Abstract:
We compute the electrical and thermal conductivities and Hall conductivities of the $d$-density wave (DDW) state in the low-temperature impurity-scattering-dominated regime for low-dopings, at which they are dominated by nodal quasiparticles. We show that the longitudinal conductivity in this limit in the DDW state is not Drude-like. However, the thermal conductivty is Drude-like; this is a reflection of the discrepancy between electrical and thermal transport at finite frequency in the DDW state. An extreme example of this occurs in the $\mu=0$, $\tau\to\infty$ limit, where there is a strong violation of the Wiedemann-Franz law: ${\kappa_{xx}}/{\sigma_{xx}} \propto {T^2}$ at $\omega=0$ and ${\kappa_{xx}}/{\sigma_{xx}}=0$ at finite frequency. The DDW electrical and thermal Hall conductivities are linear in the magnetic field, $B$, for weak fields. The formation of Landau levels at the nodes leads to the quantization of these Hall conductivities at high fields. In all of these ways, the quasiparticles of the DDW state differ from those of the $d_{{x^2}-{y^2}}$ superconducting (DSC) state.

Abstract:
We study the Josephson junction between two d-wave superconductors, which is discussed as an implementation of a qubit. We propose an approach that allows to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor.

Abstract:
We analyze how the magnetic disorder affects the properties of the two-band $s_\pm$ and $s_{++}$ models, which are subject of hot discussions regarding iron-based superconductors and other multiband systems like MgB$_2$. We show that there are several cases when the transition temperature $T_c$ is not fully suppressed by magnetic impurities in contrast to the Abrikosov-Gor'kov theory, but a saturation of $T_c$ takes place in the regime of strong disorder. These cases are: (1) the purely interband impurity scattering, (2) the unitary scattering limit. We show that in the former case the $s_\pm$ gap is preserved, while the $s_{++}$ state transforms into the $s_\pm$ state with increasing magnetic disorder. For the case (2), the gap structure remains intact.

Abstract:
While the pronounced doping dependence of the quasiparticle spectral weight in the antinodal region of the superconducting cuprates, as seen by ARPES, unambiguously points to the magnetic origin of the strong electron-boson coupling there, the nature of the electron scattering in the nodal direction remained unclear. Here we present a short review of our recent detailed investigations of the nodal direction of Bi-2212. Our findings prove the existence of well defined quasiparticles even in the pseudogap state and show that the essential part of the quasiparticle scattering rate, which appears on top of Auger-like electron-electron interaction, also implies a magnetic origin.

Abstract:
We show that the nodal quasiparticles have significant effect on the classical phase fluctuations in a quasi-two-dimensional d-wave superconductor. They give rise to singularities in the temperature behavior of some of the coupling constants in the phase-only effective action. One of the consequences is that the classical XY-model is not adequate for the description of the superconducting fluctuations in d-wave superconductors at low temperatures.

Abstract:
We present a theory for the onset of spin density wave order in the superconducting ground state of the cuprates. We compute the scaling dimensions of allowed perturbations of a `relativistic' fixed point with O(4)xO(3) symmetry, including those associated with the fermionic nodal Bogoliubov quasiparticles. Analyses of up to six loops show that all perturbations with square lattice symmetry are likely irrelevant. We demonstrate that the fermion spectral functions are primarily damped by the coupling to fluctuations of a composite field with Ising nematic order. We also discuss the influence of quenched disorder.

Abstract:
Gapless nodal quasiparticles emerge at a low-energy regime of high-$T_c$ cuprate superconductors due to the $d_{x^2 - y^2}$ gap symmetry. We study the unusual renormalizations of the Fermi velocity $v_F$ and gap velocity $v_{\Delta}$ of these quasiparticles close to various quantum critical points in a superconducting dome. Special attention is paid to the behavior of the velocity ratio, $v_{\Delta}/v_F$, since it determines a number of observable quantities. We perform a renormalization-group analysis and show that the velocity ratio may vanish, approach unity, or diverge at different quantum critical points. The corresponding superfluid densities and critical temperatures are suppressed, slightly increased, or significantly enhanced. The effects of three types of static disorders, namely, random mass, random gauge potential, and random chemical potential, on the stability of the system are also addressed. An analogous analysis reveals that both random mass and random gauge potential are irrelevant. This implies that these fixed points of the velocity ratio are stable, and hence observable effects ignited by them are unchanged. However, the random chemical potential is marginal. As a result, these fixed points are broken, and thus, the instabilities of quantum phase transitions are triggered.

Abstract:
High resolution angle-resolved photoemission measurements on underdoped (La$_{2-x}$Sr$_x$)CuO$_4$ system show that, at energies below 70 meV, the quasiparticle peak is well defined around the ($\pi$/2,$\pi$/2) nodal region and disappears rather abruptly when the momentum is changed from the nodal point to the ($\pi$,0) antinodal point along the underlying ``Fermi surface''. It indicates that there is an extra low energy scattering mechanism acting upon the antinodal quasiparticles. We propose that this mechanism is the scattering of quasiparticles across the nearly parallel segments of the Fermi surface near the antinodes.

Abstract:
We use time- and angle-resolved photoemission to measure the nodal non-equilibrium electronic states in various dopings of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We find that the initial pump-induced transient signal of these ungapped states is strongly affected by the onset of the superconducting gap at $T_c$, superconducting pairing fluctuations at $T_p$, and the pseudogap at $T^*$. Moreover, $T_p$ marks a suggestive threshold in the fluence-dependent transient signal, with the appearance of a critical fluence below $T_p$ that corresponds to the energy required to break apart all Cooper pairs. These results challenge the notion of a nodal-antinodal dichotomy in cuprate superconductors by establishing a new link between nodal quasiparticles and the cuprate phase diagram.

Abstract:
We explore a BCS Bose Einstein crossover scenario for $0 \leq T \leq T_c$ and its implications for the superfluid density and specific heat. The low lying excitations consist of nodal (fermionic) quasi-particles as well as excited (bosonic) pair states. Semi-quantitative comparison with cuprate data is reasonable, with no compelling indications for Landau parameter effects.