Abstract:
Superconductivity emerges from the cuprate antiferromagnetic Mott state with hole doping. The resulting electronic structure is not understood, although changes in the state of oxygen atoms appear paramount. Hole doping first destroys the Mott state yielding a weak insulator where electrons localize only at low temperatures without a full energy gap. At higher doping, the 'pseudogap', a weakly conducting state with an anisotropic energy gap and intra-unit-cell breaking of 90\degree-rotational (C4v) symmetry appears. However, a direct visualization of the emergence of these phenomena with increasing hole density has never been achieved. Here we report atomic-scale imaging of electronic structure evolution from the weak-insulator through the emergence of the pseudogap to the superconducting state in Ca2-xNaxCuO2Cl2. The spectral signature of the pseudogap emerges at lowest doping from a weakly insulating but C4v-symmetric matrix exhibiting a distinct spectral shape. At slightly higher hole-density, nanoscale regions exhibiting pseudogap spectra and 180\degree-rotational (C2v) symmetry form unidirectional clusters within the C4v-symmetric matrix. Thus, hole-doping proceeds by the appearance of nanoscale clusters of localized holes within which the broken-symmetry pseudogap state is stabilized. A fundamentally two-component electronic structure11 then exists in Ca2-xNaxCuO2Cl2 until the C2v-symmetric clusters touch at higher doping, and the long-range superconductivity appears.

Abstract:
We show that lightly doped holes will be self-trapped in an antiferromagnetic spin background at low-temperatures, resulting in a spontaneous translational symmetry breaking. The underlying Mott physics is responsible for such novel self-localization of charge carriers. Interesting transport and dielectric properties are found as the consequences, including large doping-dependent thermopower and dielectric constant, low-temperature variable-range-hopping resistivity, as well as high-temperature strange-metal-like resistivity, which are consistent with experimental measurements in the high-T$_c$ cuprates. Disorder and impurities only play a minor and assistant role here.

Abstract:
Lightly-doped La$_{2-x}$Sr$_x$CuO$_4$ in the so-called "insulating" spin-glass/diagonal-stripe phase has been studied by angle-resolved photoemission spectroscopy. A quasi-particle (QP) peak crossing the Fermi level has been observed in the node direction of the d-wave superconducting gap, forming an "arc" of Fermi surface consistent with the recently observed metallic transport behavior at high temperatures of lightly-doped materials. The spectral weight of the nodal QP smoothly increases with hole doping, corresponding to the $n \sim x$ behavior of the carrier number in the underdoped and lightly-doped regions.

Abstract:
We have investigated the excitation spectra of $j_{eff}$=$\frac{1}{2}$ Mott insulator Na$_2$IrO$_3$. Taking into account a relativistic multiplet structure of Ir ions, we have calculated the optical conductivity $\sigma(\omega)$ and resonant inelastic x-ray scattering (RIXS) spectra, which manifest different features from those of a canonical $j_{eff}$=$\frac{1}{2}$ system Sr$_2$IrO$_4$.Distinctly from the two-peak structure in Sr$_2$IrO$_4$, $\sigma(\omega)$ in Na$_2$IrO$_3$ has a broad single peak dominated by interband transitions from $j_{eff}$=$\frac{3}{2}$ to $\frac{1}{2}$. RIXS spectra exhibit the spin-orbit (SO) exciton that has a two-peak structure arising from the crystal-field effect, and the magnon peak at energies much lower than in Sr$_2$IrO$_4$. In addition, a small peak near the optical absorption edge is found in RIXS spectra, originating from the coupling between the electron-hole ($e$-$h$) excitation and the SO exciton. Our findings corroborate the validity of the relativistic electronic structure and importance of both itinerant and local features in Na$_2$IrO$_3$.

Abstract:
We have investigated temperature-dependent electronic structures of Na2IrO3 to unravel its insulating nature. Employing the combined scheme of the density-functional theory (DFT) and the dynamical mean-field theory (DMFT), we have shown that the insulating state persists even above the Neel temperature (T_{N}), which reveals that Na2IrO3 is classified into a Mott-type insulator. The measured photoemission spectrum in the paramagnetic (PM) state is well described by the electronic structure obtained from the DFT+DMFT for the insulating state above T_{N}. The analysis of optical conductivity, however, suggests that the non-local correlation effect is also important in Na2IrO3. Therefore, Na2IrO3 is not to be a standard Mott insulator in that the extended nature and the non-local correlation effect of Ir 5d electrons are important as well in describing its electronic and magnetic properties.

Abstract:
We show how a lightly doped Mott insulator has hugely enhanced electronic thermal transport at low temperature. It displays universal behavior independent of the interaction strength when the carriers can be treated as nondegenerate fermions and a nonuniversal "crossover" region where the Lorenz number grows to large values, while still maintaining a large thermoelectric figure-of-merit. The electron dynamics are described by the Falicov-Kimball model which is solved for arbitrary large on-site correlation with a dynamical mean-field theory algorithm on a Bethe lattice. We show how these results are generic for lightly doped Mott insulators as long as the renormalized Fermi liquid scale is pushed to very low temperature and the system is not magnetically ordered.

Abstract:
We present an anti-ferromagnetically ordered ground state of Na$_{2}$IrO$_{3}$ based on density-functional-theory calculations including both spin-orbit coupling and on-site Coulomb interaction $U$. We show that the splitting of $e_{g}'$ doublet states by the strong spin-orbit coupling is mainly responsible for the intriguing nature of its insulating gap and magnetic ground state. Due to its proximity to the spin-orbit insulator phase, the magnetic ordering as obtained with finite $U$ is found to exhibit a strong in-plane anisotropy. The phase diagram of Na$_{2}$IrO$_{3}$ suggests a possible interplay between spin-orbit insulator and Mott anti-ferromagnetic insulator phases.

Abstract:
We define a suitable quantity $Z_c$ that measures the pairing strength of two electrons added to the ground state wave function by means of the anomalous part of the one-particle Green's function. $Z_c$ discriminates between systems described by one-electron states, like ordinary metals and band insulators, for which $Z_c=0$, and systems where the single particle picture does not hold, like superconductors and resonating valence bond insulators, for which $Z_c \ne 0$. By using a numerically exact projection technique for the Hubbard model at $U/t=4$, a finite value of $Z_c$, with d-wave symmetrry, is found at half filling and in the lightly doped regime, thus emphasizing a qualitatively new feature coming from electronic correlation.

Abstract:
The physics of doped Mott insulators remains controversial after decades of active research, hindered by the interplay among possible competing orders and fluctuations. It is thus highly desired to distinguish the intrinsic characters of the Mott-metal crossover from those of other origins. We investigate the evolution of electronic structure and dynamics of the hole-doped J=1/2 Mott insulator Sr2IrO4. The effective hole doping is achieved by replacing Ir with Rh atoms, with the chemical potential immediately jumping to or near the top of the lower Hubbard band. The doped iridates exhibit multiple exotic features previously observed in doped cuprates - pseudogaps, Fermi "arcs", and marginal-Fermi-liquid-like electronic scattering rates, despite different mechanisms that forbid electron double-occupancy. We argue these universal features of the Mott-metal crossover are not related to preformed electron pairing, quantum criticality or density-wave formation as most commonly discussed. Instead, short-range antiferromagnetic correlations may play an indispensible role.

Abstract:
We have synthesized single crystals of Na_2IrO_3 and studied their structure, transport, magnetic, and thermal properties using powder x-ray diffraction (PXRD), electrical resistivity, isothermal magnetization M versus magnetic field H, magnetic susceptibility \chi versus temperature T, and heat capacity C versus T measurements. Na_2IrO_3 crystallizes in the monoclinic \emph{C2/c} (No. 15) type structure which is made up of Na and NaIr_2O_6 layers alternately stacked along the c axis. The \chi(T) data show Curie-Weiss behavior at high T > 200K with an effective moment \mu_eff = 1.82(1) \mu_B indicating an effective spin S_eff = 1/2 on the Ir^4+ moments. A large Weiss temperature \theta = - 116(3)K indicates substantial antiferromagnetic interactions between these S_eff = 1/2, Ir^4+ moments. Sharp anomalies in \chi(T) and C(T) data indicate that Na_2IrO_3 undergoes a transition into a long-range antiferromagnetically ordered state below T_N = 15 K. The magnetic entropy at T_N is only about 20% of what is expected for S_eff = 1/2 moment ordering. The reduced entropy and the small ratio T_N/\theta \approx 0.13 suggest geometrical magnetic frustration and/or low-dimensional magnetic interactions in Na_2IrO_3. In plane resistivity measurements show insulating behavior. This together with the local moment magnetism indicates that bulk Na_2IrO_3 is a Mott insulator.