High density of states in the pseudogap phase of the cuprate superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>HgBa</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>CuO</mml:mi><mml:mrow><mml:mn>4</mml:mn><mml:mo>+</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> from low-temperature normal-state specific heat

The specific heat $C$ of the single-layer cuprate superconductor ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ 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 ($p\ensuremath{\simeq}0.09$). In the normal state at $H=35$ T, a residual linear term of magnitude $\ensuremath{\gamma}=12\ifmmode\pm\else\textpm\fi{}2$ mJ/${\mathrm{K}}^{2}\phantom{\rule{0.16em}{0ex}}\mathrm{mol}$ is observed in $C/T$ as $T\ensuremath{\rightarrow}0$, a direct measure of the electronic density of states. This high value of $\ensuremath{\gamma}$ has two major implications. First, it is significantly larger than the value measured in overdoped cuprates outside the pseudogap phase ($p>\phantom{\rule{4pt}{0ex}}{p}^{★}$), such as ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ and ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ at $p\ensuremath{\simeq}0.3$, where $\ensuremath{\gamma}\ensuremath{\simeq}7$ mJ/${\mathrm{K}}^{2}\phantom{\rule{0.16em}{0ex}}\mathrm{mol}$. Given that the pseudogap causes a loss of density of states and assuming that ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ has the same $\ensuremath{\gamma}$ value as other cuprates at $p\ensuremath{\simeq}0.3$, this implies that $\ensuremath{\gamma}$ in ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ must peak between $p\ensuremath{\simeq}0.09$ and $p\ensuremath{\simeq}0.3$, namely, at (or near) the critical doping ${p}^{★}$ where the pseudogap phase is expected to end (${p}^{★}\ensuremath{\simeq}0.2$). Second, the high $\ensuremath{\gamma}$ value implies that the Fermi surface must consist of more than the single electronlike pocket detected by quantum oscillations in ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ at $p\ensuremath{\simeq}0.09$, whose effective mass ${m}^{★}=2.7{m}_{0}$ yields only $\ensuremath{\gamma}=4.0$ mJ/${\mathrm{K}}^{2}\phantom{\rule{0.16em}{0ex}}\mathrm{mol}$. 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.

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