Abstract:
Within the t-J model, we study the charge transport in underdoped bilayer cuprates by considering the bilayer interaction. Although the bilayer interaction leads to the band splitting in the electronic structure, the qualitative behavior of the charge transport is the same as in the case of single layer cuprates. The conductivity spectrum shows a low-energy peak and the unusual midinfrared band. This midinfrared band is suppressed severely with increasing temperatures, while the resistivity in the heavily underdoped regime is characterized by a crossover from the high temperature metallic-like to the low temperature insulating-like behaviors, which are consistent with the experiments.

Abstract:
The mystery of the normal state in the underdoped cuprates has deepened with the use of newer and complementary experimental probes. While photoemission studies have revealed solely `Fermi arcs' centered on nodal points in the Brillouin zone at which holes aggregate upon doping, more recent quantum oscillation experiments have been interpreted in terms of an ambipolar Fermi surface, that includes sections containing electron carriers located at the antinodal region. To address the question of whether an ambipolar Fermi surface truly exists, here we utilize measurements of the second harmonic quantum oscillations, which reveal that the amplitude of these oscillations arises mainly from oscillations in the chemical potential, providing crucial information on the nature of the Fermi surface in underdoped YBa2Cu3O6+x. In particular, the detailed relationship between the second harmonic amplitude and the fundamental amplitude of the quantum oscillations leads us to the conclusion that there exists only a single underlying quasi-two dimensional Fermi surface pocket giving rise to the multiple frequency components observed via the effects of warping, bilayer splitting and magnetic breakdown. A range of studies suggest that the pocket is most likely associated with states near the nodal region of the Brillouin zone of underdoped YBa2Cu3O6+x at high magnetic fields.

Abstract:
The recently discovered coexistence of incommensurate antiferromagnetic neutron scattering peaks and commensurate resonance in underdoped YBa$_2$Cu$_3$O$_{6+x}$ is calling for an explanation. Within the t-J model, the doping and energy dependence of the spin dynamics of the underdoped bilayer cuprates in the normal state is studied based on the fermion-spin theory by considering the bilayer interactions. Incommensurate peaks are found at $[(1\pm\delta)\pi,\pi] $ and $[\pi,(1\pm\delta)\pi]$ at low energies with $\delta$ initially increasing with doping at low dopings and then saturating at higher dopings. These incommensurate peaks are suppressed, and the parameter $\delta$ is reduced with increasing energy. Eventually it converges to the $[\pi,\pi]$ resonance peak. Thus the recently observed coexistence is interpreted in terms of bilayer interactions.

Abstract:
We report quantum oscillations in underdoped YBa2Cu3O6.56 over a significantly large range in magnetic field extending from 24 to 101 T, enabling three well-spaced low frequencies at 440 T, 532 T, and 620 T to be clearly resolved. We show that a small nodal bilayer coupling that splits a nodal pocket into bonding and antibonding orbits yields a sequence of frequencies, F0 - {\Delta}F, F0, and F0 + {\Delta}F and accompanying beat pattern similar to that observed experimentally, on invoking magnetic breakdown tunneling at the nodes. The relative amplitudes of the multiple frequencies observed experimentally in quantum oscillation measurements are shown to be reproduced using a value of nodal bilayer gap quantitatively consistent with that measured in photoemission experiments in the underdoped regime.

Abstract:
We present results on heavily underdoped Y_1-xCa_xBa_2Cu_3O_6+y which provide the evidence that the doping mechanism (cation substitution or oxygen loading) directly determines whether the corresponding injected mobile holes contribute to superconductivity or only to the normal metallic properties. We argue that this hole tagging calls for a subtler description of the correlated bands than the usual one. We also map in great detail the underdoped superconducting phase diagram T_c vs. hole doping which shows that the number of mobile holes is not the critical parameter for the superconductivity.

Abstract:
We report on a study of the influence of defects introduced in the CuO$_{2}$ planes of cuprates in a wide range of hole dopings n. T$_{c}$ and electrical resistivity $\rho (T)$ measurements have been performed on electron irradiated YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ and Tl$_{2}$Ba$_{2}$CuO$_{6+x}$ single crystals. A universal scaling between the decrease in T$_{c}$ and $\UNICODE[m]{0x394}\rho_{2D}\UNICODE[m]{0xd7}n$, where $\UNICODE[m]{0x394}\rho _{2D}$ is the increase of the 2D-resistance induced by the defects, is found for all the samples investigated here. This demonstrates that n is the relevant parameter to describe the transport properties all over the phase diagram, in contradiction with a recent suggestion of a change in the number of carriers from n to 1-n at the optimal doping. Moreover, the analysis of our data suggests that strong scattering persists on the overdoped side.

Abstract:
The phenomenological Green's function developed in the works of Yang, Rice and Zhang has been very successful in understanding many of the anomalous superconducting properties of the deeply underdoped cuprates. It is based on considerations of the resonating valence bond spin liquid approximation and is designed to describe the underdoped regime of the cuprates. Here we emphasize the region of doping, $x$, just below the quantum critical point at which the pseudogap develops. In addition to Luttinger hole pockets centered around the nodal direction, there are electron pockets near the antinodes which are connected to the hole pockets by gapped bridging contours. We determine the contours of nearest approach as would be measured in angular resolved photoemission experiments and emphasize signatures of the Fermi surface reconstruction from the large Fermi contour of Fermi liquid theory (which contains $1+x$ hole states) to the Luttinger pocket (which contains $x$ hole states). We find that the quasiparticle effective mass renormalization increases strongly towards the edge of the Luttinger pockets beyond which it diverges.

Abstract:
We survey recent experimental results including quantum oscillations and complementary measurements probing the electronic structure of underdoped cuprates, and theoretical proposals to explain them. We discuss quantum oscillations measured at high magnetic fields in the underdoped cuprates that reveal a small Fermi surface section comprising quasiparticles that obey Fermi-Dirac statistics, unaccompanied by other states of comparable thermodynamic mass at the Fermi level. The location of the observed Fermi surface section at the nodes is indicated by a body of evidence including the collapse in Fermi velocity measured by quantum oscillations, which is found to be associated with the nodal density of states observed in angular resolved photoemission, the persistence of quantum oscillations down to low fields in the vortex state, the small value of density of states from heat capacity and the multiple frequency quantum oscillation pattern consistent with nodal magnetic breakdown of bilayer-split pockets. A nodal Fermi surface pocket is further consistent with the observation of a density of states at the Fermi level concentrated at the nodes in photoemission experiments, and the antinodal pseudogap observed by photoemission, optical conductivity, nuclear magnetic resonance Knight shift, as well as other complementary diffraction, transport and thermodynamic measurements. One of the possibilities considered is that the small Fermi surface pockets observed at high magnetic fields can be understood in terms of Fermi surface reconstruction by a form of small wavevector charge order, observed over long lengthscales in experiments such as nuclear magnetic resonance and x-ray scattering, potentially accompanied by an additional mechanism to gap the antinodal density of states.

Abstract:
In order to investigate the electronic state of Ce-free and Ce-underdoped high-Tc cuprates with the so-called T' structure, we have performed muon-spin-relaxation (muSR) and specific-heat measurements of Ce-free T'-La_1.8_Eu_0.2_CuO_4+d_ (T'-LECO) polycrystals and Ce-underdoped T'-Pr_1.3-x_La_0.7_Ce_x_CuO_4+d_ (T'-PLCCO) single crystals with x=0.10. The muSR spectra of the reduced superconducting samples of both T'-LECO with Tc=15K and T'-PLCCO with x=0.10 and Tc=27K have revealed that a short-range magnetic order coexists with the superconductivity in the ground state. The formation of a short-range magnetic order due to a tiny amount of excess oxygen in the reduced superconducting samples strongly suggest that the Ce-free and Ce-underdoped T'-cuprates are regarded as strongly correlated electron systems.

Abstract:
We outline the basic ideas involved in a recently proposed derivation of a gauge theory for underdoped cuprates in the "spin-gap phase", performed essentially step by step starting from the t-J model, considered as a model Hamiltonian for the CuO_2 layers. The basic tool is the U(1)XSU(2) Chern-Simons bosonization, to which it is dedicated a somewhat detailed discussion. The basic output is a "spin-gap" not vanishing in any direction and an antiferromagnetic correlation length proportional to the inverse square root of doping concentration, in agreement with data deduced from the neutron experiments. The model also exhibits a small half-pocket Fermi surface around (\pi/2, \pi/2) and a linear in temperature dependence of in-plane resistivity in certain temperature range.