Physica Status Solidi B-basic Solid State Physics, Nov 17, 2009
The crystal-fields causing |J electron states splittings of the same second moment σ 2 can produc... more The crystal-fields causing |J electron states splittings of the same second moment σ 2 can produce different total splittings ∆E magnitudes. Based on the numerical data on crystal-field splittings for the representative sets of crystal-field Hamiltonians H CF = k q B kq C (k) q with fixed indexes either k or q, the potentials leading to the extreme ∆E have been identified. For all crystal-fields the admissible ranges (∆E min , ∆E max) have been found numerically for 1 ≤ J ≤ 8. The extreme splittings are reached in the crystal-fields for which H CF s are the definite superpositions of the C (k) q the extreme splittings. The admissible ∆E min changes with J from 2.00σ to 2.40σ, whereas the ∆E max from 2.00σ to 4.10σ. The maximal gap ∆E max − ∆E min = 2.00σ has been found for the states |J = 4. Not all the nominally allowed total splittings, preserving σ 2 = const condition, are physically available, and in consequence not all virtual splittings diagrams can be observed in real crystal-fields.
Physica Status Solidi B-basic Solid State Physics, Aug 1, 1998
Starting from the postulated, generalized form of the BCS gap equation, suitable for a wide class... more Starting from the postulated, generalized form of the BCS gap equation, suitable for a wide class of microscopic models, the thermodynamic properties of S-wave superconductors are studied. The precise analytical formulas for the main thermodynamic quantities are given and discussed in the characteristic temperature limits. In particular the inversion of the equations defining the specific heat as a function of Δ(T), i.e. the temperature dependence of the energy gap in S-wave superconductor is presented. It makes possible a reconstruction of the energy gap as a function of temperature from the heat capacity data. As predicted, in the frame of the model, the other thermodynamic quantities from the Δ(T) function seem also to be interesting.
We reconsider the Pfitzner and Wölfle results concerning the quasi-particle scattering amplitude ... more We reconsider the Pfitzner and Wölfle results concerning the quasi-particle scattering amplitude in Fermi liquid and adopt them to the sufficiently low-temperature and flat-confined systems, where solely two types of quasi-particle interactions are permitted. We find relations between the pairing interaction and Landau parameters and establish plain criteria for the creation of singlet or triplet Cooper pairs. Moreover, we present methods allowing us to estimate values of interaction parameters and transition temperatures in flat-confined systems basing on their bulk parameters. The obtained results are in agreement with experimental data for helium-3 and its films and explain an absence of superconductivity in alkali metals.
Any electron eigenstate |Ψ of the paramagnetic ion open-shell is characterized by the three indep... more Any electron eigenstate |Ψ of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities A k = Ψ||C (k) ||Ψ for k = 2, 4 and 6 related to the second moments of the relevant crystal-field splittings by σ 2 k = [1/(2J + 1)] A 2 k S 2 k , where S 2 k = [1/(2k + 1)] q |B kq | 2. The A k can serve as a reliable measure of the state |Ψ capability for the splitting produced by the k-rank component of the crystal-field Hamiltonian and allow one to verify any fitted crystalfield parameter set directly comparing the calculated and the experimental second moments of the relevant crystal-field splittings. We present the multipole characteristics A k for the extensive set of eigenstates from the lower parts of energy spectra of the tripositive 4f N ions applying in the calculations the advanced eigenfunctions of the free lanthanide ions obtained based on the M. Reid f-shell programs. Such amended asphericities are compared with those achieved for the simplified Russell-Saunders states. Next, they are classified with respect to the absolute or relative weight of the A k in the multipole structure of the considered states. For the majority of the analyzed states (about 80%) the A k variation is of order of only a few percent. Some essential changes are found primarily for several states of Tm 3+ , Er 3+ , Nd 3+ , and Pr 3+ ions. The detailed mechanisms of such A k changes are unveiled. Particularly, certain noteworthy cancelations as well as enhancements of their magnitudes are explained.
Physica Status Solidi B-basic Solid State Physics, Apr 14, 2011
The physically correct parametrization of the energy levels of transition ions in crystals in ter... more The physically correct parametrization of the energy levels of transition ions in crystals in terms of crystal-field (CF) Hamiltonians H CF = k q B kq C (k) q has to be based on the CF parameters B kq that lead to the correct CF splitting second moments, both the global one σ and the partial ones σ k. Only such parametrizations correspond to the appropriate multipolar structure of the surrounding CF. Each parametrization being characterized by its own multipolar crystal-field strengths S k = 1 2k+1 q |B kq | 2 1/2 , for k = 2, 4 and 6, yields a definite second moment σ, which can be derived from the additivity relationship σ 2 = k σ 2 k and the known asphericities Ψ||C (k) ||Ψ of the centralion eigenfunctions Ψ. The condition σ = σ exp must be satisfied to ensure the parametrization's correctness. However, our survey of literature indicates that there exists many other well-fitted crystal-field parameter sets that do not obey this condition. Therefore, such sets are erratic and non-physical, and should be reexamined or rejected. Having σ for several (≥ 3) eigenstates |Ψ along with the relevant Ψ||C (k) ||Ψ asphericities, one can estimate σ k and S k , which are wellfounded experimentally. The above findings set up the parametrization process properly. Lack of consistency between the second moments representing various parametrizations and the pertinent second moments observed in experiments is presumably the main reason for deluge of formally accurate but accidental and inequivalent parametrizations.
International Journal of Modern Physics B, Feb 20, 2001
We prove that an arbitrary crystal with anisotropic lattice and partially filled conduction band,... more We prove that an arbitrary crystal with anisotropic lattice and partially filled conduction band, for which one-electron energy spectrum is known, can be considered, after some curvilinear transformation of the reciprocal lattice as the Fermi liquid of the Landau–type quasiparticles in the isotropic system. However, the additional scalar field modifying the size of quantum-mechanical states in the reciprocal space has to be included. It is shown that the established formalism can be employed for two- and three-dimensional systems. As an example one-band Hubbard model has been investigated in details. The new precise formulas for the postulated scalar field and the density of states are derived. Additionally, assuming the microscopic mechanism which leads to the pairing interaction in a crystal, the anisotropic Fermi liquid formalism is extended to superconducting system according to the BCS theory principles. The obtained results enable us to explain and understand the great success of the BCS theory.
The D-wave paired Fermi system is considered in the frame of generalized gap equation obtained in... more The D-wave paired Fermi system is considered in the frame of generalized gap equation obtained in a BCS-like approach. It is shown that the thermodynamic functions of a system, as the thermodynamic potential, entropy and heat capacity differences between the normal and superconducting state are precisely defined functionals of the energy gap as a function of temperature. The derived formulas are identical as those obtained for S-wave paired Fermi system. It states that the developed formalism can be applied, in practice, to investigation of real superconductors in which a singlet state is realized. Some numerical results illustrating prospects and capabilities of the presented formalism are given for chosen structures of the order parameter.
The generalised form of the gap equation which comprises also some non-BCS approaches is defined ... more The generalised form of the gap equation which comprises also some non-BCS approaches is defined and solved. The parametric gap equations have been derived in a few equivalent cases and discussed in_ dissimilar limits. It is shown that the relations between the critical temperature and zero-temperature energy gap can be extended for all systems under consideration. The main benefits and incontestable advantage of the presented method are demonstrated with regard to the general BCS case.
Physica Status Solidi B-basic Solid State Physics, Apr 29, 2021
A single‐state algebraic parametrization is applied to 47 free‐ion triply ionized lanthanide elec... more A single‐state algebraic parametrization is applied to 47 free‐ion triply ionized lanthanide electronic states that originate from 11 ions embedded in four various octahedral hosts, mainly in Cs2NaLaCl6 matrix. The obtained single‐state parametrizations averaged over the considered |J⟩ states of 2J + 1 degeneracy adequately reproduce the conventional fitting parametrization, where as many pairs of the cubic B 40 and B 60 crystal field (CF) parameters as the states in the configuration are replaced by only one universal pair. This is the essence of the fitting procedure. The comparison between the single‐state parametrizations and the corresponding fitted parametrization reveals the structure of anatomy of the fitting as well as the component states of the configuration giving an untypical contribution to the mean value. The single‐state parametrization unveils directly not only the physical CF parameters of the state but also the host ligand strength, it means its position in the spectrochemical series.
D-wave paired isotropic Fermi system in the limiting cases Τ-Tc and Τ-> 0 is considered. Values o... more D-wave paired isotropic Fermi system in the limiting cases Τ-Tc and Τ-> 0 is considered. Values of the energy gap, the thermodynamic potential, and the specific heat as a function of temperature are given for admissible solutions and compared with values for S-wave paired system. It is shown that the linear term of low temperature specific heat vanishes likewise in case of S-wave pairing. The obtained results make prospects to define the geometry of the energy gap in virtue of the behavior of the specific heat in the limiting temperature cases for heavy-fermion superconductors.
The s-paired BCS superconductor with the electron density of states depending on energy in the vi... more The s-paired BCS superconductor with the electron density of states depending on energy in the vicinity of Fermi level is considered. The existence of such fluctuations of electron density of states may be referred to Van Hove singularities widely discussed in the literature. In the paper three types of small fluctuations of the electron density of states introduced about its average background's value are analysed: Lorentzian, triangle, and logarithmic ones. In order to calculate numerically the energy gap and critical temperature, the formalism of parametric BCS gap equations is applied. The positive fluctuations (peaks) correspond to the increase in occupied states number inducing a higher critical temperature. On the other hand, negative fluctuations, which decrease the number of occupied states, lead to a lower critical temperature. Such decrease in critical temperature can lead, at a specific choice of parameters, to the decease in superconductivity. The presence of fluctuations finds reflection in the shape of energy gap as a function of temperature. In the vicinity of Τ = 0 an abrupt decrease or increase in the energy gap to the original BCS value, according to the sign of the fluctuation, is observed. In turn, the fluctuations do not change the behaviour of the energy gap near 21.
A new measure of the crystal-field strength, complementary to the conventional one, is defined. I... more A new measure of the crystal-field strength, complementary to the conventional one, is defined. It is based on the rotational invariants |B k0 | av or | k B k0 | av , k = 2, 4, 6, of the crystal-(ligand)-field (CF) Hamiltonian H CF parametrizations, i.e. on the axial CF parameters modules averaged over all reference frame orientations. They turn out to be equal to H (k) CF av and |H CF | av , respectively. While the traditional measure is established on the parametrization modules or on the second moment of the CF energy levels, the introduced scale employs rather the first moment of the energy modules and has better resolving power. The new scale is able to differentiate the strength of various iso-modular parametrizations according to the classes of rotationally equivalent parametrizations. Using both the compatible CF strength measures one may draw more accurate conclusions about the Stark levels arrays and particularly their total splitting magnitudes.
Physica Status Solidi B-basic Solid State Physics, Mar 7, 2022
To facilitate the calculation of the fourth‐order crystal‐field (CF) splitting moment, which in a... more To facilitate the calculation of the fourth‐order crystal‐field (CF) splitting moment, which in a complex way depends on the split state , a time saving formula is elaborated, which is positively verified for several cubic systems RE3+: Cs2NaLaCl6. The appropriate crystal‐field parameters (CFPs) have to be substituted to the presented formula. However, the question is which ones. The clear answer proven in the paper is that single‐state CFPs should necessarily be used. To test the approach, a few cubic systems, for which such single‐state CFPs are available, have been studied. Conventionally fitted CFPs, averaged over the entire electron configuration, do not satisfy the equation, which contradicts the fundamental principle of the CF theory. Such verification significantly limits the physical meaning and applicability of the conventional fitted parameterizations.
Physica Status Solidi B-basic Solid State Physics, Feb 1, 2007
In memoriam Professor Włodzimierz Trzebiatowski on the occasion of the 100th anniversary of his b... more In memoriam Professor Włodzimierz Trzebiatowski on the occasion of the 100th anniversary of his birth.
The general method of investigation of S-paired Fermi systems is given and discussed as generaliz... more The general method of investigation of S-paired Fermi systems is given and discussed as generalization of parametric equation for the energy gaρ. The additional parametric equations for thermodynamic potential and heat capacity are obtained as functions of introduced parameters. The detailed calculations are given for a few exemplary chosen magnetic fields and superflows. Moreover, we consider the case of so-called statistical spin liquid, which constitutes non-BCS model.
The application of a method of conformal-like transformation of the two-dimensional momentum spac... more The application of a method of conformal-like transformation of the two-dimensional momentum space is presented and discussed with regard to two-dimensional anisotropic superconductors. A new function, the kernel of the density of states, and some integral formulae are derived, interpreted and studied for a few specific cases. Evidences for the incompatibility between the Van Hove scenario and the conformal transformation
Physica Status Solidi B-basic Solid State Physics, Nov 17, 2009
The crystal-fields causing |J electron states splittings of the same second moment σ 2 can produc... more The crystal-fields causing |J electron states splittings of the same second moment σ 2 can produce different total splittings ∆E magnitudes. Based on the numerical data on crystal-field splittings for the representative sets of crystal-field Hamiltonians H CF = k q B kq C (k) q with fixed indexes either k or q, the potentials leading to the extreme ∆E have been identified. For all crystal-fields the admissible ranges (∆E min , ∆E max) have been found numerically for 1 ≤ J ≤ 8. The extreme splittings are reached in the crystal-fields for which H CF s are the definite superpositions of the C (k) q the extreme splittings. The admissible ∆E min changes with J from 2.00σ to 2.40σ, whereas the ∆E max from 2.00σ to 4.10σ. The maximal gap ∆E max − ∆E min = 2.00σ has been found for the states |J = 4. Not all the nominally allowed total splittings, preserving σ 2 = const condition, are physically available, and in consequence not all virtual splittings diagrams can be observed in real crystal-fields.
Physica Status Solidi B-basic Solid State Physics, Aug 1, 1998
Starting from the postulated, generalized form of the BCS gap equation, suitable for a wide class... more Starting from the postulated, generalized form of the BCS gap equation, suitable for a wide class of microscopic models, the thermodynamic properties of S-wave superconductors are studied. The precise analytical formulas for the main thermodynamic quantities are given and discussed in the characteristic temperature limits. In particular the inversion of the equations defining the specific heat as a function of Δ(T), i.e. the temperature dependence of the energy gap in S-wave superconductor is presented. It makes possible a reconstruction of the energy gap as a function of temperature from the heat capacity data. As predicted, in the frame of the model, the other thermodynamic quantities from the Δ(T) function seem also to be interesting.
We reconsider the Pfitzner and Wölfle results concerning the quasi-particle scattering amplitude ... more We reconsider the Pfitzner and Wölfle results concerning the quasi-particle scattering amplitude in Fermi liquid and adopt them to the sufficiently low-temperature and flat-confined systems, where solely two types of quasi-particle interactions are permitted. We find relations between the pairing interaction and Landau parameters and establish plain criteria for the creation of singlet or triplet Cooper pairs. Moreover, we present methods allowing us to estimate values of interaction parameters and transition temperatures in flat-confined systems basing on their bulk parameters. The obtained results are in agreement with experimental data for helium-3 and its films and explain an absence of superconductivity in alkali metals.
Any electron eigenstate |Ψ of the paramagnetic ion open-shell is characterized by the three indep... more Any electron eigenstate |Ψ of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities A k = Ψ||C (k) ||Ψ for k = 2, 4 and 6 related to the second moments of the relevant crystal-field splittings by σ 2 k = [1/(2J + 1)] A 2 k S 2 k , where S 2 k = [1/(2k + 1)] q |B kq | 2. The A k can serve as a reliable measure of the state |Ψ capability for the splitting produced by the k-rank component of the crystal-field Hamiltonian and allow one to verify any fitted crystalfield parameter set directly comparing the calculated and the experimental second moments of the relevant crystal-field splittings. We present the multipole characteristics A k for the extensive set of eigenstates from the lower parts of energy spectra of the tripositive 4f N ions applying in the calculations the advanced eigenfunctions of the free lanthanide ions obtained based on the M. Reid f-shell programs. Such amended asphericities are compared with those achieved for the simplified Russell-Saunders states. Next, they are classified with respect to the absolute or relative weight of the A k in the multipole structure of the considered states. For the majority of the analyzed states (about 80%) the A k variation is of order of only a few percent. Some essential changes are found primarily for several states of Tm 3+ , Er 3+ , Nd 3+ , and Pr 3+ ions. The detailed mechanisms of such A k changes are unveiled. Particularly, certain noteworthy cancelations as well as enhancements of their magnitudes are explained.
Physica Status Solidi B-basic Solid State Physics, Apr 14, 2011
The physically correct parametrization of the energy levels of transition ions in crystals in ter... more The physically correct parametrization of the energy levels of transition ions in crystals in terms of crystal-field (CF) Hamiltonians H CF = k q B kq C (k) q has to be based on the CF parameters B kq that lead to the correct CF splitting second moments, both the global one σ and the partial ones σ k. Only such parametrizations correspond to the appropriate multipolar structure of the surrounding CF. Each parametrization being characterized by its own multipolar crystal-field strengths S k = 1 2k+1 q |B kq | 2 1/2 , for k = 2, 4 and 6, yields a definite second moment σ, which can be derived from the additivity relationship σ 2 = k σ 2 k and the known asphericities Ψ||C (k) ||Ψ of the centralion eigenfunctions Ψ. The condition σ = σ exp must be satisfied to ensure the parametrization's correctness. However, our survey of literature indicates that there exists many other well-fitted crystal-field parameter sets that do not obey this condition. Therefore, such sets are erratic and non-physical, and should be reexamined or rejected. Having σ for several (≥ 3) eigenstates |Ψ along with the relevant Ψ||C (k) ||Ψ asphericities, one can estimate σ k and S k , which are wellfounded experimentally. The above findings set up the parametrization process properly. Lack of consistency between the second moments representing various parametrizations and the pertinent second moments observed in experiments is presumably the main reason for deluge of formally accurate but accidental and inequivalent parametrizations.
International Journal of Modern Physics B, Feb 20, 2001
We prove that an arbitrary crystal with anisotropic lattice and partially filled conduction band,... more We prove that an arbitrary crystal with anisotropic lattice and partially filled conduction band, for which one-electron energy spectrum is known, can be considered, after some curvilinear transformation of the reciprocal lattice as the Fermi liquid of the Landau–type quasiparticles in the isotropic system. However, the additional scalar field modifying the size of quantum-mechanical states in the reciprocal space has to be included. It is shown that the established formalism can be employed for two- and three-dimensional systems. As an example one-band Hubbard model has been investigated in details. The new precise formulas for the postulated scalar field and the density of states are derived. Additionally, assuming the microscopic mechanism which leads to the pairing interaction in a crystal, the anisotropic Fermi liquid formalism is extended to superconducting system according to the BCS theory principles. The obtained results enable us to explain and understand the great success of the BCS theory.
The D-wave paired Fermi system is considered in the frame of generalized gap equation obtained in... more The D-wave paired Fermi system is considered in the frame of generalized gap equation obtained in a BCS-like approach. It is shown that the thermodynamic functions of a system, as the thermodynamic potential, entropy and heat capacity differences between the normal and superconducting state are precisely defined functionals of the energy gap as a function of temperature. The derived formulas are identical as those obtained for S-wave paired Fermi system. It states that the developed formalism can be applied, in practice, to investigation of real superconductors in which a singlet state is realized. Some numerical results illustrating prospects and capabilities of the presented formalism are given for chosen structures of the order parameter.
The generalised form of the gap equation which comprises also some non-BCS approaches is defined ... more The generalised form of the gap equation which comprises also some non-BCS approaches is defined and solved. The parametric gap equations have been derived in a few equivalent cases and discussed in_ dissimilar limits. It is shown that the relations between the critical temperature and zero-temperature energy gap can be extended for all systems under consideration. The main benefits and incontestable advantage of the presented method are demonstrated with regard to the general BCS case.
Physica Status Solidi B-basic Solid State Physics, Apr 29, 2021
A single‐state algebraic parametrization is applied to 47 free‐ion triply ionized lanthanide elec... more A single‐state algebraic parametrization is applied to 47 free‐ion triply ionized lanthanide electronic states that originate from 11 ions embedded in four various octahedral hosts, mainly in Cs2NaLaCl6 matrix. The obtained single‐state parametrizations averaged over the considered |J⟩ states of 2J + 1 degeneracy adequately reproduce the conventional fitting parametrization, where as many pairs of the cubic B 40 and B 60 crystal field (CF) parameters as the states in the configuration are replaced by only one universal pair. This is the essence of the fitting procedure. The comparison between the single‐state parametrizations and the corresponding fitted parametrization reveals the structure of anatomy of the fitting as well as the component states of the configuration giving an untypical contribution to the mean value. The single‐state parametrization unveils directly not only the physical CF parameters of the state but also the host ligand strength, it means its position in the spectrochemical series.
D-wave paired isotropic Fermi system in the limiting cases Τ-Tc and Τ-> 0 is considered. Values o... more D-wave paired isotropic Fermi system in the limiting cases Τ-Tc and Τ-> 0 is considered. Values of the energy gap, the thermodynamic potential, and the specific heat as a function of temperature are given for admissible solutions and compared with values for S-wave paired system. It is shown that the linear term of low temperature specific heat vanishes likewise in case of S-wave pairing. The obtained results make prospects to define the geometry of the energy gap in virtue of the behavior of the specific heat in the limiting temperature cases for heavy-fermion superconductors.
The s-paired BCS superconductor with the electron density of states depending on energy in the vi... more The s-paired BCS superconductor with the electron density of states depending on energy in the vicinity of Fermi level is considered. The existence of such fluctuations of electron density of states may be referred to Van Hove singularities widely discussed in the literature. In the paper three types of small fluctuations of the electron density of states introduced about its average background's value are analysed: Lorentzian, triangle, and logarithmic ones. In order to calculate numerically the energy gap and critical temperature, the formalism of parametric BCS gap equations is applied. The positive fluctuations (peaks) correspond to the increase in occupied states number inducing a higher critical temperature. On the other hand, negative fluctuations, which decrease the number of occupied states, lead to a lower critical temperature. Such decrease in critical temperature can lead, at a specific choice of parameters, to the decease in superconductivity. The presence of fluctuations finds reflection in the shape of energy gap as a function of temperature. In the vicinity of Τ = 0 an abrupt decrease or increase in the energy gap to the original BCS value, according to the sign of the fluctuation, is observed. In turn, the fluctuations do not change the behaviour of the energy gap near 21.
A new measure of the crystal-field strength, complementary to the conventional one, is defined. I... more A new measure of the crystal-field strength, complementary to the conventional one, is defined. It is based on the rotational invariants |B k0 | av or | k B k0 | av , k = 2, 4, 6, of the crystal-(ligand)-field (CF) Hamiltonian H CF parametrizations, i.e. on the axial CF parameters modules averaged over all reference frame orientations. They turn out to be equal to H (k) CF av and |H CF | av , respectively. While the traditional measure is established on the parametrization modules or on the second moment of the CF energy levels, the introduced scale employs rather the first moment of the energy modules and has better resolving power. The new scale is able to differentiate the strength of various iso-modular parametrizations according to the classes of rotationally equivalent parametrizations. Using both the compatible CF strength measures one may draw more accurate conclusions about the Stark levels arrays and particularly their total splitting magnitudes.
Physica Status Solidi B-basic Solid State Physics, Mar 7, 2022
To facilitate the calculation of the fourth‐order crystal‐field (CF) splitting moment, which in a... more To facilitate the calculation of the fourth‐order crystal‐field (CF) splitting moment, which in a complex way depends on the split state , a time saving formula is elaborated, which is positively verified for several cubic systems RE3+: Cs2NaLaCl6. The appropriate crystal‐field parameters (CFPs) have to be substituted to the presented formula. However, the question is which ones. The clear answer proven in the paper is that single‐state CFPs should necessarily be used. To test the approach, a few cubic systems, for which such single‐state CFPs are available, have been studied. Conventionally fitted CFPs, averaged over the entire electron configuration, do not satisfy the equation, which contradicts the fundamental principle of the CF theory. Such verification significantly limits the physical meaning and applicability of the conventional fitted parameterizations.
Physica Status Solidi B-basic Solid State Physics, Feb 1, 2007
In memoriam Professor Włodzimierz Trzebiatowski on the occasion of the 100th anniversary of his b... more In memoriam Professor Włodzimierz Trzebiatowski on the occasion of the 100th anniversary of his birth.
The general method of investigation of S-paired Fermi systems is given and discussed as generaliz... more The general method of investigation of S-paired Fermi systems is given and discussed as generalization of parametric equation for the energy gaρ. The additional parametric equations for thermodynamic potential and heat capacity are obtained as functions of introduced parameters. The detailed calculations are given for a few exemplary chosen magnetic fields and superflows. Moreover, we consider the case of so-called statistical spin liquid, which constitutes non-BCS model.
The application of a method of conformal-like transformation of the two-dimensional momentum spac... more The application of a method of conformal-like transformation of the two-dimensional momentum space is presented and discussed with regard to two-dimensional anisotropic superconductors. A new function, the kernel of the density of states, and some integral formulae are derived, interpreted and studied for a few specific cases. Evidences for the incompatibility between the Van Hove scenario and the conformal transformation
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