Study Of Competing Charge Spin And Superconducting Orders In Underdoped High-temperature Superconductors.

Superconductivity often emerges in the proximity of, or in competition with,rnsymmetry-breaking ground states such as antiferromagnetism or charge den-rnsity waves(CDW). A number of materials in the cuprate family, which includesrnthe high transition-temperature(high-Tc) superconductors, show spin and chargerndensity wave order. Thus a fundamental question is to what extent do these or-rndered states exist for compositions close to optimal for superconductivity. Recentrnobservations of CDWorder in Y Ba2Cu3Oy and other cuprate families have raisedrninteresting questions regarding the general role of charge modulations and thernrelation to superconductivity. It was studied that in the system La2À€€xBaxCuO4rnSDW and CDW orders appear to be intertwined with a spatially-modulatedrnsuperconductivity. Here by developing a model Hamiltonian and by using quan-rntum _eld theory Green's function formalism, we obtain mathematical expres-rnsions for superconductivity order parameter(_), and charge density wave orderrnparameter(W) in under-doped Y Ba2Cu3Oy. We plot the phase diagram of su-rnperconducting order parameter (_) against temperature(T) for di_erent valuesrnof charge density wave orders(W) in under-doped Y Ba2Cu3Oy. The relation-rnship between superconductivity(_), charge density wave(W), and spin densityrnwave(M) orders and their critical temperatures is studied theoretically for thernunder-doped La2ð€€€xBaxCuO4 superconductor and plot the phase diagrams of su-rnperconducting order parameter(_) against temperature(T) for di_erent values ofrncharge density wave(W) and spin density wave(M) orders. Finally, we examinernthe physics of combined mechanisms for cuprates and pnictides.

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