Nodal Quasiparticles Research Articles

Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor

We model the pseudogap state of the hole- and electron-doped cuprates as a metal with hole and/or electron pocket Fermi surfaces. In the absence of long-range antiferromagnetism, such Fermi surfaces violate the Luttinger requirement of enclosing the same area as free electrons at the same density. Using the Ancilla theory of such a pseudogap state, we describe the onset of conventional d-wave superconductivity by the condensation of a charge e Higgs boson transforming as a fundamental under the emergent SU(2) gauge symmetry of a background π-flux spin liquid. In all cases, we find that the d-wave superconductor has gapless Bogoliubov quasiparticles at 4 nodal points on the Brillouin zone diagonals with significant velocity anisotropy, just as in the BCS state. This includes the case of the electron-doped pseudogap metal with only electron pockets centered at wavevectors (π, 0), (0, π), and an electronic gap along the zone diagonals. Remarkably, in this case, too, gapless nodal Bogoliubov quasiparticles emerge within the gap at 4 points along the zone diagonals upon the onset of superconductivity.

On the dynamic distinguishability of nodal quasi-particles in overdoped cuprates

La_{1.67}1.67Sr_{0.33}0.33CuO_44 is not a superconductor and its resistivity follows a purely T^22 temperature dependence at very low temperatures. La_{1.71}1.71Sr_{0.29}0.29CuO_44, on the other hand, has a superconducting ground state together with a T-Linear term in its resistivity. The concomitant emergence of these two features below a critical doping is mystifying. Here, I notice that the electron-electron collision rate in the Fermi liquid above the doping threshold is unusually large. The scattering time of nodal quasi-particles expressed in a dimensionless parameter \zetaζ is very close to what has been found in liquid ^33He at its melting pressure. In the latter case, fermionic particles become dynamically distinguishable by excess of interaction. Ceasing to be dynamically indistinguishable, nodal electrons will be excluded from the Fermi sea. Such non-degenerate carriers will then scatter the degenerate ones within a phase space growing linearly with temperature.

Nodeless superconductivity in the kagome metal CsV3Sb5

The recently discovered kagome metal series AV3Sb5 (A=K, Rb, Cs) exhibits topologically nontrivial band structures, chiral charge order and superconductivity, presenting a unique platform for realizing exotic electronic states. The nature of the superconducting state and the corresponding pairing symmetry are key questions that demand experimental clarification. Here, using a technique based on the tunneling diode oscillator, the magnetic penetration depth Δλ(T) of CsV3Sb5 was measured down to 0.07 K. A clear exponential behavior in Δλ(T) with marked deviations from a T or T2 temperature dependence was observed at low temperatures, indicating an absence of nodal quasiparticles. Temperature dependence of the superfluid density and electronic specific heat can be described by two-gap s-wave superconductivity, consistent with the presence of multiple Fermi surfaces in CsV3Sb5. These results evidence nodeless superconductivity in CsV3Sb5 under ambient pressure, and constrain the allowed pairing symmetry.

Order-by-disorder from bond-dependent exchange and intensity signature of nodal quasiparticles in a honeycomb cobaltate

Recent theoretical proposals have argued that cobaltates with edge-sharing octahedral coordination can have significant bond-dependent exchange couplings thus offering a platform in 3d ions for such physics beyond the much-explored realisations in 4d and 5d materials. Here we present high-resolution inelastic neutron scattering data within the magnetically ordered phase of the stacked honeycomb magnet CoTiO3 revealing the presence of a finite energy gap and demonstrate that this implies the presence of bond-dependent anisotropic couplings. We also show through an extensive theoretical analysis that the gap further implies the existence of a quantum order-by-disorder mechanism that, in this material, crucially involves virtual crystal field fluctuations. Our data also provide an experimental observation of a universal winding of the scattering intensity in angular scans around linear band-touching points for both magnons and dispersive spin-orbit excitons, which is directly related to the non-trivial topology of the quasiparticle wavefunction in momentum space near nodal points.

Spin susceptibility of superconductors with strong spin-orbit coupling

We show that in some trigonal and hexagonal crystals the Zeeman coupling of band electrons with an external magnetic field is strongly anisotropic and necessarily vanishes along the main symmetry axis. This leads to qualitative changes in the temperature dependence of the electron spin susceptibility in the superconducting state. In particular, the power-law exponents at low temperatures due to the contribution of the nodal quasiparticles are considerably modified compared to their textbook values.

Ubiquitous suppression of the nodal coherent spectral weight in Bi-based cuprates

High-temperature superconducting cuprates exhibit an intriguing phenomenology for the low-energy elementary excitations. In particular, an unconventional temperature dependence of the coherent spectral weight (CSW) has been observed in the superconducting phase by angle-resolved photoemission spectroscopy (ARPES), both at the antinode where the d-wave paring gap is maximum, as well as along the gapless nodal direction. Here, we combine equilibrium and time-resolved ARPES to track the temperature dependent meltdown of the nodal CSW in Bi-based cuprates with unprecedented sensitivity. We find the nodal suppression of CSW upon increasing temperature to be ubiquitous across single- and double-layer Bi cuprates, and uncorrelated to superconducting and pseudogap onset temperatures. We quantitatively model both the lineshape of the nodal spectral features and the anomalous suppression of CSW within the Fermi-Liquid framework, establishing the key role played by the normal state electrodynamics in the description of nodal quasiparticles in superconducting cuprates.

Point-node gap structure of the spin-triplet superconductor UTe2.

Low-temperature electrical and thermal transport, magnetic penetration depth, and heat capacity measurements were performed on single crystals of the actinide superconductor UTe2 to determine the structure of the superconducting energy gap. Heat transport measurements performed with currents directed along both crystallographic a and b axes reveal a vanishingly small residual fermionic component of the thermal conductivity. The magnetic field dependence of the residual term follows a rapid, quasilinear increase consistent with the presence of nodal quasiparticles, rising toward the a-axis upper critical field where the Wiedemann-Franz law is recovered. Together with a quadratic temperature dependence of the magnetic penetration depth up to T/T c = 0.3, these measurements provide evidence for an unconventional spin-triplet superconducting order parameter with point nodes. Millikelvin specific heat measurements performed on the same crystals used for thermal transport reveal an upturn below 300 mK that is well described by a divergent quantum-critical contribution to the density of states (DOS). Modeling this contribution with a T -1/3 power law allows restoration of the full entropy balance in the superconducting state and a resultant cubic power law for the electronic DOS below T c , consistent with the point-node gap structure determined by thermal conductivity and penetration depth measurements.

Nodal superconducting exchange coupling.

A superconducting spin valve consists of a thin-film superconductor between two ferromagnetic layers. A change of magnetization alignment shifts the superconducting transition temperature (ΔΤc) due to an interplay between the magnetic exchange energy and the superconducting condensate. The magnitude of ΔΤc scales inversely with the superconductor thickness (dS) and is zero when dS exceeds the superconducting coherence length (ξ). Here, we report a superconducting spin-valve effect involving a different underlying mechanism in which magnetization alignment and ΔΤc are determined by nodal quasiparticle excitation states on the Fermi surface of the d-wave superconductor YBa2Cu3O7-δ sandwiched between insulating layers of ferromagnetic Pr0.8Ca0.2MnO3. We observe ΔΤc values that approach 2 K with the sign of ΔΤc oscillating with dS over a length scale exceeding 100ξ and, for particular values of dS, the superconducting state reinforces an antiparallel magnetization alignment. These results pave the way to all-oxide superconducting memory in which superconductivity modulates the magnetic state.

Dynamical properties of quasiparticles emerged in a nodal ring optical lattice

Abstract The dynamics of nodal ring quasiparticles (NRQPs) has been studied in an optical lattice. By tuning the lattice parameters, one can realize a Lifshits phase transition from a nodal ring semi-metallic to a band insulating phase. For the case where the initial state is a wavepacket, an effective Hamiltonian is obtained to simulate the system's dynamics. Analytical result is explicitly derived with the effective Hamiltonian and the dynamics shows the Zitterbewegung motion. We have analyzed the effects induced by the finite width of the atomic wave packets combined with the consideration of band structure in each phase.

Realistic estimates of superconducting properties for the cuprates: reciprocal-space diagrammatic expansion combined with variational approach

We propose a systematic approach to the systems of correlated electrons, the so-called -DE-GWF method, based on reciprocal-space (-resolved) diagrammatic expansion of the variational Gutzwiller-type wave function for parametrized models of correlated fermions. The present approach, in contrast to either variational Monte-Carlo (VMC), or the recently developed real-space diagrammatic expansion of the Gutzwiller-type wave function (direct-space DE-GWF technique), is applicable directly in the thermodynamic limit and thus is suitable for describing selected singular features of the wave-vector-dependent quantities. We employ the -DE-GWF method to extract the non-analytic part of the two leading moments of the fermion spectral-density function across the (two-dimensional) Brillouin zone for the Hubbard model and away from the half-filling. Those moments are used to evaluate the nodal quasiparticle velocities and their spectral weights in the correlated superconducting state. The two velocities determined in that manner exhibit scaling with the electron concentration qualitatively different from that obtained earlier for the excited states of the high-Tc cuprates within the projected quasi-particle ansatz, and the results are in a very good quantitative agreement with experimental data if interpreted as those characterizing the spectrum below and above the observed kink. We provide a detailed discussion of the two gaps and two excitation branches (two velocities) appearing naturally within our DE-GWF approach. The two separate sets of characteristics distinguish the renormalized quasiparticle states very close to the Fermi surface from the deeper correlated-state properties. Also, an enhancement of the -dependent magnetic susceptibility is shown to contain a spin-fluctuation contribution within our language. Finally, the -DE-GWF approach is compared to both the VMC and real-space DE-GWF results for the cases of Hubbard and t-J-U models.

Searching for Gap Zeros in Sr2RuO4 via Field-Angle-Dependent Specific-Heat Measurement

The gap structure of Sr$_2$RuO$_4$, which is a longstanding candidate for a chiral p-wave superconductor, has been investigated from the perspective of the dependence of its specific heat on magnetic field angles at temperatures as low as 0.06 K ($\sim 0.04T_{\rm c}$). Except near $H_{\rm c2}$, its fourfold specific-heat oscillation under an in-plane rotating magnetic field is unlikely to change its sign down to the lowest temperature of 0.06 K. This feature is qualitatively different from nodal quasiparticle excitations of a quasi-two-dimensional superconductor possessing vertical lines of gap minima. The overall specific-heat behavior of Sr$_2$RuO$_4$ can be explained by Doppler-shifted quasiparticles around horizontal line nodes on the Fermi surface, whose in-plane Fermi velocity is highly anisotropic, along with the occurrence of the Pauli-paramagnetic effect. These findings, in particular, the presence of horizontal line nodes in the gap, call for a reconsideration of the order parameter of Sr$_2$RuO$_4$.

Rapid enhancement of nodal quasiparticle mass with heavily underdoping in Bi2212

We report substantial advance of our low-energy angle-resolved photoemission study of nodal quasiparticles in Bi2Sr2CaCu2O8+δ. The new data cover the samples from underdoped down to heavily underdoped levels. We also present the nodal Fermi velocities that determined by using an excitation-photon energy of hν=7.0 eV over a wide doping range. The consistency between the results with hν=8.1 and 7.0eV allows us to rule out the effect of photoemission matrix elements. In comparison with the data previously reported, the nodal effective mass increases by a factor of ∼1.5 in going from optimally doped to heavily underdoped levels. We find a rapid enhancement of the nodal quasiparticle mass at low doping levels near the superconductor-to-insulator transition. The effective coupling spectrum, λ(ω), is extracted directly from the energy derivatives of the quasiparticle dispersion and scattering rate, as a causal function of the mass enhancement factor. A steplike increase in Reλ(ω) around ∼ 65meV is demonstrated clearly by the Kramers-Kronig transform of Imλ(ω). To extract the low-energy renormalization effect, we calculated a simple model for the electron-boson interaction. This model reveals that the contribution of the renormalization at |ω|≤15meV to the quasiparticle mass is larger than that around 65meV in underdoped samples.

Superconducting symmetries and magnetic responses of uranium heavy-fermion systems UBe13 and UPd2Al3

Low-temperature thermodynamic investigation for UBe13 and UPd2Al3 were performed in order to gain insight into their unusual ground states of 5f electrons. Our heat-capacity data for the cubic UBe13 strongly suggest that nodal quasiparticles are absent and its superconducting (SC) gap is fully open over the Fermi surface. Moreover, two unusual thermodynamic anomalies are also observed in UBe13 at ∼ 3T and ∼ 9T; the lower-field anomaly is seen only in the SC mixed state by dc magnetization M(H) as well as heat-capacity C(H), while the higher-field anomaly appears for C(H) in the normal phase above the upper critical field. On the other hand, field-orientation dependence of the heat capacity in the hexagonal UPd2Al3 shows a significantly anisotropic behavior of C(H)∝H1/2, reflecting the nodal gap structure of this system. Our result strongly suggests the presence of a horizontal line node on the Fermi surface with heavy effective mass in UPd2Al3.

Photoinduced filling of near-nodal gap in Bi2Sr2CaCu2O8+δ

We report time and angle resolved spectroscopic measurements in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The spectral function is monitored as a function of temperature, photoexcitation density and delay time from the pump pulse. According to our data, the superconducting gap becomes slightly stiffer when moving off the nodal direction. The nodal quasiparticles develop a faster dynamics when pumping the superconductor with a fluence that is large enough to induce the total collapse of the gap. We discuss the observed relaxation in terms of a dynamical reformation of Cooper pairs.

Switching dynamics of the spin density wave in superconducting CeCoIn5

The ordering wave vector $\mathbf{Q}$ of a spin density wave (SDW), stabilized within the superconducting state of $\mathrm{CeCoIn_5}$ in a high magnetic field, has been shown to be hypersensitive to the direction of the field. $\mathbf{Q}$ can be switched from a nodal direction of the $d$-wave superconducting order parameter to a perpendicular node by rotating the in-plane magnetic field through the antinodal direction within a fraction of a degree. Here, we address the dynamics of the switching of $\mathbf{Q}$. We use a free energy functional based on the magnetization density, which describes the condensation of magnetic fluctuations of nodal quasiparticles, and show that the switching process includes closing of the SDW gap at one $\mathbf{Q}$ and then reopening the SDW gap at another $\mathbf{Q}$ perpendicular to the first one. The magnetic field couples to $\mathbf{Q}$ through the spin-orbit interaction. Our calculations show that the width of the hysteretic region of switching depends linearly on the deviation of magnetic field from the critical field associated with the SDW transition, consistent with our thermal conductivity measurements. The agreement between theory and experiment supports our scenario of the hypersensitivity of the $Q$ phase on the direction of magnetic field, as well as the magnon condensation as the origin of the SDW phase in $\mathrm{CeCoIn_5}$.

Charge- 4e superconductors: A Majorana quantum Monte Carlo study

Many features of charge-4e superconductors remain unknown because even the "mean-field Hamiltonian" describing them is an interacting model. Here we introduce an interacting model to describe a charge-4e superconductor (SC) deep in the superconducting phase, and explore its properties using quantum Monte Carlo (QMC) simulations. The QMC is sign-problem-free, but only when a Majorana representation is employed. As a function of the chemical potential we observe two sharply-distinct behaviors: a "strong" quarteting phase in which charge-4e quartets are tightly bound (like molecules) so that charge-2e pairing does not occur even in the temperature $T \to 0$ limit, and a "weak" quarteting phase in which a further transition to a charge-2e superconducting phase occurs at a lower critical temperature. Analogous issues arise in a putative Z4 spin-liquid with a pseudo-Fermi surface and in characterizing charge-2e SCs with "odd frequency pairing" (or equivalently with a "composite order parameter") and metallic spin-nematics. Under certain circumstances, we also identified a stable T=0 charge-4e SC phase with gapless nodal quasiparticles. We further discuss possible relevance of our results to various experimental observations in 1/8-doped LBCO.

Omnidirectional Measurements of Angle-Resolved Heat Capacity for Complete Detection of Superconducting Gap Structure in the Heavy-Fermion AntiferromagnetUPd2Al3

Quasiparticle excitations in UPd_{2}Al_{3} were studied by means of heat-capacity (C) measurements under rotating magnetic fields using a high-quality single crystal. The field dependence shows C(H)∝H^{1/2}-like behavior at low temperatures for both two hexagonal crystal axes, i.e., H∥[0001] (c axis) and H∥[112[over ¯]0] (a axis), suggesting the presence of nodal quasiparticle excitations from heavy bands. At low temperatures, the polar-angle (θ) dependence of C exhibits a maximum along H∥[0001] with a twofold symmetric oscillation below 0.5T, and an unusual shoulder or hump anomaly has been found around 30°-60° from the c axis in C(θ) at intermediate fields (1≲μ_{0}H≲2 T). These behaviors in UPd_{2}Al_{3} purely come from the superconducting nodal quasiparticle excitations, and can be successfully reproduced by theoretical calculations assuming the gap symmetry with a horizontal linear line node. We demonstrate the whole angle-resolved heat-capacity measurements done here as a novel spectroscopic method for nodal gap determination, which can be applied to other exotic superconductors.

Bipartite electronic superstructures in the vortex core of Bi2Sr2CaCu2O8+δ.

The central issue in the physics of cuprate superconductivity is the mutual relationship among superconductivity, pseudogap and broken-spatial-symmetry states. A magnetic field B suppresses superconductivity, providing an opportunity to investigate the competition among these states. Although various B-induced electronic superstructures have been reported, their energy, spatial and momentum-space structures are unclear. Here, we show using spectroscopic-imaging scanning tunnelling microscopy on Bi2Sr2CaCu2O8+δ that there are two distinct B-induced electronic superstructures, both being localized in the vortex core but appearing at different energies. In the low-energy range where the nodal Bogoliubov quasiparticles are well-defined, we observe the so-called vortex checkerboard that we identify as the B-enhanced quasiparticle interference pattern. By contrast, in the high-energy region where the pseudogap develops, the broken-spatial-symmetry patterns that pre-exist at B=0 T is locally enhanced in the vortex core. This evidences the competition between superconductivity and the broken-spatial-symmetry state that is associated with the pseudogap.

Transient Dynamics of d-Wave Superconductors after a Sudden Excitation.

Motivated by recent ultrafast pump-probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a decay channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameter, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.

Topological Weyl superconductor to diffusive thermal Hall metal crossover in theBphase ofUPt3

The recent phase sensitive measurements in the superconducting $B$-phase of UPt$_3$ provide strong evidence for the triplet, chiral $k_z(k_x \pm ik_y)^2$ pairing symmetries, which endow the Cooper pairs with orbital angular momentum projections $L _z= \pm 2$ along the $c$-axis. In the absence of disorder such pairing can support both line and point nodes, and both types of nodal quasiparticles exhibit nontrivial topology in the momentum space. The point nodes, located at the intersections of the closed Fermi surfaces with the $c$-axis, act as the double monopoles and the antimonopoles of the Berry curvature, and generalize the notion of Weyl quasiparticles. Consequently, the $B$ phase should support an anomalous thermal Hall effect, the polar Kerr effect, in addition to the protected Fermi arcs on the (1,0,0) and the (0,1,0) surfaces. The line node at the Fermi surface equator acts as a vortex loop in the momentum space and gives rise to the zero energy, dispersionless Andreev bound states on the (0,0,1) surface. At the transition from the $B$-phase to the $A$-phase, the time reversal symmetry is restored, and only the line node survives inside the $A$-phase. As both line and double-Weyl point nodes possess linearly vanishing density of states, we show that weak disorder acts as a marginally relevant perturbation. Consequently, an infinitesimal amount of disorder destroys the ballistic quasiparticle pole, while giving rise to a diffusive phase with a finite density of states at the zero energy. The resulting diffusive phase exhibits $T$-linear specific heat, and an anomalous thermal Hall effect. We predict that the low temperature thermodynamic and transport properties display a crossover between a ballistic thermal Hall semimetal and a diffusive thermal Hall metal.