High density of states in the pseudogap phase of the cuprate superconductor HgBa${}_2$CuO${}_{4+\delta }$

Abstract

The specific heat $C$ of the single-layer cuprate superconductor HgBa${}_2$CuO${}_{4+\delta }$ was measured in an underdoped crystal with $T_{\mathrm{c}}=72$ 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 ($p^{\star }\simeq 0.2$). 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 $m^{\star }=2.7\times m_0$ 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.

8 pages, 5 figures

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