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Superconductors are a striking example of a quantum phenomenon in which electrons move coherently over macroscopic distances without scattering. The high-temperature superconducting oxides(cuprates) are the most studied class of…

We present a theoretical framework for understanding recent transverse field muon spin rotation (TF-$\mu$SR) experiments on cuprate superconductors in terms of localized regions of phase-coherent pairing correlations above the bulk…

The stripe phase in high Tc cuprates is modeled as a single stripe coupled to the RVB spin liquid background by the single particle hopping process. In normal state, the strong pairing correlation inherent in RVB state is thus transfered…

Nonlinear optical excitation of infrared active lattice vibrations has been shown to melt magnetic or orbital orders and to transform insulators into metals. In cuprates, this technique has been used to remove charge stripes and promote…

Charge-order stripes of different types occur when copper oxides are doped with either heterovalent metal, like $La_{2-x}Sr_xCuO_4$, or oxygen, like $YBa_2Cu_3O_{6+y}$. The difference shows up in the doping dependence of their…

We study analytically the effect of charge-neutrality breaking on the spectrum of localized Josephson plasma waves (JPWs) in a plate of layered superconductor of finite thickness for the case of layers parallel to the interface. This effect…

A profound problem in modern condensed matter physics is discovering and understanding the nature of the fluctuations and their coupling to fermions in cuprates which lead to high temperature superconductivity and the invariably associated…

The cuprate superconductor La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) near $x=0.125$ is a striking example of intertwined electronic orders, where 3D superconductivity is anomalously suppressed, allowing spin and charge stripe order to develop, in a…

We demonstrate that the recent observations of spatial oscillations in the energy position of the superconducting coherence peaks in the cuprate, transition metal dichalcogenide, iron-based and heavy-fermion superconductors are consistent…

One of the first finding concerning the superconducting (SC) density $n_{\rm sc}$ in cuprates was their small magnitudes that revealed the importance of phase fluctuations. More recently, measurements in a variety of overdoped cuprates…

We use uniaxial strain in combination with ultra-high-resolution Resonant Inelastic X-ray Scattering (RIXS) at the oxygen K- and copper L3-edges to study the excitations stemming from the charge ordering wave vector in La1.875Sr0.125CuO4.…

Monte Carlo simulations applied to the Spin-Fermion model for cuprates show the existence of antiferromagnetic spin domains and charge stripes upon doping. The stripes are partially filled, with a filling of approximately 1/2 hole per site,…

In this lectures, we have described some essential features of loss of coherence by a qubit coupled to the environment. We have first presented well known semiclassical arguments that relate both decoherence and relaxation to the…

A phase separation model is presented for the stripe phase of the cuprates, which allows the doping dependence of the photoemission spectra to be calculated. The idealized limit of a well-ordered array of magnetic and charged stripes is…

We present results from light scattering experiments on three insulating antiferromagnetic cuprates, YBa$_2$Cu$_3$O$_{6.05}$, Bi$_2$Sr$_2$YCu$_2$O$_{8+\delta}$, and La$_2$CuO$_4$ as a function of polarization and excitation energy {using…

Quantum materials are amenable to non-equilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors…

We report on 139La and 63Ccu NMR/NQR measurements in the high-Tc superconductor La1.90Sr0.10CuO4 with Tc=26.5 K. Spin fluctuations probed by 139La spin-lattice relaxation (T1), continuously slow down on cooling through Tc. We argue that…

An introduction is given to collective modes in layered, high Tc superconductors. An experimental demonstration is treated of the mechanism proposed by Anderson whereby photons travelling inside the superconductor become massive, when the…

The role of antiferromagnetic spin correlations in high-temperature superconductors remains a matter of debate. We present inelastic neutron scattering evidence that gapless spin fluctuations coexist with superconductivity in…

Suggestive, but indirect evidence of the existence of pair-density wave (PDW) order in several high-$T_{\rm c}$ cuprates has been reported. As this constitutes a new quantum phase of matter, it is important to {\it establish} its existence…