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Register a new userVariable range hopping theory for the nodal gap in strongly underdoped cuprate Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$
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Recent angle resolved photoemission spectrascope (ARPES) experiments on strongly underdoped Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$ cuprates have reported an unusual gap in the nodal direction. Transport experiments on these cuprates found variable range hopping behavior observed. These cuprates have both electron and hole doping which has led to proposals that this cuprate is analogous to a partially compensated semiconductors. The nodal gap then corresponds to the Efros-Schklovskii(ES) gap in such semiconductors. We calculate the doping dependence and temperature dependence of a ES gap model and find support for an Efros-Schklovskii model.
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Five transport coefficients of the cuprate superconductor Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$ were measured in the normal state down to low temperature, reached by applying a magnetic field (up to 66T) large enough to suppress superconductivity. The electrical resistivity, Hall coefficient, thermal conductivity, Seebeck coefficient and thermal Hall conductivity were measured in two overdoped single crystals, with La concentration $x = 0.2$ ($T_{rm c}=18$K) and $x = 0.0$ ($T_{rm c}=10$K). The samples have dopings $p$ very close to the critical doping $p^{star}$ where the pseudogap phase ends. The resistivity displays a linear dependence on temperature whose slope is consistent with Planckian dissipation. The Hall number $n_{rm H}$ decreases with reduced $p$, consistent with a drop in carrier density from $n = 1+p$ above $p^{star}$ to $n=p$ below $p^{star}$. This drop in $n_{rm H}$ is concomitant with a sharp drop in the density of states inferred from prior NMR Knight shift measurements. The thermal conductivity satisfies the Wiedemann-Franz law, showing that the pseudogap phase at $T = 0$ is a metal whose fermionic excitations carry heat and charge as do conventional electrons. The Seebeck coefficient diverges logarithmically at low temperature, a signature of quantum criticality. The thermal Hall conductivity becomes negative at low temperature, showing that phonons are chiral in the pseudogap phase. Given the observation of these same properties in other, very different cuprates, our study provides strong evidence for the universality of these five signatures of the pseudogap phase and its critical point.
We have performed a temperature-dependent angle-integrated photoemission study of lightly-doped to heavily-overdoped La$_{2-x}$Sr$_{x}$CuO$_4$ and oxygen-doped La$_2$CuO$_{4.10}$. We found that both the magnitude $Delta$* of the (small) pseudogap and the temperature textit{T}* at which the pseudogap is opened increases with decreasing hole concentration, consistent with previous studies. On the other hand, the superconducting gap $Delta_{sc}$ was found to remain small for decreasing hole concentration. The results can be explained if the superconducting gap opens only on the Fermi arc around the nodal (0,0)-($pi,pi$) direction while the pseudogap opens around $sim$($pi$, 0).
We report detailed thermodynamic and transport measurements for non-superconducting La$_{1.7}$Sr$_{0.3}$CuO$_4$. Collectively, these data reveal that a highly-correlated Fermi-liquid ground state exists in La$_{2-x}$Sr$_x$CuO$_4$ beyond the superconducting dome, and confirm that charge transport in the cuprates is dominated at finite temperatures by intense electron-electron scattering.
Due to the orthorhombic distortion of the lattice, the electronic hopping integrals along the $a$ and $b$ diagonals, the orthorhombic directions, are slightly different. We calculate their difference in the LDA and find $t_{a}^{prime}-t_{b}^{prime}approx 8 $meV. We argue that electron correlations in the insulating phase of La$_{2-x}$Sr$_{x}$CuO$_{4}$, i. e. at doping $xleq 0.055,$ dramatically enhance the $(t_{a}^{prime}-t_{b}^{prime}) $-splitting between the $a$- and $b$-hole valleys. In particular, we predict that the intensity of both angle-resolved photoemission and of optical absorption is very different for the $a$ and $b$ nodal points.
The specific heat $C$ of the cuprate superconductors La$_{2-x}$Sr$_x$CuO$_4$ and Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$ was measured at low temperature (down to $0.5~{rm K}$), for dopings $p$ close to $p^star$, the critical doping for the onset of the pseudogap phase. A magnetic field up to $35~{rm T}$ was applied to suppress superconductivity, giving direct access to the normal state at low temperature, and enabling a determination of $C_e$, the electronic contribution to the normal-state specific heat, at $T to 0$. In La$_{2-x}$Sr$_x$CuO$_4$ at $x=p = 0.22$, $0.24$ and $0.25$, $C_e / T = 15-16~{rm mJmol}^{-1}{rm K}^{-2}$ at $T = 2~{rm K}$, values that are twice as large as those measured at higher doping ($p > 0.3$) and lower doping ($p < 0.15$). This confirms the presence of a broad peak in the doping dependence of $C_e$ at $p^starsimeq 0.19$, as previously reported for samples in which superconductivity was destroyed by Zn impurities. Moreover, at those three dopings, we find a logarithmic growth as $T to 0$, such that $C_e / T sim {rm B}ln(T_0/T)$. The peak vs $p$ and the logarithmic dependence vs $T$ are the two typical thermodynamic signatures of quantum criticality. In the very different cuprate Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$, we again find that $C_e / T sim {rm B}ln(T_0/T$) at $p simeq p^star$, strong evidence that this $ln(1/T)$ dependence - first discovered in the cuprates La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ - is a universal property of the pseudogap critical point. All four materials display similar values of the $rm B$ coefficient, indicating that they all belong to the same universality class.
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