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The specific heat $C$ of the single-layer cuprate superconductor HgBa$_2$CuO$_{4 + delta}$ was measured in an underdoped crystal with $T_{rm c} = 72$ K at temperatures down to $2$ K in magnetic fields up to $35$ T, a field large enough to suppress superconductivity at that doping ($p simeq 0.09$). In the normal state at $H = 35$ T, a residual linear term of magnitude $gamma = 12 pm 2$ mJ/K$^2$mol is observed in $C/T$ as $T to 0$, a direct measure of the electronic density of states. This high value of $gamma$ has two major implications. First, it is significantly larger than the value measured in overdoped cuprates outside the pseudogap phase ($p >p^star$), such as La$_{2-x}$Sr$_x$CuO$_4$ and Tl$_2$Ba$_2$CuO$_{6 + delta}$ at $p simeq 0.3$, where $gamma simeq 7$ mJ/K$^2$mol. Given that the pseudogap causes a loss of density of states, and assuming that HgBa$_2$CuO$_{4 + delta}$ has the same $gamma$ value as other cuprates at $p simeq 0.3$, this implies that $gamma$ in HgBa$_2$CuO$_{4 + delta}$ must peak between $p simeq 0.09$ and $p simeq 0.3$, namely at (or near) the critical doping $p^star$ where the pseudogap phase is expected to end ($p^starsimeq 0.2$). Secondly, the high $gamma$ value implies that the Fermi surface must consist of more than the single electron-like pocket detected by quantum oscillations in HgBa$_2$CuO$_{4 + delta}$ at $p simeq 0.09$, whose effective mass $m^star= 2.7times m_0$ yields only $gamma = 4.0$ mJ/K$^2$mol. This missing mass imposes a revision of the current scenario for how pseudogap and charge order respectively transform and reconstruct the Fermi surface of cuprates.
The pseudogap phenomenon in cuprates is the most mysterious puzzle in the research of high-temperature superconductivity. In particular, whether the pseudogap is associated with a crossover or phase transition has been a long-standing controversial i
Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of co
High magnetic fields have revealed a surprisingly small Fermi-surface in underdoped cuprates, possibly resulting from Fermi-surface reconstruction due to an order parameter that breaks translational symmetry of the crystal lattice. A crucial issue co
We present an inelastic neutron scattering study of the structurally simple single-layer compound HgBa$_2$CuO$_{4+delta}$ close to optimal doping ($T_c approx 96$ K). A well-defined antiferromagnetic resonance with energy $omega_r = 56$ meV ($approx
Phonons in nearly optimally doped HgBa$_2$CuO$_{4+delta}$ were studied by inelastic X-ray scattering. The dispersion of the low energy modes is well described by a shell model, while the Cu-O bond stretching mode at high energy shows strong softening