Abstract:
Motivated by recent experimental study of antiferromagnetic property of honeycomb compound In$_{3}$Cu$_{2}$VO$_{9}$ [Yan \textit{et al.}, PRB \textbf{85}, 085102 (2012)], we explore possible superconductivity and its coexistence with antiferromagnetism. We use the t-t$^\prime$-J model on the honeycomb lattice as our starting point and employ the slave-boson mean-field theory. In the antiferromagnetic normal state, the characteristic doping evolution of Fermi surface shows that only one effective singe band is active, which suggests that the potential pairing symmetry is the time-reversal symmetry breaking $d+id$, rather than the extended $s$-wave. It is found that this superconducting state coexists with the antiferromagnetism in a broad doping regime, which is consistent with the numerical calculations. The local density of states and its thermodynamic property of the superconducting state has been studied in detail with an effective single-band picture for understanding other physical observable such as superfluid density. The present work may be useful in experimentally exploring possible superconductivity of this kind of materials on the honeycomb lattice and contributes to the understanding of the unconventional superconductivity on general two-dimensional correlated electron systems.

Abstract:
The coexistence of antiferromagnetism with superconductivity is studied theoretically within the t-J model with the Zeeman term included. The strong electron correlations are accounted for by means of the extended Gutzwiller projection method within a statistically-consistent approach proposed recently. The phase diagram on the band filling - magnetic field plane is shown, and subsequently the system properties are analyzed for the fixed band filling n=0.97. In this regime, the results reflect principal qualitative features observed recently in selected heavy fermion systems. Namely, (i) with the increasing magnetic field the system evolves from coexisting antiferromagnetic-superconducting phase, through antiferromagnetic phase, towards polarized paramagnetic state, and (ii) the onset of superconducting order suppresses partly the staggered moment. The superconducting gap has both the spin-singlet and the staggered-triplet components, a direct consequence of a coexistence of the superconducting state with antiferromagnetism.

Abstract:
We discuss the $t$-$J$-$U$ model in the mean-field approximation. The role of spin-exchange coupling $J$ and the second nearest hopping $t'$ are examined in the context of the coexistence of superconductivity (SC) and antiferromagnetism (AF). Stability of the phases is studied with respect to temperature. The coexistence region exists for the sufficiently large Coulomb repulsion ($U>U_{cr}$), and in the vicinity of the half-filled band (hole doping $\delta < \delta_{cr}$). The critical hole doping is relatively small ($\delta_{cr} \approx 0.006$ for $J/|t| = 1/3$) and linear with respect to $J$. The decrease of $U_{cr}$ is proportional to $J$, except the limit of small $J$ ($J/|t|< 0.03)$, where $U_{cr}$ grows rapidly with decreasing $J$. The effect of the second nearest hopping is limited -- the phase diagram does not change in a qualitative manner when the $t'$ value is changed. In the limit of $T \rightarrow 0$, SC phase is stable even for large hole-doping (such as $\delta = 0.5$). Additional paramagnetic (PM) phase appears for large $\delta$ or small $U$ at non-zero temperature. When temperature increases, both SC and AF+SC phase regions are reduced.

Abstract:
We discuss the coexistence of antiferromagnetism and d-wave superconductivity within the so-called statistically-consistent Gutzwiller approximation (SGA) applied to the t-J-U model. In this approach, the averages calculated in a self-consistent manner coincide with those determined variationally. Such consistency is not guaranteed within the standard renormalized mean field theory. With the help of SGA, we show that for the typical value J/|t| = 1/3, coexistence of antiferromagnetism (AF) and superconductivity (SC) appears only for U/|t| > 10.6 and in a very narrow range of doping (\delta < 0.006) in the vicinity of the Mott insulating state, in contrast to some previous reports. In the coexistent AF+SC phase, a staggered spin-triplet component of the superconducting gap appears also naturally; its value is very small.

Abstract:
We investigate coexistence of antiferromagnetic and superconducting correlations in bilayered materials using a two-dimensional t-J model with couplings across the layers using variational Monte Carlo calculations. It is found that the underdoped regime supports a coexisting phase, beyond which the (d-wave) superconducting state becomes stable. Further, the effects of interplanar coupling parameters on the magnetic and superconducting correlations as a function of hole doping are studied in details. The magnetic correlations are found to diminish with increasing interplanar hopping away from half filling, while the exchange across the layers strengthens interplanar antiferromagnetic correlations both at and away from half filling. The superconducting correlations show more interesting features where larger interplanar hopping considerably reduces planar correlations at optimal doping, while an opposite behaviour, i.e. stabilisation of the superconducting state is realised in the overdoped regime, with the interplanar exchange all the while playing a dormant role.

Abstract:
The authors discuss the possibility of coexistence of antiferromagnetism and triplet superconductivity as a particular example of a broad class of systems where the interplay of magnetism and superconductivity is important. This paper focuses on the case of quasi-one-dimensional metals, where it is known experimentally that antiferromagnetism is in close proximity to triplet superconductivity in the temperature versus pressure phase diagram. Over a narrow range of pressures, the authors propose an intermediate non-uniform phase consisting of alternating insulating antiferromagnetic and triplet superonducting stripes.

Abstract:
The possibility of coexistence of superconductivity (SC) and antiferromagnetic long range order (AFLRO) of the two-dimensional extended $t-J$ model in the very underdoped region is studied by the variational Monte-Carlo (VMC) method. In addition to using previously studied wave functions, a recently proposed new wave function generated from the half-filled Mott insulator is used. For hole-doped systems, the phase boundary between AFLRO and $d-$wave SC for the physical parameters, $J/t=0.3$, $t'/t=-0.3$ and $t''/t=0.2$, is located near hole density $\delta_c = 0.06$, and there is {\it no} coexistence. The phase transition is first-order between these two homogeneous phases at $\delta_c$.

Abstract:
We discuss t-J-U model on a honeycomb monolayer that has the same low-energy description of the kinetic term as graphene bilayer, and in particular study coexistence of antiferromagnetism and superconducting correlations that originate from Cooper pairs without phase coherence. We show that the model is relevant for the description of graphene bilayer and that the presence of the d + i d superconducting correlations with antiferromagnetism can lead to quadratic dependence in small magnetic fields of the gap of the effective monolayer consistent with the transport measurements of Velasco et al. on the graphene bilayer.

Abstract:
We report a coexistence of superconductivity and antiferromagnetism in five-layered compound HgBa$_2$Ca$_4$Cu$_5$O$_y$ (Hg-1245) with $T_c=108$ K, which is composed of two types of CuO$_2$ planes in a unit cell; three inner planes (IP's) and two outer planes (OP's). The Cu-NMR study has revealed that the optimallydoped OP undergoes a superconducting (SC) transition at $T_c=108$ K, whereas the three underdoped IP's do an antiferromagnetic (AF) transition below $T_N\sim$ 60 K with the Cu moments of $\sim (0.3-0.4)\mu_B$. Thus bulk superconductivity with a high value of $T_c=108$ K and a static AF ordering at $T_N=60$ K are realized in the alternating AF and SC layers. The AF-spin polarization at the IP is found to induce the Cu moments of $\sim0.02\mu_B$ at the SC OP, which is the AF proximity effect into the SC OP.

Abstract:
Superconductivity and magnetism have been interesting topics in condensed mater physics and they have been studied experimentally and theoretically for many years. These two cooperative phenomena are antagonistic until the discovery of some rare earth ternary compounds that show the coexistence of superconductivity and magnetism. In some of the recently discovered iron-based layered superconductors, superconductivity and magnetism coexist. In the present work we examine the possibility of coexistence of antiferromagnetism and superconductivity in samarium arsenide oxide superconductor (SmAsO1-xFxFe). Using a model of the Hamiltonian and retarded double time Greens function formalism, we found expressions AFM order Parameter (η) and AFM transition temperature (T_{m}). We obtained the phase diagrams (T_{c} vs η) and(T_{m} vs η) to obtain the region where orders, i.e., superconductivity and AFM (antiferromagnetism), coexisted. The region under the intersection of the two merged graphs shows that superconductivity and AFM coexist in the system (SmAsO1-xFxFe).