arXiv subjects
Publications and source records attributed to Kazuhiro Kuboki.
Kitaev chain is a one-dimensional spinless fermion model that has $p$-wave superconducting (SC) states and Majorana zero modes at the edge. Usually this model is analyzed by taking only SC order parameter (OP) into account, but the situation significantly changes when OPs other than the SCOP are included. It turns out that the SC state in the latter case is prone to phase separation for moderate to strong attractiive interactions.
We study phase separation in the $t-t'-J$ model in which the constraint of no double occupancy due to strong electron correlations leads to effective narrowing of the band width. Using a mean-field approximation, we calculate the compressibility in the normal state and show that the phase separation can be induced by the variation of the band width.
We study theoretically the spatial distribution of spontaneous magnetic fields near a (110) surface of cuprate high-$T_C$ superconductor YBCO by treating a bilayer $t-J$ model with the Bogoliubov-de Gennes method. Near a (110) surface where $d_{x^2-y^2}$-wave superconductivity is strongly suppressed, flux phase order occurs locally leading to a time-reversal symmetry broken surface state. Since the spontaneous currents flowing in the flux phase in two layers are antiparallele, resulting spontaneous magnetic fields are quite small. They exist in a narrow region inside the superconductor, and essentially vanish outside irrespective of the temperature. This result, together with the splitting of zero-energy peak of the local density of states, can provide consistent explanations for several experiments on YBCO.
Spatial distributions of spontaneous magnetic fields near a surface of cuprate high-$T_C$ superconductor YBCO with broken time-reversal symmetry are calculated using the Ginzburg-Landau theory derived from the $t-J$ model. It is found that the magnetic field exists in a narrow region inside the superconductor, and it decays quickly outside the surface. Experimental approaches possible to detect such spontaneous magnetic fields are discussed.
Ginzburg-Landau (GL) equations and GL free energy for flux phase and superconductivity are derived microscopically from the $t-J$ model on a square lattice. Order parameter (OP) for the flux phase has direct coupling to a magnetic field, in contrast to the superconducting OP which has minimal coupling to a vector potential. Therefore, when the flux phase OP has unidirectional spatial variation, staggered currents would flow in a perpendicular direction. The derived GL theory can be used for various problems in high-$T_c$ cuprate superconductors, e.g., states near a surface or impurities, and the effect of an external magnetic field. Since the GL theory derived microscopically directly reflects the electronic structure of the system, e.g., the shape of the Fermi surface that changes with doping, it can provide more useful information than that from phenomenological GL theories.
We report that special care is needed when longitudinal magnetic susceptibility is computed in a magnetically ordered phase, especially in metals. We demonstrate this by studying static susceptibility in both a ferromagnetic and an antiferromagnetic state in the random phase approximation to the two-dimensional Hubbard model on a square lattice. In contrast to the case in the disordered phase, a first derivative of the chemical potential (or the density) with respect to a magnetic field does not vanish in a magnetically ordered phase when the field is applied parallel to the magnetic moment. This effect is crucial and should be included when computing magnetic susceptibility in the ordered phase, otherwise an unphysical result would be obtained. In addition, consequently the magnetic susceptibility becomes different when computed at a fixed density and a fixed chemical potential in the ordered phase. In particular, we cannot employ magnetic susceptibility at a fixed chemical potential to describe a system with a fixed density even if the chemical potential is tuned to reproduce the correct density.
We study surface states of high-$T_C$ cuprate superconductor YBCO using the bilayer $t-J$ model. Calculations based on the Bogoliubov de Gennes method show that a flux phase that breaks time-reversal symmetry (${\cal T}$) may arise near a (110) surface where the $d_{x^2-y^2}$-wave superconductivity is strongly suppressed. It is found that the flux phase in which spontaneous magnetic fields in two layers have opposite directions may be stabilized in a wide region of doping rate, and split peaks in the local density of states appear. Near the surface, spontaneous magnetic field may not be observed experimentally, because the contributions from two layers essentially cancel out. This may explain the absence of local magnetic filed near the (110) surface of YBCO, for which the sign of ${\cal T}$ violation has been detected.
In order to study the time-reversal symmetry (${\cal T}$) breaking near a (110) surface of a high-$T_C$ cuprate YBCO, we consider the flux phase in a bilayer $t-J$ model. Although the stable solution in the bulk is the $d_{x^2-y-2}$-wave superconducting (SC) state, free energy of the flux phase is close to it, and thus the flux phase may occur when the SC order is disturbed by inhomogeneity, e.g., surface or impurity. It is found that, depending on the doping rate, the flux phase in which spontaneous magnetic fields in two layers have opposite signs may be stabilized. This may lead to a surface state with local ${\cal T}$ violation but without local magnetic field.
At a (110) surface of a $d_{x^2-y-2}$-wave superconductor, superconducting order is strongly suppressed. In such a situation, ordered states that are forbidden in the bulk may arise. This problem is studied for high-$T_C$ cuprate superconductors by treating the $t-J$ model with extended transfer integrals using the Bogoliubov de Gennes method. It is found that a flux phase with staggered currents along the surface, or an antiferromagnetic state can occur near the surface. Stability of the emergent surface states is different from system to system depending on the shapes of their Fermi surfaces. Possible relation to the experiments on the Kerr effect that suggest time-reversal symmetry breaking is discussed.
In high-Tc cuprate superconductors, violation of time-reversal symmetry (${\cal T}$) has been observed experimentally. In order to explain this phenomenon, we consider a flux phase in the t-J model. The flux phase has a free energy higher than that of a superconducting (SC) state, but it may occur near a [110] surface of a $d_{x^2-y^2}$-wave superconductor where the SC order is strongly suppressed. In this case the system would break ${\cal T}$ locally near the surface. In this short note we estimate the bare transition temperature of the flux phase, $T_{FL}$, assuming the absence of the SC state. It is found that $T_{FL}$ is finite for rather large doping rate $δ$ ($δ\lesssim 0.15$) if the shape of Fermi surface of the system is favorable to this state.
The mean-field phase diagram of antiferromagnetic order in t-J model has been examined, using the free energy obtained by Ginzburg-Landau (GL) expansion. We extended the usual GL theory in two ways: First, we have included higher order terms with respect to the spatial derivative (or wave number) to incorporate the incommensurate antiferromagnetic order. Second, we have also included higher order terms with respect to the order parameter amplitude, in order to treat the first order phase transition between paramagnetic and antiferromagnetic phase, which appears at some doping rates. We found the possibility of tricritical point and critical endpoint in the magnetic phase diagram of the high-Tc oxides associated with the commensurate and incommensurate antiferromagnetic order. The possible effects of thermal fluctuations and randomness (spin glass) are also discussed qualitatively based on the GL free energy.
Ginzburg-Landau (GL) equations for the coexistent states of superconductivity and magnetism are derived microscopically from the extended Hubbard model with on-site repulsive and nearest-neighbor attractive interactions. In the derived GL free energy a cubic term that couples the spin-singlet and spin-triplet components of superconducting order parameters (SCOP) with magnetization exists. This term gives rise to a spin-triplet SCOP near the interface between a spin-singlet superconductor and a ferromagnet, consistent with previous theoretical studies based on the Bogoliubov de Gennes method and the quasiclassical Green's function theory. In coexistent states of singlet superconductivity and antiferromagnetism it leads to the occurrence of pi-triplet SCOPs.
Ginzburg-Landau (GL) equations for the coexistent state of superconductivity and antiferromagnetism are derived microscopically from the t-J model with extended transfer integrals. GL equations and the GL free energy, which are obtained based on the slave-boson mean-field approximation, reflect the electronic structure of the microscopic model, especially the evolution of the Fermi surface due to the change of the doping rate. Thus they are suitable for studying the material dependence of the coexistent states in high-$T_C$ cuprate superconductors.
Coexistence of antiferromagnetism and d-wave superconductivity within a CuO_2 plane was recently observed in a wide doping region for multilayer high-temperature cuprate superconductors. We find that the experimental phase diagram is well reproduced in the slave-boson mean-field scheme of the two-dimensional t-J model by including antiferromagnetic order. We argue that weak three dimensionality coming from a multilayer structure is sufficient to stabilize antiferromagnetic order and its coexistence with superconductivity.
Surface states of d_{x^2-y^2}-wave superconductors are studied using the Ginzburg-Landau (GL) theory. For a [110] surface it has been known that the time-reversal symmetry (T) breaking surface state, (d+-is)-wave state, can occur if the bare transition temperature of the s-wave order parameter (OP) is positive. We show that even if this bare T_c is negative, it is possible to break T because the coupling to the spontaneously generated magnetic field may induce the s-wave OP. The T-breaking state is favored when the GL parameter (kappa) is small.
We study theoretically the structure of domain walls in ferromagnetic states on Mobius strips. A two-dimensional classical Heisenberg ferromagnet with single-site anisotropy is treated within a mean-field approximation by taking into account the boundary condition to realize the Mobius geometry. It is found that two types of domain walls can be formed, namely, parallel or perpendicular to the circumference, and that the relative stability of these domain walls is sensitive to the change in temperature and an applied magnetic field. The magnetization has a discontinuity as a function of temperature and the external field.
Charge-density-wave (CDW) phase transition in a ring-shaped crystals, recently synthesized by Tanda et al. [Nature, 417, 397 (2002)], is studied based on a mean-field-approximation of Ginzburg-Landau free energy. It is shown that in a ring-shaped crystals CDW undergoes frustration due to the curvature (bending) of the ring (geometrical frustration) and, thus, forms a mixed state analogous to what a type-II superconductor forms under a magnetic field. We discuss the nature of the phase transition in the ring-CDW in relation to recent experiments.
Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is pointed out and the phase diagram of the ring-crystal, which depends on radius and thickness, is discussed.