A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T_cdw. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe₂ intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at T_cdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states.

We study the superconducting state of the two-dimensional electron gas (2DEG) at the ${\mathrm{LaAlO}}_3$/${\mathrm{SrTiO}}_3$ interface using Josephson junctions as spectroscopic probes. The transport properties of these devices reveal the presence of two superconducting gap structures and of an unconventional superconducting $\pi$ channel. These features provide evidence of an unconventional superconducting ground state, possibly related to the interplay between superconductivity and the large Rashba spin-orbit coupling in the 2DEG.

We report a pronounced peak effect in the magnetization of ${\text{Co}}_x{\text{NbSe}}_2$ single crystals with critical temperatures $T_c$ ranging between 7.1 and 5.0 K, and ${\text{Mn}}_x{\text{NbSe}}_2$ single crystals with critical temperatures down to 3.4 K. We correlate the peak effect in magnetization with the structure of the vortex lattice across the peak-effect region using scanning-tunneling microscopy. Magnetization measurements show that the amplitude of the peak effect in the case of ${\text{Co}}_x{\text{NbSe}}_2$ exhibits a nonmonotonic behavior as a function of the Co content, reaching a maximum for concentration of Co of about $0.4\text{at}\text{.}\%$ (corresponding to a $T_c$ of 5.7 K) and after that gradually decreasing in amplitude with the increase in the Co content. The normalized value of the peak position $H_p/H_{c2}$ has weak dependence on Co concentration. In the case of ${\text{Mn}}_x{\text{NbSe}}_2$ the features of the peak effect as a function of the Mn content are different and they can be understood in terms of strong pinning.

We present scanning tunneling microscopy and spectroscopy measurements of the charge-density wave state in $1T$-TiSe${}_2$, Cu${}_{0.05}$TiSe${}_2$, and Cu${}_{0.06}$TiSe${}_2$ single crystals. Topography images at $4.2$ K reveal that the charge density waves are present in all samples studied, although the amplitude of the charge modulation decreases with the Cu doping. Moreover, the chiral phase of the charge density wave is preserved also in Cu-doped samples. Tunneling spectroscopy shows that there is only a partial gap in the pure compound, with bands crossing the Fermi surface. In the Cu-doped samples, the system becomes more metallic due to the increase of the chemical potential.