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Dirac points in two-dimensional massless Dirac fermions are topologically protected. Although single Dirac point cannot disappear solely, a pair of two Dirac points annihilates after merging at a time-reversal invariant momentum (TRIM). This process triggers a topological phase transition. In this paper, we numerically calculate the electronic specific heat ($C$) of the systems with a honeycomb lattice and $\alpha$-(BEDT-TTF)$_2$I$_3$ in the case that two Dirac points are moving and merging by changing the ratio of the magnitude between the transfer integrals, which can be controlled by uniaxial pressure for example. When two Dirac points are close to but not at TRIM, the temperature dependence exhibits a crossover from $C\propto T^{2.0}$ (expected for separated Dirac points) at low temperatures ($T\leq T_{\rm co}$) to $C\propto T^{1.5}$ (expected in the case of the merged Dirac points) at high temperatures ($T\geq T_{\rm co}$). Here, $T_{\rm co}$ denotes the crossover temperature, which is determined by the potential barrier magnitude between two Dirac points. Our findings demonstrate that the precursor of the topological phase transition is observed through the temperature-dependence of the electronic specific heat., Comment: 8pages, 12 figures, submitted to Phys. Rev. B

We theoretically study the de Haas-van Alphen (dHvA) oscillations in the system with changing the topology of the Fermi surface (the Lifshitz transition) by electron dopings. We employ the two-dimensional tight binding model for $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure which has two Dirac points in the first Brillouin zone. When this system is slightly doped, there exists two closed Fermi surfaces with the same area and the dHvA oscillations become saw-tooth pattern or inversed saw-tooth pattern for both cases of fixed electron filling ($\nu$) or fixed chemical potential ($\mu$) with respect to the magnetic field, respectively. By increasing dopings, the system approaches the Lifshitz transition, where two closed Fermi surfaces are close each other. Then, we find that the pattern of the dHvA oscillations changes. A jump of the magnetization appears at the center of the fundamental period and its magnitude increases in the case of the fixed electron filling, while a jump is separated into a pair of jumps and its separation becomes large in the case of the fixed chemical potential. This is due to the lifting of double degeneracy in the Landau levels. Since this lifting is seen in the two-dimensional Dirac fermion system with two Dirac points, the obtained results in this study can be applied to not only $\alpha$-(BEDT-TTF)$_2$I$_3$ but also other materials with closely located Dirac points such as graphene under the uniaxial strain, in black phosphorus, twisted bilayer graphene, and so on., Comment: arXiv admin note: text overlap with arXiv:2010.13329

We study the de Haas-van Alphen (dHvA) oscillations in the two-dimensional compensated metal with overtilted Dirac cones near the Lifshitz transition. We employ the tight-binding model of $\alpha$-(BEDT-TTF)$_2$I$_3$, in which the massless Dirac fermions are realized. When a uniaxial pressure $(P)$ along the $y$-axis is applied above $P\simeq 0.2$ kbar in $\alpha$-(BEDT-TTF)$_2$I$_3$, one electron pocket, which encloses the overtilted Dirac points, is changed to two electron pockets, i.e., Lifshitz transition happens, while a hole pocket does not change a topology. We show that the Fourier components corresponding to the $3/2$ and $5/2$ areas of the hole pocket are anomalously enhanced in the region of pressure where the Lifshitz transition occurs. This phenomenon will be observed in the two-dimensional overtilted Dirac fermions near the Lifshitz transition., Comment: 16 pages, 17 figures

We study the commensurately-tilted bilayer graphene in the tight-binding model with changing the interlayer distance, which can be tuned by pressure. We find that at the commensurately-tilted bilayer graphene with moderate rotating angles, when the energy gap at K point is not negligible, the other Dirac points within the upper two bands move along the $\Gamma$-K-M line in the bilayer Brillouzone, when the interlayer distance is changed. The velocity at K point becomes zero due to the merging of the four Dirac points within upper two bands. This mechanism of zero velocity at K point is expected to be the origin of the magic angle with flat band at ambient pressure, at which the upper two bands are almost degenerate and the band gap at K can be neglected., Comment: 10 pages 13 figures

The quantization of the energy in a magnetic field (Landau quantization) at a three-quarter Dirac point is studied theoretically. The three-quarter Dirac point is realized in the system of massless Dirac fermions with the critically tilted Dirac cone in one direction, where a linear term disappears and a quadratic term $\alpha_2 q_x^2$ with aconstant $\alpha_2$ plays an important role. The energy is obtained as $E_n \propto \alpha_2^{\frac{3}{5}} (n B)^{\frac{4}{5}}$, where $n=1, 2, 3, \dots$, by means of numerically and analytically solving the differential equation, as well as by the semiclassical quantization rule. The existence of the $n=0$ state is studied by introducing the energy gap due to the inversion-symmetry-breaking term, and it is obtained that the $n=0$ state exists in one of a pair of three-quarter Dirac points, depending on the direction of the magnetic field when the energy gap is finite., Comment: 9 pages

The magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the 1/3 and 2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the 1/3 plateau are obtained by using the approximated state in the unit cell and compared with the nu- merical results of the exact diagonalization of 42 sites., Comment: 10 pages, 10 figures

The energies as a function of the magnetic field ($H$) and the pressure are studied theoretically in the tight-binding model for the two-dimensional organic conductor, $\alpha$-(BEDT-TTF)$_2$I$_3$, in which massless Dirac fermions are realized. The effects of the uniaxial pressure ($P$) are studied by using the pressure-dependent hopping parameters. The system is semi-metallic with the same area of an electron pocket and a hole pocket at $P < 3.0$~kbar, where the energies $(\varepsilon_{\rm D}^0$) at the Dirac points locate below the Fermi energy $(\varepsilon_{\rm F}^0$) when $H=0$. We find that at $P=2.3$~kbar the Dirac cones are critically tilted. In that case a new type of band crossing occurs at "three-quarter"-Dirac points, i.e., the dispersion is quadratic in one direction and linear in the other three directions. We obtain new magnetic-field-dependences of the Landau levels $(\varepsilon_n)$; $\varepsilon_n-\varepsilon^0_{\textrm{D}} \propto (n H)^{4/5}$ at $P=2.3$~kbar ("three-quarter"-Dirac points) and $|\varepsilon_n-\varepsilon_{\rm F}^0| \propto (n H)^2$ at $P=3.0$~kbar (the critical pressure for the semi-metallic state). We also study the magnetization as a function of the inverse magnetic field. We obtain two types of quantum oscillations. One is the usual de Haas van Alphen (dHvA) oscillation, and the other is the unusual dHvA-like oscillation which is seen even in the system without the Fermi surface., Comment: 25 pages, 31 figures

Quantized Hall conductance and de Haas van Alphen (dHvA) oscillation are studied theoretically in the tight-binding model for (TMTSF)$_2$NO$_3$, in which there are small pockets of electron and hole due to the periodic potentials of anion ordering in the $a$-direction. The magnetic field is treated by hoppings as complex numbers due to the phase caused by the vector potential, i.e. Peierls substitution. In realistic values of parameters and the magnetic field, the energy as a function of a magnetic field (Hofstadter butterfly diagram) is obtained. It is shown that energy levels are broadened and the gaps are closed or almost closed periodically as a function of the inverse magnetic field, which are not seen in a semi-classical theory of the magnetic breakdown. Hall conductance is quantized with an integer obtained by Diophantine equation when the chemical potential lies in an energy gap. When electrons or holes are doped in this system, Hall conductance is quantized in some regions of a magnetic field but it is not quantized in other regions of a magnetic field due to the broadening of the Landau levels. The amplitude of the dHvA oscillation at zero temperature decreases as the magnetic field increases, while it is constant in the semi-classical Lifshitz Kosevich formula., Comment: 16 pages, 14 figures

We study the magnetization process of the spin-$1/2$ Heisenberg antiferromagnet on a distorted square-kagome lattice by the numerical-diagonalization method. The magnetization jump at one-third of the height of the saturation is examined in detail; we find that the jump becomes larger when a small distortion is switched on and that it is accompanied by an abrupt change in lines along microscopic spin directions. Our finite-size results successfully confirm that the magnetization jump in a spin-isotropic system is a macroscopic jump that survives in the thermodynamic limit and that the changes in spin directions are common to a spin-flop phenomenon observed in spin-anisotropic systems., Comment: 6pages, 5figures, 1table, to be published in J. Phys. Soc. Jpn

We numerically calculate the magnetization by applying the magnetic field ($B$) perpendicular to two-dimensional corbino disk system without electron spin. We obtain that the period of the Aharonov-Bohm (AB) oscillations of magnetization $[M(B)]$ exhibit $\phi_0$, $\phi_0/2$ and almost $\phi_0/3$ as a function of $\phi$, depending on numbers of electrons ($N$), where $\phi_0=\frac{hc}{e}$ is a unit flux and $\phi$ is the magnetic flux through the hollow of the disk. The oscillations of $M(B)$ are classified into five patterns at $1\leq N\leq 27$ investigated in this study. These are expected to be observed in the two-dimensional semiconductor corbino disk with the hollow radius of about 10 nm and small electron numbers at the high magnetic field., Comment: 9 pages, 18 Postscript figures

We show that the new quantum oscillations of the magnetization can occur when the Fermi surface consists of points (massless Dirac points) or even when the chemical potential is in a energy gap by studying the tight-binding electrons on a honeycomb lattice in a uniform magnetic field. The quantum oscillations of the magnetization as a function of the inverse magnetic field are known as the de Haas-van Alphen (dHvA) oscillations and the frequency is proportional to the area of the Fermi surface. The dominant period of the new oscillations corresponds to the area of the first Brillouin zone and its phase is zero. The origin of the new quantum oscillations is the characteristic magnetic field dependence of the energy known as the Hofstadter butterfly and the Harper broadening of Landau levels. The new oscillations are not caused by the crossing of the chemical potential and Landau levels, which is the case in the dHvA oscillations. The new oscillations can be observed experimentally in systems with large supercell such as graphene antidot lattice or ultra cold atoms in optical lattice at an external magnetic field of a few Tesla when the area of the supercell is ten thousand times larger than that of graphene., Comment: 6 pages, 8 Postscript figures

Motivated by a recent finding of a spin-flop phenomenon in a system without anisotropy in spin space reported in the S=1/2 Heisenberg antiferromagnet on the square-kagome lattice, we study the S=1/2 Heisenberg antiferromagnets on two other lattices composed of vertex-sharing triangles by the numerical diagonalization method. One is a novel lattice including a shuriken shape with four teeth; the other is the kagome lattice with $\sqrt{3}\times\sqrt{3}$-structure distortion, which includes a shuriken shape with six teeth. We find in the magnetization processes of these systems that a magnetization jump accompanied by a spin-flop phenomenon occurs at the higher-field-side edge of the magnetization plateau at one-third the height of saturation. This finding indicates that the spin-flop phenomenon found in the isotropic system on the square-kagome lattice is not an exceptional case., Comment: 7 pages, 7 figures, to be published in J. Phys. Soc. Jpn

Energy versus magnetic field (Hofstadter butterfly diagram) in twisted bilayer graphene is studied theoretically. If we take the usual Landau gauge, we cannot take a finite periodicity even when the magnetic flux through a supercell is a rational number. We show that the \textit{periodic} Landau gauge, which has the periodicity in one direction, makes it possible to obtain the Hofstadter butterfly diagram. Since a supercell can be large, magnetic flux through a supercell normalized by the flux quantum can be a fractional number with a small denominator, even when a magnetic field is not extremely strong. As a result, quantized Hall conductance can be a solution of nontrivial Diophantine equation., Comment: 9 pages, 10 figures revised

Moving, merging and annihilating Dirac points are studied theoretically in the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor hoppings. We obtain a rich phase diagram of the topological phase transitions in the parameter space of direction-dependent hoppings. We obtain the conditions for the three Dirac points to merge and for the tricritical points. We find that only very small third-nearest-neighbor hoppings are enough for the existence of the merging of three-Dirac-points and the tricritical points, if the system is sufficiently anisotropic. The density of states is obtained to be $D(\epsilon) \propto |\epsilon|^{1/3}$ when three Dirac points merge, and $D(\epsilon) \propto |\epsilon|^{1/4}$ at the tricritical points. It is possible to realize these topological phase transitions in the ultracold atoms on the optical lattice, strained monolayer graphene or strained bilayer graphene., Comment: 19 pages, 25 figures

The edge states in the hybrid system of single-layer and double-layer graphene are studied in the tight-binding model theoretically. The edge states in one side of the interface between single-layer and double-layer graphene are shown to penetrate into the single-layer region when the perpendicular electric field is applied, while they are localized in the double-layer region without electric field. The edge states in another side of the interface are localized in the double-layer region independent of the electric field. This field-induced penetration of the edge states can be applied to switching devices. We also find a new type of the edge states at the boundary between single-layer and the double-layer graphene., Comment: 9 pages

We study the edge states in the two-dimensional conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ theoretically. We show that the Dirac points and the edge states appear at the 3/4 and 1/4 filling as well as the half filling, due to four sites in the unit cell. This situation is in contract with the graphene, where the Dirac points and the edge states appear only at the half filling case. It is shown that the localization length of the edge states can become very large.

The nesting vector and the magnetic susceptibility of the quasi-one-dimensional system having imperfectly nested Fermi surface are studied analytically and numerically. The magnetic susceptibility has the plateau-like maximum in ``\textit{sweptback}'' region in the momentum space, which is surrounded by $\mathbf{Q}=(2 k_F, \pi) + \mathbf{q}_i$ ($k_F$ is the Fermi wave number, $i=1,3,4$, and $\mathbf{q}_1$, $\mathbf{q}_3$ and $\mathbf{q}_{4}$ are given in this paper). The best nesting vector, at which the susceptibility $\chi_0(\mathbf{Q})$ has the absolute maximum at T=0, is obtained near but not at the inflection point, $\mathbf{Q}=(2 k_F, \pi)+\mathbf{q}_4$. The effect of the periodic potential $V$ on the susceptibility is studied, which is important for the successive transitions of the field-induced spin density wave in (TMTSF)$_2$ClO$_4$. We obtain that the sweptback region (surrounded by $\mathbf{q}_2$, $\mathbf{q}_3$ and $\mathbf{q}_4$ when $V>0$) becomes small as $V$ increases and it shrinks to $\mathbf{q}_3$ for $V \geq 4 t_b'$, where $t_b'$ gives the degree of imperfect nesting of the Fermi surface, i.e. the second harmonics of the warping in the Fermi surface. The occurrence of the sign reversal of the Hall coefficient in the field-induced spin density wave states is discussed to be possible only when $V<2 t_b'-2 t_4$, where $t_4$ is the amplitude of the fourth harmonics of the warping in the Fermi surface. This gives the novel limitation for the magnitude of $V$.

The honeycomb lattice in the cylinder geometry with zigzag edges, bearded edges, zigzag and bearded edges (zigzag-bearded), and armchair edges are studied. The tight-binding model with nearest-neighbor hoppings is used. Edge states are obtained analytically for these edges except the armchair edges. It is shown, however, that edge states for the armchair edges exist when the the system is anisotropic. These states have not been known previously. We also find strictly localized states, uniformly extended states and states with macroscopic degeneracy., Comment: 6 pages 8 figures

We show that the nonuniform state (Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state) of the spin triplet superconductivity in noncentrosymmetric systems is stabilized by antisymmetric spin-orbit coupling even if the magnetic field is absent. The transition temperature of the spin triplet superconductivity is reduced by the antisymmetric spin-orbit coupling in general. This pair breaking effect is shown to be similar to the Pauli pair breaking effect due to magnetic field for the spin singlet superconductivity, in which FFLO state is stabilized near the Pauli limit (or Chandrasekhar-Clogston limit) of external magnetic field. Since there are gapless excitations in nonuniform superconducting state, some physical quantities such as specific heat and penetration depth should obey the power low temperature-dependences. We discuss the possibility of the realization of nonuniform state in CePt$_3$Si., Comment: 8 pages, 6 figures

When the inversion symmetry is broken, the spin-orbit coupling reduces the transition temperature of some types of spin triplet superconductivity, which is similar to the case that magnetic field reduces the spin singlet superconductivity due to Zeeman splitting. It is well known that Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state of spin singlet superconductivity is realized near the Pauli limit (or Chandrasekhar-Clogston limit) of external magnetic field. In FFLO state the amplitude of the order parameter is not uniform in space. In this paper we study the FFLO state in the spin triplet superconductivity in the absence of magnetic field due to the spin-orbit coupling. Although the FFLO state is not realized in the simple model with spherical Fermi surface, it will be stabilized if some condition is favorable for it. We discuss the possibility of FFLO state in CePt$_3$Si in the absence of external magnetic field., Comment: 2 pages, 1 figure, M2S-HTSC VIII

Tight binding electrons on the honeycomb lattice are studied where nearest neighbor hoppings in the three directions are $t_a,t_b$ and $t_c$, respectively. For the isotropic case, namely for $t_a=t_b=t_c$, two zero modes exist where the energy dispersions at the vanishing points are linear in momentum $k$. Positions of zero modes move in the momentum space as $t_a,t_b$ and $t_c$ are varied. It is shown that zero modes exist if $||\frac{t_b}{t_a}| -1| \leq |\frac{t_c}{t_a}| \leq ||\frac{t_b}{t_a}|+1|$. The density of states near a zero mode is proportional to $|E|$ but it is propotional to $\sqrt{|E|}$ at the boundary of this condition., Comment: 4 pages, 6 figures

Recently unusual integer quantum Hall effect was observed in graphene in which the Hall conductivity is quantized as $\sigma_{xy}=(\pm 2, \pm 6, \pm 10, >...) \times \frac{e^2}{h}$, where $e$ is the electron charge and $h$ is the Planck constant. %\cite{Novoselov2005,Zheng2005}, %although it can be explained in the argument of massless Dirac fermions, To explain this we consider the energy structure as a function of magnetic field (the Hofstadter butterfly diagram) on the honeycomb lattice and the Streda formula for Hall conductivity. The quantized Hall conductivity is obtained to be odd integer, $\pm1, \pm3, \pm5, ...$ times two (spin degrees of freedom) when a uniform magnetic field is as high as 30T for example. When the system is anisotropic and described by the generalized honeycomb lattice, Hall conductivity can be quantized to be any integer number. We also compare the results with those for the square lattice under extremely strong magnetic field., Comment: 4 pages, 10 figures

The effect of electron correlation on the angle dependence of magnetoconductivity is studied in quasi-one-dimensional organic conductors. We investigated the effect on the basis of the momentum dependence of both quasi-particle's lifetime and velocity near the spin-density-wave (SDW). We found that the momentum dependence of quasi-particle's lifetime mainly governs the angle dependence of one-dimensional axis magnetoconductivity. On the other hand, the change in velocity originating from the electron correlation gives the dominant effects on the angle dependence of the interchain axis magnetoconductivity. The effect of electron correlation is clarified from the association of the momentum dependences of lifetime and velocity with the momentum dependences of commensurate orbitals on a Fermi surface in magnetic fields., Comment: 5 pages, 4 figures

In quasi-one-dimensional conductors, the conductivity in both one-dimensional axis and interchain direction shows peaks when magnetic field is tilted at the magic angles in the plane perpendicular to the conducting chain. Although there are several theoretical studies to explain the magic angle effect, no satisfactory explanation, especially for the one-dimensional conductivity, has been obtained. We present a new theory of the magic angle effect in the one-dimensional conductivity by taking account of the momentum-dependence of the Fermi velocity, which should be large in the systems close to a spin density wave instability. The magic angle effect is explained in the semiclassical equations of motion, but neither the large corrugation of the Fermi surface due to long-range hoppings nor hot spots, where the relaxation time is small, on the Fermi surface are required., Comment: 4 pages, 3 figures

Dipole interaction in the triplet superconductivity is studied. If the Cooper pairs are formed by the electrons at $\mib{r}$ and $\mib{r}+(\pm\frac{a}{2},\pm\frac{a}{2},\pm\frac{c}{2})$ in the body centered tetragonal lattice, (in this case the line nodes run horizontally on the cylindrical Fermi surface), the dipole energy is low when the ${\mib{d}}$-vector is perpendicular to the direction of the angular momentum of the Cooper pairs ($\mib{l}$-vector). This result is in contrast with the dipole energies in the ABM state of superfluid $^3$He, where $\mib{d}$-vector is forced to be parallel or antiparallel to the $\mib{l}$-vector by the dipole interaction. The recent NQR experiment in Sr$_2$RuO$_4$ by Ishida et al. can be explained by this result., Comment: 4 pages

A possible mechanism for the horizontal line nodes in triplet superconductor, Sr$_2$RuO$_4$, is proposed. We consider the interlayer Coulomb interaction, as well as the on-site Coulomb repulsion, between electrons in different bands. In the second order perturbation in the interband interaction, the effective interaction becomes dependent on $\cos \frac{q_z}{2}$, resulting in the horizontal line nodes., Comment: 4 pages, 5 figures

We study the de Haas-van Alphen (dHvA) oscillation in two-dimensional and quasi-two-dimensional systems. We give a general formula of the dHvA oscillation in two-dimensional multi-band systems. By using this formula, the dHvA oscillation and its temperature-dependence for the two-band system are shown. By introducing the interlayer hopping $t_z$, we examine the crossover from the two-dimension, where the oscillation of the chemical potential plays an important role in the magnetization oscillation, to the three-dimension, where the oscillation of the chemical potential can be neglected as is well know as the Lifshitz and Kosevich formula. The crossover is seen at $4 t_z \sim 8 ta b H /\phi_0$, where a and b are lattice constants, $\phi_0$ is the flux quantum and 8t is the width of the total energy band. We also study the dHvA oscillation in quasi-two-dimensional magnetic breakdown systems. The quantum interference oscillations such as $\beta-\alpha$ oscillation as well as the fundamental oscillations are suppressed by the interlayer hopping $t_z$, while the $\beta+\alpha$ oscillation gradually increases as $t_z$ increases and it has a maximum at $t_z/t\approx 0.025$. This interesting dependence on the dimensionality can be observed in the quasi-two-dimensional organic conductors with uniaxial pressure., Comment: 11 pages, 14 figures

The effect of the four-spin cyclic exchange interaction at each plaquette in the $S=1/2$ two-leg spin ladder is investigated at T=0, especially focusing on the field-induced gap. The strong rung coupling approximation suggests that it yields a plateau at half of the saturation moment ($m=1/2$) in the magnetization curve, which corresponds to a field-induced spin gap with a spontaneous breaking of the translational symmetry. A precise phase diagram at $m=1/2$ is also presented based on the level spectroscopy analysis of the numerical data obtained by Lanczos method. The boundary between the gapless and plateau phases is confirmed to be of the Kosterlitz-Thouless (KT) universality class., Comment: 10 pages, 3 eps figures (embedded), to be published in J. Phys.: Cond. Matter

We comment on the study of the spin-damping factor on the de Haas-van Alphen (dHvA) discussed by Han et al. (Phys. Rev. Lett. 85, 1500 (2000))., Comment: 2 pages, 1 figures

The coexistent state of the spin density wave (SDW) and the charge density wave (CDW) in the one-dimensional quarter-filled system and with the Coulomb interaction up to the next-nearest sites under magnetic fields is studied. It is found that, in the coexistent state of $2k_{\rm F}$-SDW and $2k_{\rm F}$-CDW, the charge order is suppressed and $2k_{\rm F}$-SDW changes to $2k_{\rm F}$-SDW having the different alignment of spin under high magnetic fields, whereas, in the coexistent state of $2k_{\rm F}$-SDW and $4k_{\rm F}$-CDW, $4k_{\rm F}$-CDW still remains and $2k_{\rm F}$-SDW is suppressed. The critical temperature of the charge order is higher than that of the spin order when the inter-site Coulomb interaction is strong. These will be observed in experiments such as the X-ray scattering measurement and NMR., Comment: 9 pages, 20 figures

We theoretically study how the coexistent state of the charge density wave and the spin density wave in the one-dimensional quarter filled band is enhanced by magnetic fields. We found that when the correlation between electrons is strong the spin density wave state is suppressed under high magnetic fields, whereas the charge density wave state still remains. This will be observed in experiments such as the X-ray measurement., Comment: 7 pages, 15 figures

A reduction of the density of states near the Fermi energy in the normal state (pseudogap) of high-temperature oxide superconductors is examined on the basis of the two-dimensional tight-binding model with effective interactions due to antiferromagnetic fluctuations. By using antiferromagnetic correlation lengths which are phenomenologically assumed, the doping dependence of the pseudogap is obtained. The superconducting transition temperature decreases and eventually vanishes due to the pseudogap as the hole concentration is reduced., Comment: 4 pages (Latex with revtex.sty, epsf.sty), 4 figures. J. Phys. Soc. Jpn. Vol.69, No.6, in press

Several possible odd-parity states are listed up group-theoretically and examined in light of recent experiments on Sr$_2$RuO$_4$. Those include some of the $f$-wave pairing states, ${\mib d}({\mib k})\propto{\hat{\mib z}} k_xk_y(k_x + {\rm i}k_y)$ and ${\hat{\mib z}} (k_x^2-k_y^2)(k_x + {\rm i}k_y)$ and other ${\hat{\mib z}} (k_x + {\rm i}k_y)\cos ck_z$ ($c$ is the $c$-axis lattice constant) as most plausible candidates. These are time-reversal symmetry broken states and have line nodes running either vertically (the former two) or horizontally (the latter), consistent with experiments. Characterizations of these states and other possibilities are given., Comment: 4 pages, no figures

We study the effects of the Zeeman term on the de Haas van Alphen (dHvA) oscillation in two-dimensional two-band systems. We found that the Fourier transform amplitudes of the oscillations are not described by the spin reduction factor in the Lifshitz-Kosevich formalism in two-dimensional systems. The anomalous dependence on the effective $g$-factor can be observed by tilting-angle dependence of the dHvA oscillation in quasi-two-dimensional organic conductors and Sr$_2$RuO$_4$., Comment: 4 pages, 7 figures

We study the transition temperature Tc(H) of a quasi-one-dimensional (Q1D) superconductivity which is derived from the quantum effect of an electron motion in a strong magnetic field. We calculate Tc(H) of both isotropic and anisotropic superconductivity by taking account of the optimal momentum of the Cooper pairs and the effect of higher harmonic terms along second conducting axis in the tight-binding model. We find that, although Tc(H) of the spin-singlet superconductivity is suppressed strongly by the Zeeman effect, the suppression of Tc(H) is not very severe if we take the optimal pair-momentum and the higher harmonic terms into account. The obtained Tc(H) for the spin-singlet superconductivity is consistent with the experimental results in TMTSF salts., Comment: 4pages

The effects of the Zeeman term on the de Haas-van Alphen oscillation is studied in the magnetic breakdown system. We find that the amplitude of the oscillation with the frequencies of $f_{\beta} + f_{\alpha}$ and $f_{\beta} + 2f_{\alpha}$ are enhanced by the Zeeman term, while they are expected to be reduced in the semiclassical theory. A possible interpretation of the experiments in organic conductors is discussed., Comment: 4 pages,4 figures. Submitted to Journal of Physical Society of Japan

We have investigated the transition temperature $T_{\rm c}(H)$ of superconductiv ity in quasi-two-dimensional (Q2D) tight-binding electrons in a strong magnetic field. When the magnetic field is parallel to 2D conducting plane, $T_{\rm c}(H) $ of the Q2D superconductor is shown to increase in an oscillatory manner as the magnetic field becomes large and to reach $T_{\rm c}(0)$ in a strong magnetic f ield limit for the spin-triplet superconductor. We consider the cases of on-site and nearest sites attractive interaction, and calculate the magnetic field depe ndences of the transition temperature for various types of symmetry. The first o rder transition from $p_y$-wave to $p_x$-wave is shown to occur at $H\sim 35$T w hen the magnetic field is parallel to the $y$ direction, which will be observed in a triplet superconductor, Sr$_2$RuO$_4$., Comment: 13pages,6figures

The Josephson effect between triplet and singlet superconductors is studied. Josephson current can flow between triplet and singlet superconductors due to the spin-orbit coupling in the spin-triplet superconductor but it is finite only when triplet superconductor has $L_z=-S_z=\pm 1$, where $L_z$ and $S_z$ are the perpendicular components of orbital angular momentum and spin angular momentum of the triplet Cooper pairs, respectively. The recently observed temperature and orientational dependence of the critical current through a Josephson junction between UPt$_3$ and Nb is investigated by considering a non-unitary triplet state., Comment: 4 pages, no figures

The magnetization process of the $S$=1/2 antiferromagnetic spin ladder with the four-spin cyclic exchange interaction at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value if the ratio of the four- and two-spin exchange coupling constants $J_4$ is larger than the critical value $J_{4c}=0.05\pm$0.04. The phase transition with respect to $J_4$ at $J_{4c}$ is revealed to be the Kosterlitz-Thouless-type., Comment: 4 pages, Revtex, with 5 eps figures

The upper critical field $H_{c2}(T)$ of the tight-binding electrons in the three-dimensional lattice is investigated. The electrons make Cooper pairs between the eigenstates with the same energy in the strong magnetic field. The transition lines in the quasi-one dimensional case are shown to deviate from the previously obtained results where the hopping matrix elements along the magnetic field are neglected. In the absence of the Pauli pair breaking the transition temperature $T_c(H)$ of the quasi-two dimensional electrons is obtained to oscillationally increase as the magnetic field becomes large and reaches to $T_c(0)$ in the strong field as in the quasi-one dimensional case., Comment: 4pages,4figures,to be published in J.Phys.Soc.Jpn

We show that the density of states in an anisotropic superconductor with intersecting line nodes in the gap function is proportional to $E log (\alpha \Delta_0 /E)$ for $|E| << \Delta_0$, where $\Delta_0$ is the maximum value of the gap function and $\alpha$ is constant, while it is proportional to $E$ if the line nodes do not intersect. As a result, a logarithmic correction appears in the temperature dependence of the NMR relaxation rate and the specific heat, which can be observed experimentally. By comparing with those for the heavy fermion superconductors, we can obtain information about the symmetry of the gap function., Comment: 7 pages, 4 PostScript Figures, LaTeX, to appear in J. Phys. Soc. Jpn

We study theoretically the transition temperature of a quasi-one-dimensional anisotropic superconductor in a magnetic field, which is thought to be realized in organic conductors,(TMTSF)2X. In the weak field limit,-dH_c2/dT for the anisotropic singlet is shown to be \sqrt{3} times larger than that for the anisotropic triplet in the case of attractive interaction of electrons at nearest-sites along c axis and magnetic field along the b axis. In the strong field region the transition temperature for spin-triplet is restored to zero field critical temperature while the anisotropic spin-singlet is suppressed by the Zeeman effect., Comment: Latex,figures upon request,to be published in J.Phys.Soc.Jpn

The superconductivity of quasi-one-dimensional electrons in the magnetic field is studied. The system is described as the one-dimensional electrons with no frustration due to the magnetic field. The interaction is assumed to be attractive between electrons in the nearest chains, which corresponds to the lines of nodes of the energy gap in the absence of the magnetic field. The effective interaction depends on the magnetic field and the transverse momentum. As the magnetic field becomes strong, the transition temperature of the spin-triplet superconductivity oscillates, while that of the spin-singlet increases monotonically., Comment: 15 pages, RevTeX, 3 PostScript figures in uuencoded compressed tar file are appended

The quantum Hall effect in the three-dimensional anisotropic tight-binding electrons is investigated in the field-induced spin density wave phases with a magnetic field tilted to any direction. The Hall conductivity, $\sigma_{xy}$ and $\sigma_{xz}$, are shown to be quantized as a function of the wave vector of FISDW, while $\sigma_{yz}$ stays zero, where $x$ is the most conducting direction and $y$ and $z$ are perpendicular to $x$., Comment: 18 pages, REVTeX 3.0, 1 figure is available upon request, to be published in Physical Review B