We identify an intrinsic Hall effect in multiband chiral superconductors in the absence of a magnetic field (i.e., an anomalous Hall effect). This effect arises from interband transitions involving time-reversal symmetry-breaking chiral Cooper pairs. We discuss the implications of this effect for the putative chiral p-wave superconductor, Sr2RuO4, and show that it can contribute significantly to Kerr rotation experiments. Since the magnitude of the effect depends on the structure of the order parameter across the bands, this result may be used to distinguish between different models proposed for the superconducting state of Sr2RuO4.
Transverse-field muon spin rotation ($μ$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $λ(T)$ is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency (rf) inductive measurements yield a stronger temperature dependence of $λ(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the…
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…
We studied the effects of multiband electronic structure on the thermoelectric and electrical transport properties in the normal state of kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs). In all three members, the multiband nature is manifested by sign changes in the temperature dependence of the Seebeck and Hall resistivity, together with sublinear response of the isothermal Nernst and Hall effects to external magnetic fields in the charge ordered state. Moreover, ambipolar transport effects appear ubiquitously in all three systems, giving rise to sizable Nernst signal. Finally, possib…
Magnetoresistivity \r{ho}xx and Hall resistivity \r{ho}xy in ultra high magnetic fields up to 88T are measured down to 0.15K to clarify the multiband electronic structure in high-quality single crystals of superconducting FeSe. At low temperatures and high fields we observe quantum oscillations in both resistivity and Hall effect, confirming the multiband Fermi surface with small volumes. We propose a novel and independent approach to identify the sign of corresponding cyclotron orbit in a compensated metal from magnetotransport measurements. The observed significant differences in the relativ…
We investigated the transport properties of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ single crystals with different amounts of excess Fe prepared by O$_2$ annealing. The O$_2$ annealing remarkably improves transport properties. In particular, a strongly nonlinear Hall resistivity was observed only in the fully-annealed crystal, and the magnetoresistance (MR) is drastically enhanced after annealing, reaching a value larger than 17% at 16 K and 14 T. The obvious change of transport properties after the annealing indicates that the band structure of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ is affected by the excess …
Signatures of time-reversal-symmetry breaking in multiband 2H-TaS2 revealed by zero-field Josephson nonreciprocity
CIC nanoGUNE BRTA（纳米科学中心）；Centro de Física de Materiales – Materials Physics Center (CFM-MPC) CSIC-EHU（材料物理中心）；Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche（意大利国家研究理事会材料结构研究所）
We study optical responses of Leggett modes in multiband superconductors in the linear response regime. The Leggett mode is a collective mode unique to multiband superconductors that arises from relative phase fluctuations of superconducting orders for different bands. We use the Ginzburg-Landau (GL) description to study the collective modes in multiband systems. We find that multiband superconductors generally allow a linear coupling between the Leggett mode and external electric fields due to the presence of a cross term between different components of superconducting orders in the GL theory…
We present results of in field directional point contact spectroscopy (DPCS) study in the quaternary borocarbide superconductor YNi2B2C, which is characterized by a highly anisotropic superconducting gap function. For I||a, the superconducting energy gap (D), decreases linearly with magnetic field and vanishes around 3.25T which is well below the upper critical field (Hc2~6T) measured at the same temperature (2.2K). For I||c, on the other hand, D decreases weakly with magnetic field but the broadening parameter (G) increases rapidly with magnetic field with the absence of any resolvable featur…
Superconductivity in the heavy-fermion compound CeCu2Si2 is a prototypical example of Cooper pairs formed by strongly correlated electrons. For more than 30 years, it has been believed to arise from nodal d-wave pairing mediated by a magnetic glue. Here, we report a detailed study of the specific heat and magnetization at low temperatures for a high-quality single crystal. Unexpectedly, the specific-heat measurements exhibit exponential decay with a two-gap feature in its temperature dependence, along with a linear dependence as a function of magnetic field and the absence of oscillations in t…
We present the upper critical fields Hc2(T) and Hall effect in beta-FeSe single crystals. The Hc2(T) increases as the temperature is lowered for field applied parallel and perpendicular to (101), the natural growth facet of the crystal. The Hc2(T) for both field directions and the anisotropy at low temperature increase under pressure. Hole carriers are dominant at high magnetic fields. However, the contribution of electron-type carriers is significant at low fields and low temperature. Our results show that multiband effects dominate Hc2(T) and electronic transport in the normal state.
A method is proposed to extend the zero-temperature Hall-Klemm microscopic theory of the Knight shift $K$ in an anisotropic and correlated, multi-band metal to calculate $K(T)$ at finite temperatures $T$ both above and into its superconducting state. The transverse part of the magnetic induction ${\bf B}(t)={\bf B}_0+{\bf B}_1(t)$ causes adiabatic changes suitable for treatment with the Keldysh contour formalism and analytic continuation onto the real axis. We propose that the Keldysh-modified version of the Gor'kov method can be used to evaluate $K(T)$ at high ${\bf B}_0$ both in the normal s…
We investigate theoretically the properties of s-wave multiband superconductors in the weak coupling (BCS) limit in the presence of pair-breaking effects of magnetic field. It is shown that a qualitatively new gapless superconducting state must appear in quasi-2D superconductors in magnetic fields parallel to the plane, corresponding to a Sarma state induced on one of the Fermi surfaces. The emergence of the new state in s-wave multiband superconductors in the absence of anisotropy or spin-orbit interaction is usually accompanied by a zero-temperature first-order metamagnetic phase transition.…
Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux. In the absence of pinning such paramagnetic response is weak, and ceases with increasing sample thickness. Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate - even multiply larger than the diamagnetic Meissner response for the same applied magnetic field. We link the appearance of this giant paramagnetic response to the broad crossover between conventiona…
We have successfully grown the single crystal of a low carrier density system Y$_3$Ru$_4$Ge$_{13}$ which crystallizes in the cubic crystal structure with the space group Pm3n. Y$_3$Ru$_4$Ge$_{13}$ exhibits super conductivity below 2.85 K as determined from the electrical resistivity, magnetic susceptibility and heat capacity measurements. The bulk measurements indicate multiband superconductivity in this low carrier system. Hall effect measurements show that the Hall coefficient R$_H$ is positive and it decreases rapidly with temperature which is highly unusual. The simple estimation of the ca…
We study how the multiplicity of the Fermi surface affects the zero-bias peak in conductance spectra of tunneling spectroscopy. As case studies, we consider models for organic superconductors $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ and (TMTSF)$_2$ClO$_4$. We find that multiplicity of the Fermi surfaces can lead to a splitting of the zero-bias conductance peak (ZBCP). We propose that the presence/absence of the ZBCP splitting is used as a probe to distinguish the pairing symmetry in $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$.
The superconductivity of a kagome superconductor CsV3Sb5 is studied by scanning tunneling microscopy / spectroscopy at an ultralow temperature with high resolution. Two kinds of superconducting gaps with multiple sets of coherent peaks and residual zero-energy density of states are observed on both half-Cs and Sb surfaces, implying multiband superconductivity with gap nodes. Sixfold star-shaped magnetic vortex is observed with conventional Caroli-de Gennes-Matricon bound states inside. Magnetic impurities suppress the superconductivity, while nonmagnetic impurities do not, suggesting the absen…
We report a systematic investigation, together with a theoretical analysis, of the resistivity and Hall effect in single crystals of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$, over a wide doping range. We find a surprisingly great disparity between the relaxation rates of the holes and the electrons, in excess of an order of magnitude in the low-doping, low-temperature regime. The ratio of the electron to hole mobilities diminishes with temperature and doping (away from the magnetically ordered state) and becomes more conventional. We also find a straightforward explanation of the large asymmetry (…
There is a tacit assumption that multiband superconductors are essentially the same as multigap superconductors. More precisely, it is usually assumed that the number of excitation gaps in the single-particle energy spectrum of a uniform superconductor determines the number of contributing bands in the corresponding superconducting model. Here we demonstrate that contrary to this widely accepted viewpoint, the superconducting magnetic properties are sensitive to the number of contributing bands even when the corresponding excitation gaps are degenerate and cannot be distinguished. In particula…
In search of the origin of superconductivity in diluted rhenium superconductors and their significantly enhanced $T_c$ compared to pure Be (0.026 K), we investigated the intermetallic ReBe$_{22}$ compound, mostly by means of muon-spin rotation/relaxation ($μ$SR). At a macroscopic level, its bulk superconductivity (with $T_c=9.4$ K) was studied via electrical resistivity, magnetization, and heat-capacity measurements. The superfluid density, as determined from transverse-field $μ$SR and electronic specific-heat measurements, suggest that ReBe$_{22}$ is a fully-gapped superconductor with some mu…
We present results of precise measurements of the thermal and electrical transport in the optimally- and over-doped Ba1-xKxFe2As2 single crystals (x = 0.35, 0.55, 0.88) and compare them to the previously reported data on Ba(Fe1-yCoy)2As2. A contraction of the electron pocket is observed upon substitution potassium for barium, but even at the extreme doping (x = 0.88) there is still a noticeable contribution from negative charge carriers to the electronic transport. The size of the electron pocket in all K-doped samples is small enough to cause a significant enhancement of the respective Hall-L…
We investigated the superconducting and transport properties in FeTe$_{1-x}$Se$_{x}$ (0.1 $\leq$ $x$ $\leq$ 0.4) single crystals prepared by O$_2$-annealing. Sharp superconducting transition width observed in magnetization measurement and the small residual resistivity prove the high quality of the crystals. All the crystals manifest large, homogeneous, and isotropic critical current density \emph{J}$_c$ with self-field value over 10$^5$ A/cm$^2$ at 2 K. The large and field-robust critical current densities prove that the superconductivity in FeTe$_{1-x}$Se$_{x}$ (0.1 $\leq$ $x$ $\leq$ 0.4) is…
We have measured the normal state temperature dependence of the Hall effect and magnetoresistance in epitaxial MgB2 thin films with variable disorders characterized by the residual resistance ratio RRR ranging from 4.0 to 33.3. A strong nonlinearity of the Hall effect and magnetoresistance have been found in clean samples, and they decrease gradually with the increase of disorders or temperature. By fitting the data to the theoretical model based on the Boltzmann equation and ab initio calculations for a four-band system, for the first time, we derived the scattering rates of these four bands …
We present superconducting properties of single crystalline Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ by measuring magnetization, resistivity, upper critical field, Hall coefficient, and magneto-optical images. The magnetization measurements reveal fish-tail hysteresis loop at high temperatures and relatively high critical current density above $J_{c}=10^{5}$ A/cm$^{2}$ at low temperatures. Upper critical field determined by resistive transition is anisotropic with anisotropic parameter $\sim$ 3.5. Hall effect measurements indicate that Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ is a multiband system…
We synthesized large superconducting single crystal Ca0.77La0.18Fe0.90As2 ('112' type) of 2 millimeter size. Scanning electron microscopy (SEM) measurements revealed that bright and dark stripes alternately spread on the surface of crystals, indicating possible existence of intrinsic phase separation. Temperature (T) -dependent resistivity, Hall effect and magneto-resistance (MR) were measured with magnetic field (H) applied to different directions of crystal. The upper critical field (Hc2) anisotropy was estimated with a moderate value around 2.8. Positive Hall coefficient (RH) and anisotropi…
Resistivity, Hall effect and magnetization have been investigated on the new superconductor Bi4O4S3. A weak insulating behavior has been induced in the normal state when the superconductivity is suppressed. Hall effect measurements illustrate clearly a multiband feature dominated by electron charge carriers, which is further supported by the magnetoresistance data. Interestingly, a kink appears on the temperature dependence of resistivity at about 4 K at all high magnetic fields when the bulk superconductivity is completely suppressed. This kink can be well traced back to the upper critical fi…
We report a detailed study of the electrical transport properties of single crystals of Pr$_4$Fe$_2$As$_2$Te$_{1-x}$O$_4$, a recently discovered iron-based superconductor. Resistivity, Hall effect and magnetoresistance are measured in a broad temperature range revealing the role of electrons as dominant charge carriers. The significant temperature dependence of the Hall coefficient and the violation of Kohler's law indicate multiband effects in this compound. The upper critical field and the magnetic anisotropy are investigated in fields up to 16 T, applied parallel and perpendicular to the cr…
Thermal Hall effect in elemental niobium, a two-gap superconductor
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院及武汉国家强磁场中心）；Laboratoire de Physique et d’Étude de Matériaux (CNRS) ESPCI Paris, PSL Research University（巴黎高等物理化工大学校PSL研究大学材料物理与研究所（CNRS））
