Superconducting States with the Lattice Distortion in the Extended Hubbard Model

1997 ◽  
Vol 11 (09) ◽  
pp. 1153-1186
Author(s):  
Eiji Miyai ◽  
Masa-Aki Ozaki
Keyword(s):  
Hubbard Model ◽  
Order Parameter ◽  
Lattice Distortion ◽  
Mean Field ◽  
Square Lattice ◽  
Extended Hubbard Model ◽  
S Wave ◽  
Irreducible Components ◽  
Anisotropic Lattice ◽  
D Wave

We give group theoretical classification of superconducting (SC) states with a single SC order parameter in the extended Hubbard model with uniform lattice distortion on the two-dimensional square lattice, by using the mean field approach. We obtain two singlet SCs (s-wave and d-wave) and eight triplet SCs by decomposing the pairing interaction into irreducible components (A1g, B1g and Eu) of point symmetry D4h. We show that in the singlet SC state with a single SC order parameter (s-wave or d-wave) no anisotropic lattice distortion occurs. In the case of triplet SC states, two SC states among eight must be accompanied with anisotropic lattice distortion. The symmetry of SC order parameter uniquely determines the lattice symmetry. We have performed numerical calculations for these SC states, and shown the possibility that one of the SC states with anisotropic lattice distortion becomes most stable of all SC states in the extended Hubbard model. We also discuss singlet SC states with multiple SC order parameters (s-wave and d-wave). It is shown that the anisotropic distortion must occur in (s+d)-SC states and not in (s+id)-SC state.

SUPERCONDUCTING CLASSES IN THE EXTENDED HUBBARD MODEL

1996 ◽  
Vol 10 (12) ◽  
pp. 1397-1423 ◽  
Author(s):  
MASA-AKI OZAKI ◽  
EIJI MIYAI ◽  
TOMOAKI KONISHI ◽  
KAORU HANAFUSA
Keyword(s):  
Hubbard Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Square Lattice ◽  
Extended Hubbard Model ◽  
S Wave ◽  
Ferromagnetic Order ◽  
Numerical Studies ◽  
The Mean

This paper describes group theoretical classification of superconducting states (SC) in the extended Hubbard model with on-site repulsion (U), nearest neighbor attraction (V) and nearest neighbour exchange interaction (J) on the two-dimensional square lattice using the mean field approach. By decomposing the pairing interaction into irreducible parts; A1g, B1g and Eu of D4h point symmetry, we have derived two singlet SCs (s-wave and d-wave) from A1g and B1g, eight triplet SCs from Eu. The first three types of triplet SC have pairing by electrons with antiparallel spin, the second two types have pairing by electrons with equal spin and the last three types are non-unitary and have pairing by only up-spin electrons. We showed that three non-unitary states have to be accompanied with a ferromagnetic order from the structure of the maximal little groups. We performed numerical studies for these SCs. For parameters and electron density favorable for the ferromagnetic order, a non-unitary SC coexistent with ferromagnetism is most stable.

scholarly journals SUPERCONDUCTING ORDER PARAMETERS IN THE EXTENDED HUBBARD MODEL: A SIMPLE MEAN-FIELD STUDY

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2371-2383 ◽  
Author(s):  
J. S. THAKUR ◽  
M. P. DAS
Keyword(s):  
Hubbard Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Order Parameters ◽  
Square Lattice ◽  
Extended Hubbard Model ◽  
Self Consistent ◽  
Frame Work ◽  
Field Formalism ◽  
Superconducting Pairing

The extended Hubbard model with nearest neighbor hopping and intersite interaction for a 2D square lattice has been studied within the frame work of a simple mean-field formalism. The self-consistent solutions of superconducting order parameters have been obtained for various fillings. The results indicate that superconducting pairing occurs on doping for the repulsive on-site U and attractive nearest neighbor V.

PHASE DIAGRAM OF STRIPE ORDER IN THE EXTENDED HUBBARD MODEL

2000 ◽  
Vol 14 (29n31) ◽  
pp. 3508-3513 ◽  
Author(s):  
MASARU KATO
Keyword(s):  
Hubbard Model ◽  
Coulomb Interaction ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Extended Hubbard Model ◽  
Stable States ◽  
Stripe Order

The extended Hubbard model with the nearest-neighbor Coulomb interaction on the square lattice is studied within the mean-field approximation. The stable states for 8×8 sites lattice with the periodic boundary condition and the electron filling n=0.875, as well as for 10×10 lattice and n=0.80, are obtained. For 8×8 lattice where quarter-filled straight stripe is expected because of the long-range Coulomb interaction, the cross stripe phases become stable.

scholarly journals Optimal electronic doping in p-wave superconductors

2021 ◽  
Vol 67 (6 Nov-Dec) ◽  
Author(s):  
Benjamín Millan ◽  
Ivonne Judith Hernández ◽  
Luis Antonio Pérez ◽  
José Samuel Millan
Keyword(s):  
Critical Temperature ◽  
Ground State Energy ◽  
Electron Concentration ◽  
Ground State ◽  
State Energy ◽  
P Wave ◽  
Square Lattice ◽  
S Wave ◽  
Optimal Doping ◽  
D Wave

Recently, within a generalized Hubbard model which includes correlated nearest (∆t) and next-nearest hopping interactions (∆t_3 ), a comparative study between d- and s*- wave superconducting ground states on a square lattice was performed. It was found that the critical temperature of transition T_c (n), as a function of the electron concentration n, reaches a maximum (T_(c-max) at a given optimal doping (n_op) for each value of the ratio (t’)⁄t, where t and t’ are the tight-binding nearest and next-nearest hopping parameter of a square lattice, respectively. From all values obtained for T_(c-max) ((t’)⁄(t,n_op) a global minimum one was encountered for both symmetries. Likewise, in the same space, a minimal ground state energy E_g was also obtained. For d-wave channel both minima are localized around the same optimal doping, however, for s* symmetry, the two minima are located at different electron concentrations. In this work, we additionally study how the p-wave ground-state energy and the critical temperature depend on the hoppings parameters and the electron concentration. The results show that for p-wave, minimum global values of  and  in the space do exist too, they are found around half filling but, as occurs for s*- wave, the minimum of T_(c-max) does not occur at the same point as . Moreover, we present a ground-state phase diagram in the space (t’)⁄(t,n_op) where it is possible to find zones of coexistence and competition between the s*-, p- and d-wave symmetries. Also, an analysis of the shape of the Fermi surface and the single-particle energy, as functions of the wave vector of an electron in the Cooper pair, has been done for different regions of the mentioned space.

GROUND STATE OF THE 2D EXTENDED HUBBARD MODEL WITH MORE THAN NEAREST-NEIGHBOR INTERACTIONS

2012 ◽  
Vol 26 (29) ◽  
pp. 1250156 ◽  
Author(s):  
S. HARIR ◽  
M. BENNAI ◽  
Y. BOUGHALEB
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Ground State ◽  
State Energy ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Extended Hubbard Model ◽  
Eigenvalues And Eigenvectors ◽  
Repulsion Energy

We investigate the ground state phase diagram of the two dimensional Extended Hubbard Model (EHM) with more than Nearest-Neighbor (NN) interactions for finite size system at low concentration. This EHM is solved analytically for finite square lattice at one-eighth filling. All eigenvalues and eigenvectors are given as a function of the on-site repulsion energy U and the off-site interaction energy Vij. The behavior of the ground state energy exhibits the emergence of phase diagram. The obtained results clearly underline that interactions exceeding NN distances in range can significantly influence the emergence of the ground state conductor–insulator transition.

ULTRASONIC ATTENUATION IN d-WAVE SUPERCONDUCTORS

2001 ◽  
Vol 15 (09n10) ◽  
pp. 269-276 ◽  
Author(s):  
TRIBIKRAM GUPTA ◽  
D. M. GAITONDE
Keyword(s):  
Dopant Concentration ◽  
Ultrasonic Attenuation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Square Lattice ◽  
Clean Limit ◽  
Sign Change ◽  
Attenuation Rate ◽  
Interacting Electrons ◽  
D Wave

We consider a BCS-like model of interacting electrons on a square lattice. Within mean field theory, our model has an instability towards the formation of a d-wave superconducting state. We calculate the longitudinal ultrasonic attenuation rate in the superconducting phase in the clean limit for parameters appropriate to the cuprates. We find that the temperature dependence of the attenuation rate is similar to that observed in conventional superconductors for phonon wavevectors along the direction of the anti-nodes of the gap. However, the attenuation rate for phonon wavevectors along the nodal direction is found to be strikingly different in its temperature and doping dependence. The attenuation rate α S (T) increases in magnitude and shows a sign change in its curvature (when plotted as a function of temperature) with increasing value of dopant concentration.

Pair Symmetry and Degree of Gap Depression at S-I Interfaces in HTS Josephson Junctions

1999 ◽  
Vol 13 (09n10) ◽  
pp. 1301-1306
Author(s):  
G. A. Ummarino ◽  
R. S. Gonnelli ◽  
C. Bravi ◽  
Masumi Inoue
Keyword(s):  
Josephson Junctions ◽  
Order Parameter ◽  
Reference Value ◽  
High Tc Superconductors ◽  
S Wave ◽  
General Reference ◽  
High Tc ◽  
Wave Symmetry ◽  
Set Up ◽  
D Wave

A new possible indirect way of testing pair symmetry in high-Tc superconductors has been set up. The degree of intrinsic gap depression at Superconductor-Insulator [S-I] interfaces required to match Ic(T)Rn(T) data in HTS Josephson junctions depends on the pair symmetry of the material itself, so that an higher fraction of d-wave symmetry for the order parameter requires less gap depression, while an higher fraction of s-wave corresponds to a larger degree of gap depression. In order to obtain a general reference value for the intrinsic amount of gap depression at S-I interfaces the de Gennes condition has been used, and resulting reduced Ic(T)Rn(T) data have been calculated in the framework of a mixed (s+id)-wave pair symmetry for the depressed order parameter ranging from pure s to pure d-wave. This model has been tentatively applied to two junctions' made of very different HTSs: YBCO and BKBO, yielding a result of almost pure d-wave for YBCO and of pure s-wave for BKBO.

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