Thermal Hall Conductivity as a Probe of Gap Structure in Multi-band Superconductors: The Case of $\rm Ba_{1-x}K_xFe_2As_2$
J. G. Checkelsky, R. Thomale, Lu Li, G. F. Chen, J. L. Luo, N. L. Wang, N. P. Ong
备注：
5 pages, 4 figures. Orientation significantly updated from previous (0811.4668v1) reflecting new theoretical understanding of experimental results and physical implications. Introduction, discussion, and figures updated including additional figure for model calculation
The sign and profile of the thermal Hall conductivity $κ_{xy}$ gives important insights into the gap structure of multi-band superconductors. With this perspective, we have investigated $κ_{xy}$ and the thermal conductivity $κ_{xx}$ in $\rm Ba_{1-x}K_xFe_2As_2$ which display large peak anomalies in the superconducting state. The anomalies imply that a large hole-like quasiparticle (qp) population exists below the critical temperature $T_c$. We show that the qp mean-free-path inferred from $κ_{xx}$ reproduces the observed anomaly in $κ_{xy}$, providing a consistent estimate of a large qp population. Further, we demonstrate that the hole-like signal is consistent with a theoretical scenario where despite potentially large gap variations on the electron pockets, the minimal homogeneous gap of the superconducting phase resides at a hole pocket. Implications for probing the gap structure in the broader class of pnictide superconductors are discussed.
Superconductivity at about 15.6 K was achieved in Tb_{1-x}Ca_xFeAsO by partially substituting Tb^{3+} with Ca^{2+} in the nominal doping region x = 0.40 \sim 0.50. A detailed investigation was carried out in a typical sample with doping level of x = 0.44. The upper critical field of this sample was estimated to be 77 Tesla from the magnetic field dependent resistivity data. The domination of hole-like charge carriers in the low-temperature region was confirmed by Hall effect measurements. The comparison between the calcium-doped sample Pr_{1-x}Ca_xFeAsO (non-superconductive) and the Strontium-…
We report on a hierarchy of temperatures Tc < Tgap < Tmet in superconducting Rb1-xFe2-ySe2 observed by THz spectroscopy. Above Tmet = 90 K the material reveals semiconducting characteristics. Below Tmet a coherent metallic THz response emerges. This metal-to-insulator type, orbital selective transition is clearly indicated by an isosbestic point in the temperature dependence of the optical conductivity and dielectric constant at THz-frequencies. At Tgap = 61 K a gap opens in the THz regime and then the superconducting transition occurs at Tc = 32 K. This sequence of temperatures seems to refle…
In underdoped YBa_2Cu_3O_x (YBCO) with x = 6.63, the opening of the pseudogap at T^* ~ 160 K has a strong effect on the Hall angle tan(theta). While the Hall response is significantly reduced, the diagonal current is relatively unaffected. The Hall conductivity suppression continues deep into the flux-flow state (from T_c to 40 K), as an anomalous suppression of the vortex Hall current.
Motivated by Sr2RuO4, we consider a chiral superconductor where the gap is strongly suppressed along certain momentum directions. We evaluate the thermal Hall conductivity in the gapless regime, i.e., at temperature small compared with the impurity band width γ, taking the simplest model of isotropic impurity scattering. We find that, under favorable circumstances, this thermal Hall conductivity can be quite significant, and is smaller than the diagonal component (the universal thermal conductivity) only by a factor of 1/ ln(2 Δ_M/γ), where Δ_M is the maximum gap.
Superconductivity was achieved in PrFeAsO by partially substituting Pr^{3+} with Sr^{2+}. The electrical transport properties and structure of this new superconductor Pr_{1-x}Sr_xFeAsO at different doping levels (x = 0.05$\sim$ 0.25) were investigated systematically. It was found that the lattice constants (a-axis and c-axis) increase monotonously with Sr or hole concentration. The superconducting transition temperature at about 16.3 K (95% $ρ_n$) was observed around the doping level of 0.20$\sim$ 0.25. A detailed investigation was carried out in the sample with doping level of x = 0.25. The d…
The excess Hall conductivity, resulting from thermal fluctuations of the superconducting order parameter, is calculated for a layered superconductor for an arbitrarily strong in-plane electric field and a perpendicular magnetic field in the frame of the time-dependent Ginzburg-Landau theory. The fluctuation Hall conductivity is suppressed in high electric fields much stronger than the longitudinal one. For high-temperature superconductors we predict a pronounced non-Ohmic behavior of the excess Hall effect near the critical temperature in moderate magnetic fields and electric fields of the ord…
The sign change in the Hall conductivity has been studied in thin amorphous Nb$_{1-x}$Ge$_x (x\approx$0.3) films. By changing the film thickness it is shown that the field at which the sign reversal occurs shifts to lower values (from above to below the mean-field transition field $H_{c2}$) with increasing film thickness. This effect can be understood in terms of a competition between a positive normal and a negative fluctuation contribution to the Hall conductivity.
We have studied the Hall effect in superconducting tantalum nitride films. We find a large contribution to the Hall conductivity near the superconducting transition, which we can track to temperatures well above $T_c$ and magnetic fields well above the upper critical field, $\text{\text{H}}_{c2}(0)$. This contribution arises from Aslamazov-Larkin superconducting fluctuations, and we find quantitative agreement between our data and recent theoretical analysis based on time dependent Ginzburg-Landau theory.
Motivated by the spin-triplet superconductor Sr2RuO4, the thermal Hall conductivity is investigated for several pairing symmetries with broken time-reversal symmetry. In the chiral p-wave phase with a fully opened quasiparticle excitation gap, the temperature dependence of the thermal Hall conductivity has a temperature linear term associated with the topological property directly, and an exponential term, which shows a drastic change around the Lifshitz transition. Examining f-wave states as alternative candidates with $\bm d=Δ_0\hat{z}(k_x^2-k_y^2)(k_x\pm ik_y)$ and $\bm d=Δ_0\hat{z}k_xk_y(k…
We study the intrinsic Hall conductivity of the ordinary and topological superconducting phases of a Rashba metal in a perpendicular Zeeman field. In this system the normal metal breaks time reversal symmetry while the superconducting order parameter does not, in contrast to the chiral p-wave superconducting state predicted in the monolayer strontium ruthenate (Sr$_2$RuO$_4$) whose Hall conductivity has been studied extensively. We study the effects of intra-band and inter-band pairing and find there is qualitatively larger change in the intrinsic Hall conductivity when there is inter-band pai…
We analyze here the behavior of the Hall conductivity $σ_{xy}$ near a $z=2$ insulator-superconductor quantum critical point in a perpendicular magnetic field. We show that the form of the conductivity is sensitive to the presence of dissipation $η$, and depends non-monotonically on $H$ once $η$ is weak enough. $σ_{xy}$ passes through a maximum at $H \sim ηT$ in the quantum critical regime, suggesting that the limits $H \to 0$ and $η\to 0$ do not commute.
The magnetic-field dependencies of the longitudinal and Hall resistivity of the electron-doped compounds $Nd_{2-x}Ce_xCuO_{4+δ}$ in underdoped region (x=0.14) were investigated. It was established experimentally a strong magnetic field dependence of the Hall conductivity, $σ_{xy}(B)=C-b/B$, in the region of magnetic fields corresponding to a transition from superconducting to resistive state. The observed feature can be explained with the sum of contributions of the quasiparticles and moving Abrikosov vortices into Hall effect in a mixed state of type-II superconductor.
In high-purity crystals of YBa_2Cu_3O_7, the quasiparticle (qp) lifetime τand the (weak-field) thermal Hall conductivity κ_{xy} undergo dramatic increases below 90K. We present a detailed picture of the behavior of κ_{xy} at low temperature, in particular its scaling properties, which are directly relevant to the issue of whether Landau quantization of the qp states occurs.
The Wiedemann-Franz (WF) ratio compares the thermal and electrical conductivities in a metal. We describe a new way to determine its value, based on the thermal Hall conductivity. The technique is applied to copper and to untwinned YBaCuO. In the latter, we uncover a T-linear dependence and suppression of the Hall-channel WF ratio. We discuss the implications of this suppressions. The general suppression of the WF ratio in systems with predominant electron-electron scattering is discussed.
In his the Comment, P. Ao affirms that his vortex many-body theory explains the observations reported in G. D'Anna et al., Phys. Rev. Lett. 81, 2530 (1998). Indeed, we provide here some arguments to show the lack of a satisfactory explanation within the known theoretical frameworks.
The effect of out-of-plane impurities on the thermal Hall conductivity $κ_{xy}$ of in-plane marginal-Fermi-liquid (MFL) quasiparticles in high-$T_c$ cuprates is examined by following the work on electrical Hall conductivity $σ_{xy}$ by Varma and Abraham [Phys. Rev. Lett. 86, 4652 (2001)]. It is shown that the effective Lorentz force exerted by these impurities is a weak function of energies of the MFL quasiparticles, resulting in nearly the same temperature dependence of $κ_{xy}/T$ and $σ_{xy}$, indicative of obedience of the Wiedemann-Franz law. The inconsistency of the theoretical result wit…
We report the success in introducing Mn into (Li1-xFex)OHFe1-ySe superconducting crystals by applying two different hydrothermal routes, ion exchange (1-Step) and ion release/introduction (2-Step). The micro-region x-ray diffraction and energy dispersive x-ray spectroscopy analyses indicate that the Mn has been doped into the lattice, and its content in the 1-Step fabricated sample is higher than that in the 2-Step one. Magnetic susceptibility and electric transport properties reveal that Mn doping influences little on the superconducting transition, regardless of 1-Step or 2-Step routes. By c…
We calculate the Hall conductivity for a spin-triplet superconductor, using a generalized pairing symmetry dependent on an arbitrary phase, $\vphi$. A promising candidate for such an order parameter is Sr$_{2}$RuO$_{4}$, whose superconducting order parameter symmetry is still subject to investigation. The value of this phase can be determined through Kerr rotation and DC Hall conductivity measurements. Our calculations impose significant constraints on $\vphi$.
In CeCoIn$_5$, the thermal conductivity $κ_{xx}$ and Hall conductivity $κ_{xy}$ below $T_c$ display large anomalies below $T_c$. The strong suppression of the anomalies in weak fields implies the existence of long-lived quasiparticles. We also discuss briefly the Wiedemann-Franz ratio and the existence of a strongly field-dependent spin-fluctuation heat current.
Presented is the theory of thermal Hall conductivity $κ_{xy}$ in the vortex state of high temperature cuprate superconductors in the clean limit. We show that $\lim_{T \to 0} κ_{xy}/T$ is a {\em staircase} function of 1/B with an envelope that scales as 1/B. The relation to the experiments is discussed.
We propose a spin Hall device to induce a large spin Hall effect in a superconductor/normal metal (SN) junction. The side jump and skew scattering mechanisms are both taken into account to calculate the extrinsic spin Hall conductivity in the normal metal. We find that both contributions are anomalously enhanced when the voltage between the superconductor and the normal metal approaches to the superconducting gap. This enhancement is attributed to the resonant increase of the density of states in the normal metal at the Fermi level. Our results demonstrate a novel way to control and amplify th…
We calculate frequency and temperature dependence of the anomalous ac Hall conductivity induced by impurity scattering in a chiral px+ipy superconductor, such as Sr2RuO4, with spontaneous time-reversal-symmetry breaking in the absence of an external magnetic field. We consider two models of disorder, Gaussian and non-Gaussian, characterized by the second and third moments of the random impurity potential, respectively. Within both models, we find that the anomalous Hall conductivity has a finite real value at zero frequency, exhibits singularities at the threshold of photon absorption across t…
Building on previous work, we calculate the temperature- and frequency-dependent {\it anomalous} Hall conductivity for the putative multiband chiral superconductor $\Sr$ using a simple microscopic two-orbital model without impurities. A Hall effect arises in this system without the application of an external magnetic field due to the time-reversal-symmetry breaking chiral superconducting state. The anomalous Hall conductivity is nonzero only when there is more than one superconducting order parameter, involving inter- as well as intra-band Cooper pairing. We find that such a multiband supercon…
Motivated by a previous "$sd^2$-graphene" study, the pairing symmetry in the superconducting state and the thermal Hall conductivity are investigated by a self-consistent Bogoliubov--de Gennes approach on the kagome lattice with intrinsic spin-orbit coupling near van Hove fillings. While the topologically trivial state with broken time-reversal symmetry appears in the absence of spin-orbit coupling, the highest flat band becomes dispersive with a hexagonal symmetry due to spin-orbit coupling, which leads to a topological superconducting state. Since the thermal Hall conductivity in the low-tem…
We compute the longitudinal dc conductivity and the Hall conductivity in a two-dimensional metal with spiral magnetic order. Scattering processes are modeled by a momentum-independent relaxation rate $Γ$. We derive expressions for the conductivities, which are valid for arbitrary values of $Γ$. Both intraband and interband contributions are fully taken into account. For small $Γ$, the ratio of interband and intraband contributions is of order $Γ^2$. In the limit $Γ\to 0$, the conductivity formulas assume a simple quasiparticle form, as derived by Voruganti et. al. [Phys. Rev. B 45, 13945 (1992…
We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chiral superconductors, where fermions pair due to a short-range attractive potential, e.g. $p+\mathrm{i}p$ pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chir…
