Theory of the nodal nematic quantum phase transition in superconductors
Eun-Ah Kim, Michael J. Lawler, Paul Oreto, Subir Sachdev, Eduardo Fradkin, Steven A. Kivelson
备注：
9 page, 4 figures, an error in one of expressions corrected and a new author was added. New references and footnotes are added and this is the version to appear in PRB
We study the character of an Ising nematic quantum phase transition (QPT) deep inside a d-wave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N, quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existence of a nematic glass phase in the presence of weak disorder. Some possible implications for cuprate physics are also discussed.
Unconventional superconductivity often intertwines with various forms of order, such as the "nematic" order which breaks the rotational symmetry of the lattice. Investigation of these ordered phases sheds crucial light on the superconductivity itself. Here we report a low-temperature scanning tunneling microscopy (STM) study on RbFe2As2, a heavily hole-doped Fe-based superconductor (FeSC). We observe significant symmetry breaking in its electronic structure and magnetic vortex which differentiates the (π, π) and (π, -π) directions of the unfolded Brillouin zone (BZ). It is thus a novel nematic…
Superconductivity in FeSe has recently attracted a great deal of attention because it emerges out of an electronic nematic state of elusive character. Here we study both the electronic normal state and the superconducting gap structure using heat-capacity measurements on high-quality single crystals. The specific-heat curve, from 0.4 K to Tc = 9.1 K, is found to be consistent with a recent gap determination using Bogoliubov quasiparticle interference [P. O. Sprau et al., Science 357, 75 (2017)], however only if nodes are introduced on either the electron or the hole Fermi-surface sheets. Our a…
There is now copious direct experimental evidence of various forms of (short-range) charge order in underdoped cuprate high temperature superconductors, and spectroscopic signatures of a nodal-antinodal dichotomy in the structure of the single-particle spectral functions. In this context, we analyze the Bogoliubov quasiparticle spectrum in a superconducting nematic glass. The coincidence of the superconducting "nodal points" and the nematic "cold-spots" on the Fermi surface naturally accounts for many of the most salient features of the measured spectral functions (from angle-resolved photoemi…
Charge-$4e$ superconductivity as a novel phase of matter remains elusive so far. Here we show that charge-$4e$ phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. On the one hand, the nontrivial topological defect -- nematic vortex -- is energetically favored over the superconducting phase vortex when the nematic stiffness is less than the superfluid stiffness; consequently the charge-$4e$ phase emerges by proliferation of nematic vortices upon increasing temperatures. On the other hand, the Ginzburg-…
In contrast to multigap superconductors (e.g. MgB$_{2}$), the low-temperature properties of nodal superconductors are dominated by nodal excitations. Here we extend for a variety of nodal superocnductors the earlier work by Simon and Lee and Kübert and Hirschfeld. The scaling relations seen in the thermodynamics and the thermal conductivity will provide an unequivocal test of nodal superconductivity.
A nematic superconductor can in principle support a vestigial order phase above its superconducting transition temperature, with rotational symmetry spontaneously broken while remain nonsuperconducting. We examine the condition for this vestigial nematic order to occur, within a Ginzburg-Landau theory with order parameter fluctuations included. Contrary to prior theoretical results, we found that this vestigial order actually requires very stringent conditions to be met: the material must be sufficiently deep in the nematic regime (i.e. far away from the boundary separating the nematic and chi…
Electronic nematicity is often found in unconventional superconductors, suggesting its relevance for electronic pairing. In the strongly hole-doped iron-based superconductors, the symmetry channel and strength of the nematic fluctuations, as well as the possible presence of long-range nematic order, remain controversial. Here, we address these questions using transport measurements under elastic strain. By decomposing the strain response into the appropriate symmetry channels, we demonstrate the emergence of a giant in-plane symmetric contribution, associated with the growth of both strong ele…
We perform a non-perturbative analysis of the strong interaction between gapless nodal fermions and the nematic order parameter in two-dimensional d_{x^2-y^2} superconductors. We predict that the critical nematic fluctuation can generate a dynamical nodal gap if the fermion flavor N is smaller than a threshold N_c. Such gap generation leads to an additional is-wave Cooper pairing instability, which induces a fully gapped d_{x^2-y^2}+is superconducting dome in the vicinity of the nematic quantum critical point. The opening of a dynamical gap has important consequences, including the saturation …
In recent years, a number of nodal superconductors have been identified; d-wave superconductors in high T_c cuprates, CeCoIn$_5$, and κ-(ET)_2Cu(NCS)_2, 2D f-wave superconductor in Sr_2RuO_4 and hybrid s+g-wave superconductor in YNi_2B_2C. In this work we conduct a theoretical study of nodal superconductors in the presence of supercurrent. For simplicity, we limit ourselves to d-wave and 2D f-wave superconductors. We compute the quasiparticle density of states and the temperature dependence of the depairing critical current in nodal superconductors, both of which are accessible experimentally.
A d-wave high temperature cuprate superconductor exhibits a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effect on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization gro…
In a fully-gapped superconductor the electronic Raman response has a pair-breaking peak at twice the superconducting gap $Δ$, if the Bogoliubov excitations are uncorrelated. Motivated by the iron based superconductors, we study how this peak is modified if the superconducting phase hosts a nematic-structural quantum critical point. We show that, upon approaching this point by tuning, e.g., doping, the growth of nematic correlations between the quasiparticles transforms the pair-breaking peak into a nematic resonance. The mode energy is below 2$Δ$, and stays finite at the quantum critical point…
The origin of the electronic nematicity and its remarkable material-dependence are famous longstanding unsolved issues in Fe-based superconductors. To attack these issues, we focus on the in-plane anisotropy of the resistivity: In the nematic state in FeSe, the relation $ρ_x>ρ_y$ holds, where $ρ_{x(y)}$ is the resistivity along the longer (shorter) Fe-Fe axis. In contrast, the opposite anisotropy $ρ_x<ρ_y$ is realized in other undoped Fe-based superconductors. Such nontrivial material dependence is naturally explained in terms of the strongly orbital-dependent inelastic quasiparticle scatterin…
Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr$_{1-x}$Na$_x$Fe$_2$As$_2$ measured via inelastic X-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped ($x=0.36$) sample, which harbors a magnetically-ordered tetragonal phase, we find it hosts a short nematic correlation length $ξ$ ~ 10 $Å$ and a large nematic susceptibility $χ_{\rm ne…
Transition metal dichalcogenides like 2H-NbSe2 in their two-dimensional (2D) form exhibit Ising superconductivity with the quasiparticle spins are firmly pinned in the direction perpendicular to the basal plane. This enables them to withstand exceptionally high magnetic fields beyond the Pauli limit for superconductivity. Using field-angle-resolved magnetoresistance experiments for fields rotated in the basal plane we investigate the field-angle dependence of the upper critical field (Hc2), which directly reflects the symmetry of the superconducting order parameter. We observe a six-fold nodal…
We report Raman scattering measurement of charge nematic fluctuations in the tetragonal phase of BaFe$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (x=0.04) single crystals. In both systems, the observed nematic fluctuations are found to exhibit divergent Curie-Weiss like behavior with very similar characteristic temperature scales, indicating a universal tendency towards charge nematic order in 122 iron-based superconductors.
Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quant…
There are now many nodal superconductors in heavy fermion (HF) systems, charge conjugated organic metals, high Tc cuprates and ruthenates. On the other hand only few of them have a well established gap function. We present here a study of the angular dependent thermal conductivity in the vortex state of some of the nodal superconductors. We hope it will help to identify the nodal directions in the gap function of UPd_2Al_3, UNi_2Al_3, UBe_13 and URu_2Si_2.
The origin of diverse nematicity and their order parameters in Fe-based superconductors have been attracting increasing attention. Recently, a new type of nematic order has been discovered in heavily hole-doped ($n_d=5.5$) compound AFe$_2$As$_2$ (A=Cs, Rb). The discovered nematicity has $B_{2g}$ (=$d_{xy}$) symmetry, rotated by $45^\circ$ from the $B_{1g}$ (=$d_{x^2-y^2}$) nematicity in usual compounds with $n_d\approx6$. We predict that the "nematic bond order", which is the symmetry-breaking of the correlated hopping, is responsible for the $B_{2g}$ nematic order in AFe$_2$As$_2$. The Dirac …
This course has a dual purpose. First we review the successes of the weak-coupling BCS theory in describing new classes of superconductors discovered since 1979. They include the heavy-fermion superconductors, high-Tc cuprate superconductors, organic superconductors, Sr2RuO4, etc. Second, we present the quasiclassical approximation introduced by Volovik, which we extend to describe the thermodynamics and the thermal conductivity of the vortex state in nodal superconductors. This approach provides the most powerful tool to identify the symmetry of the energy gap function Delta(k) in these new s…
The emergence of the nematic order and fluctuations has been discussed as a central issue in Fe-based superconductors. To clarify the origin of the nematicity, we focus on the shear modulus $C_{66}$ and the Raman quadrupole susceptibility $χ_{x^2-y^2}^{Raman}$. Due to the Aslamazov-Larkin vertex correction, the nematic-type orbital fluctuations are induced, and they enhances both $1/C_{66}$ and $χ_{x^2-y^2}^{Raman}$ strongly. However, $χ_{x^2-y^2}^{Raman}$ remains finite even at the structure transition temperature $T_S$, because of the absence of the band Jahn-Teller effect and the Pauli (=in…
We propose that impurity-induced electronic nematic state is realized above the orthorhombic structure transition temperature $T_S$ in iron-pnictide superconductors. In the presence of strong orbital fluctuations near $T_S$, it is theoretically revealed that a single impurity induces non-local orbital order with $C_2$-symmetry, consistently with recent STM/STS measurements. Each impurity-induced $C_2$ orbital order aligns along a-axis by applying tiny uniaxial pressure along b-axis. In this impurity-induced nematic phase, the resistivity shows sizable in-plane anisotropy ($ρ_b/ρ_a \sim 2$) eve…
We examine the quantum theory of the spontaneous breaking of lattice rotation symmetry in d-wave superconductors on the square lattice. This is described by a field theory of an Ising nematic order parameter coupled to the gapless fermionic quasiparticles. We determine the structure of the renormalization group to all orders in a 1/N_f expansion, where N_f is the number of fermion spin components. Asymptotically exact results are obtained for the quantum critical theory in which, as in the large N_f theory, the nematic order has a large anomalous dimension, and the fermion spectral functions a…
Nematic order resulting from the partial melting of density-waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems -- the multi-orbital Hubbard model -- displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard RPA method. Here, by including fluctuations beyond RPA in the multi-orbital Hubbard model, we derive …
The theoretical understanding of the nematic state of iron-based superconductors and especially of FeSe is still a puzzling problem. Although a number of experiments calls for a prominent role of local correlations and place iron superconductors at the entrance of a Hund metal state, the effect of the electronic correlations on the nematic state has been theoretically poorly investigated. In this work we study the nematic phase of iron superconductors accounting for local correlations, including the effect of the Hund's coupling. We show that Hund's physics strongly affects the nematic propert…
Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics),resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ iron-based superconductors…
We analyze the scattering rate for 2D fermions interacting via soft nematic fluctuations. The ground state is an s-wave superconductor, but other pairing channels are almost equally attractive. This strongly alters the scattering rate: At energies beyond the pairing gap $Δ$, it is renormalized by contributions from all pairing channels. At energies of order $Δ$, it is determined by the competition between scattering into a gapped continuum and dispersing nematic resonance. The outcome is a "peak-peak-dip-hump" spectrum, similar, but not identical, to the "peak-dip-hump" structure in the cuprat…
We show that the nodal quasiparticles have significant effect on the classical phase fluctuations in a quasi-two-dimensional d-wave superconductor. They give rise to singularities in the temperature behavior of some of the coupling constants in the phase-only effective action. One of the consequences is that the classical XY-model is not adequate for the description of the superconducting fluctuations in d-wave superconductors at low temperatures.
Motivated by the recent experiments suggesting the importance of nematicity in the phase diagrams of ironbased and cuprate high-Tc superconductors, we study the influence of nematicity on the collective modes inside the superconducting state in a non-equilibrium. In particular, we consider the signatures of collective modes in short-time dynamics of a system with competing nematic and s- and d-wave superconducting orders. In the rotationally symmetric state, we show that the Bardasis-Schrieffer mode, corresponding to the subdominant pairing, hybridizes with the nematic collective mode and merg…
The electronic nematic responses in Fe-based superconductors have been observed ubiquitously in various experimental probes. One novel nematic character is the d-wave {\it bond} orbital-relevant nematic charge order which was firstly proposed by symmetry analysis and then conformed by angle-resolved photoemission spectroscopy. In this paper, we present a mechanism that the driving force of the orbital-relevant nematic charge order is the reduction of the large Hubbard energy in the particle-hole charge channel by virtual hopping processes. This is one scenario from strong-coupling consideratio…
The role of nematic fluctuations for unconventional superconductivity has been subject of intense discussions for many years. In iron-based superconductors, the most established probe for electronic-nematic fluctuations, i.e. the elastoresistivity seems to imply that superconductivity is reinforced by electronic-nematic fluctuations, since the elastoresistivity amplitude peaks at or close to optimal $T_C$. However, on the over-doped side of the superconducting dome, the diminishing elastoresistivity suggests a negligible importance in the mechanism of superconductivity. Here we introduce the N…
The momentum dependence of the nematic order parameter is an important ingredient in the microscopic description of iron-based high-temperature superconductors. While recent reports on FeSe indicate that the nematic order parameter changes sign between electron and hole bands, detailed knowledge is still missing for other compounds. Combining angle-resolved photoemission spectroscopy (ARPES) with uniaxial strain tuning, we measure the nematic band splitting in both FeSe and BaFe$_2$As$_2$ without interference from either twinning or magnetic order. We find that the nematic order parameter exhi…
Recently, complex phase transitions accompanied by the rotational symmetry breaking have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various charge susceptibilities in an unbiased way, by applying the functional-renormalization-group method to the realistic $d$-$p$ Hubbard model. Without assuming the wavevector of the order parameter, we reveal that the most dominant instability is the uniform ($q = 0$) charge modulation on the $p_x$ and $p_y$ orbitals, which possesses the d-symmetry. This uniform nematic order triggers another nem…
Recent findings of anomalous super-linear scaling of low temperature ($T$) penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates which are poster child nodal superconductors have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points. Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group c…
An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model (RFIM). Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network, and use what is known about the RFIM to predict new ways to test for electron nematicity using nois…
Since 1979, many new classes of superconductors have been discovered, including heavy-fermion compounds, organic conductors, high-Tc cuprates, and Sr2RuO4. Most of these superconductors are unconventional and/or nodal. Therefore it is of central importance to determine the symmetry of the order parameter in each of these superconductors. In particular, the angular-controlled thermal conductivity in the vortex state provides a unique means of investigating the nodal structure of the superconducting energy gap when high-quality single crystals in the extremely clean limit are available. Using th…
In several families of iron-based superconducting materials, a d-wave pairing instability may compete with the leading s-wave instability. Here we show that when both states have comparable free energies, superconducting and nematic degrees of freedom are strongly coupled. While nematic order causes a sharp non-analytic increase in $T_{c}$, nematic fluctuations can change the character of the s-wave to d-wave transition, favoring an intermediate state that does not break time-reversal symmetry but does break tetragonal symmetry. The coupling between superconductivity and nematicity is also man…
In this paper we study an effective model for the normal state of iron-based superconductors. It has separate, but interacting itinerant and localized degrees of freedom, originating from the d_xz and d_yz, and from d_xy iron orbitals respectively. At low temperatures, below a mean-field phase transition, these different states condense together in an excitonic order parameter. We show that at even lower temperature, after another phase transition, this ordered state can spontaneously break the C_4 lattice symmetry and become nematic. We propose this mechanism as an explanation of the tendency…
Strong interplay of spin and charge/orbital degrees of freedom is the fundamental characteristic of the iron-based superconductors (FeSCs), which leads to the emergence of a nematic state as a rule in the vicinity of the antiferromagnetic state. Despite intense debate for many years, however, whether nematicity is driven by spin or orbital fluctuations remains unsettled. Here, by use of transport, magnetization, and $^{75}$As nuclear magnetic resonance (NMR) measurements, we show a striking transformation of the relationship between nematicity and spin fluctuations (SFs) in Na$_{1-x}$Li$_x$FeA…
Using a variational Monte Carlo method, we investigate the nematic state in iron-base superconductors based on a three-band Hubbard model. Our results demonstrate that the nematic state, formed by introducing an anisotropic hopping order into the projected wave function, can arise in the underdoped regime when a realistic off-site Coulomb interaction $V$ is considered. {\color {red} We demonstrate that the off-site Coulomb interaction $V$, which is neglected so far in the analysis of iron-base superconductors, make a dominant contribution to the stabilization of nematic state. We calculate the…
Charge order in cuprate superconductors is a possible source of anomalous electronic properties in the underdoped regime. Intra-unit cell charge ordering tendencies point to electronic nematic order involving oxygen orbitals. In this context we investigate charge instabilities in the Emery model and calculate the charge susceptibility within diagrammatic perturbation theory. In this approach, the onset of charge order is signalled by a divergence of the susceptibility. Our calculations reveal three different kinds of order: a commensurate ($q=0$) nematic order, and two incommensurate nematic p…
We establish a condition for the perturbative stability of zero energy nodal points in the quasi-particle spectrum of superconductors in the presence of coexisting \textit{commensurate} orders. The nodes are found to be stable if the Hamiltonian is invariant under time reversal followed by a lattice translation. The principle is demonstrated with a few examples. Some experimental implications of various types of assumed order are discussed in the context of the cuprate superconductors.
We review the recent developments in electronic Raman scattering measurements of charge nematic fluctuations in iron-based superconductors. A simple theoretical framework of a $d$-wave Pomeranchuk transition is proposed in order to capture the salient features of the spectra. We discuss the available Raman data in the normal state of 122 iron-based systems, particularly Co doped BaFe$_2$As$_2$, and we show that the low energy quasi-elastic peak, the extracted nematic susceptibility and the scattering rates are consistent with an electronic driven structural phase transition. In the superconduc…
Superconductivity originates from pairing of electrons. Pairing channel on Fermi surface and pairing glue are thus two pivotal issues for understanding a superconductor. Recently, high-temperature superconductivity over 40 K was found in electron-doped FeSe superconductors including K$_x$Fe$_{2-y}$Se$_2$, Li$_{0.8}$Fe$_{0.2}$OHFeSe, and 1 monolayer FeSe thin film. However, their pairing mechanism remains controversial. Here, we studied the systematic evolution of electronic structure in potassium-coated FeSe single crystal. The doping level is controlled precisely by in situ evaporating potass…
We report the results of our in-depth analysis of spectroscopic and thermodynamic properties of a multi-orbital metal, like FeSe, which first develops a nematic order and then undergoes a transition into a superconducting state, which co-exists with nematicity. We analyze the angular dependence of the gap function and specific heat $C_V (T)$ of such nematic superconductor. We specifically address three issues: (i) angular dependence of the gap in light of the competition between nematicity-induced $s$-$d$ mixture and orbital transmutation of low-energy excitations in the nematic state, (ii) th…
The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here, we compare results from determinant quantum Monte Carlo simulations of the Hubbar…
Recent experimental and theoretical studies have highlighted the possible role of a electronic nematic liquid in underdoped cuprate superconductors. We calculate, within a model of d-wave superconductor with Hubbard correlations, the spin susceptibility in the case of a small explicitly broken rotational symmetry of the underlying lattice. We then exhibit how the induced spin response asymmetry is strongly enhanced by correlations as one approaches the instability to stripe order. In the disorder-induced stripe phase, impurities become spin nematogens with a C_2 symmetric impurity resonance st…
The electronic nematic state without magnetization emerges in various strongly correlated metals such as Fe-based and cuprate superconductors. To understand this universal phenomenon, we focus on the nematic state in Ti-oxypnictide BaTi2(As,Sb)2O, which is expressed as the three-dimensional 10-orbital Hubbard model. The antiferromagnetic fluctuations are caused by the Fermi surface nesting. Interestingly, we find the spin-fluctuation-driven orbital order due to the strong orbital-spin interference, which is described by the Aslamazov-Larkin vertex correction (AL-VC). The predicted intra-unit-c…
To understand the interplay between nematic fluctuation and superconductivity in iron-based superconductors, we performed a systematic study of the realistic two-orbital Hubbard model by using the constrained-path quantum Monte Carlo method. Our numerical results showed that the on-site nematic interaction induces a strong enhancement of nematic fluctuations at various momentums, especially at ($π$,$π$). Simultaneously, it was found that the on-site nematic interaction suppresses the ($π$,0)/(0,$π$) antiferromagnetic order and long-range electron pairing correlations for dominant pairing chann…
We present a microscopic derivation of the nematic charge-density-wave (CDW) formation in cuprate superconductors based on the three-orbital d-p Hubbard model, by introducing the vertex correction (VC) into the charge susceptibility. The CDW instability at $q=(Δ_{FS},0)$, $(0,Δ_{FS})$ appears when the spin fluctuations are strong, due to the strong charge-spin interference represented by the VC. Here, $Δ_{FS}$ is the wavenumber between the neighboring hot spots. The obtained spin-fluctuation-driven CDW is expressed as the "intra-unit-cell orbital order" accompanied by the charge transfer betwe…
Recently, we discovered a mistake in our Letter on phase dynamics in granular d-wave superconductors, which we corrected in an Erratum published last week. This is an expanded version of the Erratum, containing details and supporting numerical results.
Unconventional superconductors are most frequently identified by the observation of power-law behaviour on low-temperature thermodynamic or transport properties, such as specific heat. Here we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. These new types of nodes typically occur when there are transitions between different types of gap node topology, for example when point or line nodes first appear as a function of some physical parameter. We identify anomalous, non-integer thermodynamic power laws associated with these new no…
High-resolution laser-based angle-resolved photoemission measurements have been carried out on the electron-doped (Nd$_{1.85}$Ce$_{0.15}$)CuO$_4$ high temperature superconductor. We have revealed a clear kink at $\sim$60 meV in the dispersion along the (0,0)-($π$,$π$) nodal direction, accompanied by a peak-dip-hump feature in the photoemission spectra. This indicates that the nodal electrons are coupled to collective excitations (bosons) in electron-doped superconductors, with the phonons as the most likely candidate of the boson. This finding has established a universality of nodal electron c…
Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors, particularly in the Fe-based systems. We used inelastic x-ray scattering to extract the temperature-dependent nematic correlation length $ξ$ from the anomalous softening of acoustic phonon modes in FeSe, underdoped Ba(Fe$_{0.97}$Co$_{0.03}$)$_2$As$_2$ and optimally doped Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. In all cases, we find that $ξ$ is well described by a power law $(T-T_0)^{-1/2}$ extending over a wide temperature range. We attributed this mean-field behavior and the extended fluctuation regime to a sizable nem…
We report field-orientation specific heat studies of the pressure-induced heavy fermion superconductor CeRhIn5. Theses experiments provide the momentum-dependent superconducting gap function for the first time in any pressure-induced superconductor. In the coexisting phase of superconductivity and antiferromagnetism, field rotation within the Ce-In plane reveals four-fold modulation in the density of states, which favors a d-wave order parameter and constrains a theory of the interplay between superconductivity and magnetism.
Massachusetts Institute of Technology（麻省理工学院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Institute for Materials Science（国立材料研究所）；Princeton University（普林斯顿大学）
