalization to material particles by A. Einstein (1924; 1925) is regarded as the most direct and transparent, but involves the concept of grand canonical ensemble of J. W. Gibbs (1902/1981), which in a way obscures the indistinguishability of the particles involved.
It was ingeniously reintroduced by P. A. M. Dirac (1926) via postulating (imposing) the transposition symmetry onto the many-particle wave function.
The above statements are discussed in this paper, including the recent idea of the author (Spałek 2020) of transformation (transmutation) – under specific conditions – of the indistinguishable particles into the corresponding to them distinguishable quantum particles.
The last remark may serve as a form of the author’s post scriptum to the indistinguishability principle.Zasadnicza idea matematyczna opisu własności statystycznych promieniowania ciała doskonale czarnego (fotonów) wprowadzona została już przez L. Boltzmanna (1877/2015) i użyta przez M. Plancka (1900; 1906) do uzasadnienia wyprowadzenia rozkładu po częstościach dla tego promieniowania (prawo Plancka), jeśli jego dyskretna (kwantowa) struktura została dodatkowo dodana do tego rozumowania.
Fundamentalna idea fizyczna – zasada nierozróżnialności kwantów (fotonów) jest w pewnym stopniu ukryta w tym formalizmie i ewoluowała powoli.
Tutaj omawiamy krótko rolę P. Debye’a (1910), H. Kamerlingha Onnesa i P. Ehrenfesta (1914), a przede wszystkim podkreślamy zasadniczy wkład W. Natansona (1911a; 1911b; 1913).
Ponowne wprowadzenie tej statystyki przez S. N. Bosego (1924/2009) dla kwantów światła (zwanych fotonami od końca lat dwudziestych XX wieku) i następującej po niej statystyki A. Einsteina (1924,1925) dla cząstek materialnych jest uważane za najbardziej bezpośrednie i przejrzyste, ale zawiera koncepcje dużego rozkładu kanonicznego J. W. Gibbsa (1902/1981) i do pewnego stopnia przesłania także zasadę nierozróżnialności cząstek.
Tę zasadę wprowadził ponownie w sposób genialny P. A. M. Dirac (1926), włączając (narzucając) symetrię względem przestawień pary współrzędnych cząstek (inwersji) w wielocząstkowej funkcji falowej.
Powyższe stwierdzenia są przedyskutowane w tej pracy, włącznie z niedawno sformułowaną ideą autora (Spałek 2020) przekształcenia (transmutacji) – w specyficznych warunkach – cząstek nierozróżnialnych w korespondujące z nimi, rozróżnialne cząstki.
Ta ostatnia uwaga ma służyć jako post scriptum autora do zasady nierozróżnialności
Mott Physics in Correlated Nanosystems: Localization-Delocalization Transition of Electrons by Exact Diagonalization Ab Initio Method
The electronic states of selected nanosystems are discussed within the Exact
Diagonalization Ab Initio (EDABI) method. In particular, incipient
Mott--Hubbard localization effects and associated with it properties analyzed
in detail
Fulde-Ferrell state induced purely by the orbital effect in a superconducting nanowire
We demonstrate that the Fulde-Ferrell (FF) phase can be induced uniquely by
the orbital effect in a cylindrical metallic nanowire. In the external magnetic
field the two-fold degeneracy with respect to the orbital quantum number is
lifted what leads to a Fermi wave vector mismatch between the subbands with
opposite orbital momenta in the paired state. This mismatch can be compensated
by the nonzero total momentum of the Cooper pairs created by electrons from
split subbands what results in the formation of the FF phase. With increasing
magnetic field a series of FF stability regions appear in between which the
standard BCS superconducting phase is stable.Comment: 8 pages, 6 figure
Discontinuous transition of molecular-hydrogen chain to the quasi-atomic state: Exact diagonalization - ab initio approach
We obtain in a direct and rigorous manner a transition from a stable
molecular hydrogen single chain to the quasiatomic two-chain
state. We devise an original method composed of an exact diagonalization in the
Fock space combined with an ab initio adjustment of the single-particle wave
function in the correlated state. In this approach the well-known problem of
double-counting the interparticle interaction does not arise at all. The
transition is strongly discontinuous, and appears even for relatively short
chains possible to tackle, . The signature of the transition as a
function of applied force is a discontinuous change of the equilibrium
intramolecular distance. The corresponding change of the Hubbard ratio
reflects the Mott--Hubbard-transition aspect of the atomization. Universal
feature of the transition relation to the Mott criterion for the
insulator--metal transition is also noted. The role of the electron
correlations is thus shown to be of fundamental significance.Comment: 6 pages, 5 figures, 1 tabl
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