Tracing the dynamics of superconducting order via transient terahertz third-harmonic generation.

Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity has attracted much of attention. To identify nonequilibrium superconductivity, it is necessary to measure fingerprints of superconductivity on ultrafast timescales. Recently, nonlinear THz third-harmonic generation (THG) was shown to directly probe the collective degrees of freedoms of the superconducting condensate, including the Higgs mode. Here, we extend this idea to light-driven nonequilibrium states in superconducting La2-xSrxCuO4, establishing an optical pump-THz-THG drive protocol to access the transient superconducting order-parameter quench and recovering on few-picosecond timescales. We show in particular the ability of two-dimensional TH spectroscopy to disentangle the effects of optically excited quasiparticles from the pure order-parameter dynamics, which are unavoidably mixed in the pump-driven linear THz response. Benchmarking the gap dynamics to existing experiments shows the ability of driven THG spectroscopy to overcome these limitations in ordinary pump-probe protocols.

Fano interference between collective modes in cuprate high-Tc superconductors.

Cuprate high-Tc superconductors are known for their intertwined interactions and the coexistence of competing orders. Uncovering experimental signatures of these interactions is often the first step in understanding their complex relations. A typical spectroscopic signature of the interaction between a discrete mode and a continuum of excitations is the Fano resonance/interference, characterized by the asymmetric light-scattering amplitude of the discrete mode as a function of the electromagnetic driving frequency. In this study, we report a new type of Fano resonance manifested by the nonlinear terahertz response of cuprate high-Tc superconductors, where we resolve both the amplitude and phase signatures of the Fano resonance. Our extensive hole-doping and magnetic field dependent investigation suggests that the Fano resonance may arise from an interplay between the superconducting fluctuations and the charge density wave fluctuations, prompting future studies to look more closely into their dynamical interactions.

Quench-drive spectroscopy of cuprates.

Cuprates are d-wave superconductors which exhibit a rich phase diagram: they are characterized by superconducting fluctuations even above the critical temperature, and thermal disorder can reduce or suppress the phase coherence. However, photoexcitation can have the opposite effect: recent experiments have shown an increasing phase coherence in optimally doped BSCCO with mid-infrared driving. Time-resolved terahertz spectroscopies are powerful techniques to excite and probe the non-equilibrium states of superconductors, directly addressing collective modes, such as amplitude (Higgs) oscillations. In this work, we calculate the full time evolution of the current generated by a cuprate with a quench-drive spectroscopy setup. Analyzing the response in Fourier space with respect to both the real time and the quench-drive delay time, we look for the signature of a transient modulation of higher harmonics, as well as the Higgs mode, in order to characterize the ground state phase. In particular, this approach can provide a smoking gun for induced or increased phase coherence when applied to the pseudogap phase. These results can pave the way for future experimental schemes to characterize and study superconductors alongside incoherent phases and phase transitions, including induced and transient superconductivity.

Phase-resolved Higgs response in superconducting cuprates.

In high-energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be inferred from the decay product of the Higgs boson, i.e., the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a close analogy to the Higgs field. Interaction between the Cooper pairs and other degrees of freedom provides dissipation channels for the amplitude mode, which may reveal important information about the microscopic pairing mechanism. To this end, we investigate the Higgs (amplitude) mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG). In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above Tc.

Anomalous Nonlocal Conductance as a Fingerprint of Chiral Majorana Edge States.

A chiral p-wave superconductor is the primary example of topological systems hosting chiral Majorana edge states. Although candidate materials exist, the conclusive signature of chiral Majorana edge states has not yet been observed in experiments. Here, we propose a smoking-gun experiment to detect the chiral Majorana edge states on the basis of theoretical results for the nonlocal conductance in a device consisting of a chiral p-wave superconductor and two ferromagnetic leads. The chiral nature of Majorana edge states causes an anomalously long-range and chirality-sensitive nonlocal transport in these junctions. These two drastic features enable us to identify the moving direction of chiral Majorana edge states in the single experimental setup.

Coherent order parameter oscillations in the ground state of the excitonic insulator Ta2NiSe5.

The excitonic insulator is an intriguing electronic phase of condensed excitons. A prominent candidate is the small bandgap semiconductor Ta2NiSe5, in which excitons are believed to undergo a Bose-Einstein condensation-like transition. However, direct experimental evidence for the existence of a coherent condensate in this material is still missing. A direct fingerprint of such a state would be the observation of its collective modes, which are equivalent to the Higgs and Goldstone modes in superconductors. We report evidence for the existence of a coherent amplitude response in the excitonic insulator phase of Ta2NiSe5. Using nonlinear excitations with short laser pulses, we identify a phonon-coupled state of the condensate that can be understood as a novel amplitude mode. The condensate density contribution substantiates the picture of an electronically driven phase transition and characterizes the transient order parameter of the excitonic insulator as a function of temperature and excitation density.

Effect of quantum tunneling on spin Hall magnetoresistance.

We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on the spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y3Fe5O12) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.

Erratum: Minimal Model of Spin-Transfer Torque and Spin Pumping Caused by the Spin Hall Effect [Phys. Rev. Lett. 115, 217203 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.115.217203.

Leggett Modes and the Anderson-Higgs Mechanism in Superconductors without Inversion Symmetry.

We develop a microscopic and gauge-invariant theory for collective modes resulting from the phase of the superconducting order parameter in noncentrosymmetric superconductors. Considering various crystal symmetries, we derive the corresponding gauge mode ω_{G}(q) and find, in particular, new Leggett modes ω_{L}(q) with characteristic properties that are unique to noncentrosymmetric superconductors. We calculate their mass and dispersion that reflect the underlying spin-orbit coupling and thus the balance between triplet and singlet superconductivity occurring simultaneously. Finally, we demonstrate the role of the Anderson-Higgs mechanism: while the long-range Coulomb interaction shifts ω_{G}(q) to the condensate plasma mode ω_{P}(q), it leaves the mass Λ_{0} of the new Leggett mode unaffected and only slightly modifies its dispersion.

Minimal Model of Spin-Transfer Torque and Spin Pumping Caused by the Spin Hall Effect.

In the normal-metal-ferromagnetic-insulator bilayer (such as Pt/Y_{3}Fe_{5}O_{12}) and the normal-metal-ferromagnetic-metal-oxide trilayer (such as Pt/Co/AlO_{x}) where spin injection and ejection are achieved by the spin Hall effect in the normal metal, we propose a minimal model based on quantum tunneling of spins to explain the spin-transfer torque and spin pumping caused by the spin Hall effect. The ratio of their dampinglike to fieldlike component depends on the tunneling wave function that is strongly influenced by generic material properties such as interface s-d coupling, insulating gap, and layer thickness, yet the spin relaxation plays a minor role. The quantified result renders our minimal model an inexpensive tool for searching for appropriate materials.

Spin-orbital coupling in a triplet superconductor-ferromagnet junction.

We study the interplay of spin and orbital degrees of freedom in a triplet superconductor-ferromagnet junction. Using a self-consistent spatially dependent mean-field theory, we show that increasing the angle between the ferromagnetic moment and the triplet vector order parameter enhances or suppresses the p-wave gap close to the interface, according to whether the gap antinodes are parallel or perpendicular to the boundary, respectively. The associated change in condensation energy establishes an orbitally dependent preferred orientation for the magnetization. When both gap components are present, as in a chiral superconductor, first-order transitions between different moment orientations are observed as a function of the exchange field strength.

Functional superconductor interfaces from broken time-reversal symmetry.

The breaking of time-reversal symmetry in a triplet superconductor Josephson junction is shown to cause a magnetic instability of the tunneling barrier. Using a Ginzburg-Landau analysis of the free energy, we predict that this novel functional behavior reflects the formation of an exotic Josephson state, distinguished by the existence of fractional flux quanta at the barrier. The crucial role of the orbital pairing state is demonstrated by studying complementary microscopic models of the junction. Signatures of the magnetic instability are found in the critical current of the junction.

0-pi transition in magnetic triplet superconductor josephson junctions.

We examine a Josephson junction involving two arbitrary equal-spin-pairing unitary triplet superconductors and a ferromagnetic tunneling barrier. Using perturbation theory, we show how the interaction of the barrier moment with the spin of the tunneling triplet Cooper pairs can reverse the sign of the Josephson charge current. This also results in a Josephson spin current, which contains a phase-independent contribution due to reflection processes at the barrier. We verify our analytic predictions using a nonperturbative Bogoliubov-de Gennes method.

Electronic Raman scattering in noncentrosymmetric superconductors.

We formulate a theory for the polarization dependence of the electronic (pair-breaking) Raman response for the recently discovered noncentrosymmetric superconductors in the clean limit at zero temperature. Possible applications include the systems CePt3Si and Li2PdxPt3-xB which reflect the two important classes of the involved spin-orbit coupling. We provide analytical expressions for the Raman vertices for these two classes and calculate the polarization dependence of the electronic spectra. We predict a two-peak structure and different power laws with respect to the unknown relative magnitude of the singlet and triplet contributions to the superconducting order parameter, revealing a large variety of characteristic fingerprints of the underlying condensate.

Momentum dependence of the electron-phonon coupling and self-energy effects in superconducting YBa2Cu3O7 within the local density approximation.

Using the local density approximation and a realistic phonon spectrum we determine the momentum and frequency dependence of alpha(2)F(k,omega) in YBa(2)Cu(3)O(7) for the bonding, antibonding, and chain band. The resulting self-energy Sigma is rather small near the Fermi surface. For instance, for the antibonding band the maximum of ReSigma as a function of frequency is about 7 meV at the nodal point in the normal state and the ratio of bare and renormalized Fermi velocities is 1.18. These values are a factor of 3-5 too small compared to the experiment showing that only a small part of Sigma can be attributed to phonons. Furthermore, the frequency dependence of the renormalization factor Z(k,omega) is smooth and has no anomalies at the observed kink frequencies which means that phonons cannot produce well-pronounced kinks in stoichiometric YBa(2)Cu()3)O(7), at least, within the local density approximation.

Novel Josephson effect in triplet-superconductor-ferromagnet-triplet-superconductor junctions.

We predict a novel type of Josephson effect to occur in triplet-superconductor-ferromagnet-triplet-superconductor Josephson junctions. We show that the Josephson current, IJ, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional sign change of IJ with increasing temperature.