Excitations In Superconductors Research Articles

Phase crystals

Superconductivity owes its properties to the phase of the electron pair condensate that breaks the $U(1)$ symmetry. In the most traditional ground state, the phase is uniform and rigid. The normal state can be unstable towards special inhomogeneous superconducting states: the Abrikosov vortex state, and the Fulde-Ferrell-Larkin-Ovchinnikov state. Here we show that the phase-uniform superconducting state can go into a fundamentally different and more ordered non-uniform ground state, that we denote as a phase crystal. The new state breaks translational invariance through formation of a spatially periodic modulation of the phase, manifested by unusual superflow patterns and circulating currents, that also break time-reversal symmetry. We list the general conditions needed for realization of phase crystals. Using microscopic theory we then derive an analytic expression for the superfluid density tensor for the case of a non-uniform environment in a semi-infinite superconductor. We demonstrate how the surface quasiparticle states enter the superfluid density and identify phase crystallization as the main player in several previous numerical observations in unconventional superconductors, and predict existence of a similar phenomenon in superconductor-ferromagnetic structures. This analytic approach provides a new unifying aspect for the exploration of boundary-induced quasiparticles and collective excitations in superconductors. More generally, we trace the origin of phase crystallization to non-local properties of the gradient energy, which implies existence of similar pattern-forming instabilities in many other contexts.

Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor (Li0.84Fe0.16)OHFeSe**Supported by the National Natural Science Foundation of China, the National Key R&D Program of China under Grant Nos 2016YFA0300200, 2017YFA0303004 and 2017YFA0303003, and the Key Research of Frontier Sciences of CAS under Grant No QYZDY-SSW-SLH001.

The Majorana zero mode (MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in (Li0.84Fe0.16)OHFeSe. Here using scanning tunneling spectroscopy, we demonstrate that Majorana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state, and consequently, the conductance at zero bias is quantized as 2e2/h. Our results present a hallmark signature of the MZM in the vortex of an intrinsic topological superconductor, together with its intriguing behavior.

Surface symmetry breaking and disorder effects on superconductivity in perovskite BaBi3 epitaxial films

The structural or electronic symmetry breaking of the host lattice is a recurrent phenomenon in many quantum materials, including superconductors. Yet, how these broken symmetry states affect the electronic pair wave function of superconductivity have been rarely elucidated. Here, using low-temperature scanning tunneling microscopy and first-principles calculations, we identify the broken rotational symmetry via stripe ordering on the (001) surface of perovskite BaBi3 films grown by molecular beam epitaxy, and show that it consequently leads to anisotropic superconductivity with twofold symmetry. In contrast, the structural disorder smears out the anisotropy of electron pairing and fills superconducting subgap density of states as the film thickness is reduced. A quasi-long range model of superconducting fluctuations is revealed to describe the tunneling conductance spectra of thin BaBi3 films well, and to exemplify how disorders contribute to the low-energy quasiparticle excitations in superconductors. Our findings help understand the effects of symmetry breaking states and disorders on superconductivity, particularly the existing tunneling conductance spectra there.

Neutral edge modes in a superconductor–topological-insulator hybrid structure in a perpendicular magnetic field

We study the low-energy edge states of a superconductor–3D topological-insulator hybrid structure (NS junction) in the presence of a perpendicular magnetic field. The hybridization of electron-like and hole-like Landau levels due to Andreev reflection gives rise to chiral edge states within each Landau level. We show that by changing the chemical potential of the superconductor, this junction can be placed in a regime where the sign of the effective charge of the edge state within the zeroth Landau level changes more than once resulting in neutral edge modes with a finite value of the guiding-center coordinate. The appearance of these neutral edge modes is related to the level repulsion between the zeroth and the first Landau levels in the spectra. We also find that these neutral edge modes come in pairs, one in the zeroth Landau level and its corresponding pair in the first. Unlike ordinary neutral bogolon excitations in superconductors, the neutral modes found by us have a finite speed and, thus, the potential to carry a heat current.

Fermion Pairing in Flatland

Superconductivity and superfluidity in two dimensions (2D) has long been a subject of great interest. Materials with the highest known transition temperature Tc, the cuprates, are quasi-2D systems with superconductivity originating in the 2D copper-oxide planes. A deeper understanding of strongly interacting 2D superconductors and their normal states could potentially give insights into the unsolved problem of high-Tc superconductivity. Further, 2D is known to be the lower critical, or marginal, dimension both for pairing of fermions and for superfluidity. Thus 2D represents a borderline dimensionality, above and below which the system behaves qualitatively differently from a classical and a quantum perspective. Classically, thermal fluctuations of the order parameter destroy long-range order in 2D and lead to algebraic order at finite temperatures. In quantum mechanics, 2D is the marginal dimension for bound-state formation, which has important implications for the pairing of fermions that is essential for superfluidity. Finally, the effects of strong interactions in 2D Fermi systems present a formidable theoretical challenge. A paper [1] appearing in Physical Review Letters reports experiments with ultracold Fermi gas of lithium-6 atoms that give new insight into how dimensionality and interactions affect the binding of fermions to form a superfluid. Ariel Sommer and his colleagues at the Massachusetts Institute of Technology, Cambridge, use two independent knobs: a magnetic field to tune interatomic interactions and an optical lattice to tune the dimensionality between 3D and 2D. They then use radio-frequency (rf) spectroscopy to probe pairing in the many-particle system and relate it to bound-state formation in the twobody problem in the 2D limit. Although theorists have predicted how this pairing energy evolves with interaction strength and dimensionality, until now there were no real systems on which to test these ideas. In recent years there has been tremendous progress in controlling the interaction between atoms in ultracold gases with the Feshbach resonance technique, in which a magnetic field is used to tune the attractive s-wave interaction between Fermi atoms in two different hyperfine states [2–4]. This is the analog of tuning the attraction between spin-up and spin-down electrons in a metal, which is, of course, impossible in solid-state materials. An important outcome of this progress has been the ability to explore the crossover from a condensate of Cooper pairs, described by Bardeen-Cooper-Schrieffer (BCS) theory, to a Bose-Einstein condensate (BEC) of tightly bound diatomic molecules in 3D ultracold gases. The most significant new insights have come from studies of the very strongly interacting states at resonance [2, 3], which has scale-invariant properties [4] analogous to problems in nuclear physics and string theory. The experiment of Sommer et al.[1] builds on all of this progress with an optical lattice, which is a periodic potential that arises from interfering laser beams. By tuning the strength of this potential, V0, one can go from an anisotropic 3D system, for weak V0, to an essentially decoupled stack of 2D layers, in the limit of strong V0, which is shown schematically in Fig. 1. The MIT team probes the pairing between atoms with rf spectroscopy [2], in which photons transfer Fermi atoms from one hyperfine state to another. The resulting absorption intensity as a function of photon energy has a characteristic asymmetric line shape with a threshold for bound-to-free transitions that contains information about the spectrum of fermionic excitations. The meanfield theory for a BCS-BEC crossover predicts that the rf threshold is given by [2] hωth = √ μ2 + ∆2 − μ, where μ is the chemical potential and ∆ the BCS gap parameter. It is important to emphasize that the rf threshold is not simply ∆, in contrast to spectroscopic probes of electronic excitations in superconductors like tunneling. The reason is that rf photons excite Fermi atoms in all k states and the threshold is determined by k = 0 fermions. Sommer et al. interpret the rf threshold hωth as the “pair binding energy” in the many-body system. In 2D, the zero temperature mean-field equations for

Vortex core excitations in superconductors with frustrated antiferromagnetism

Motivated by recent discovery of cobalt oxide and organic superconductors, we apply an effective model with strong antiferromagnetic and superconducting pairing interaction to a related lattice structure. It is found that the antiferromagnetism is highly frustrated and a broken-time-reversal-symmetry chiral d+id′-wave pairing state prevails. In the mixed state, we have solved the local electronic structure near the vortex core and found no local induction of antiferromagnetism. This result is in striking contrast to the case of copper oxide superconductors. The calculated local density of states indicates the existence of low-lying quasiparticle bound states inside the vortex core, due to a fully gapped chiral pairing state. The prediction can be directly tested by scanning tunneling microscopy.

Anisotropic spin and charge excitations in superconductors: Signature of electronic nematic order

We study spin and charge susceptibilities in the d-wave superconducting state whose underlying electronic dispersion is anisotropic due to the formation of the electronic nematic order. We show that the amplitude of the incommensurate peaks in the spin susceptibility near (\pi,\pi) reveals a pronounced anisotropy in the momentum space. The relevance of our findings to the magnetic scattering pattern observed in a recent neutron scattering measurement on untwinned YBa_2Cu_3O_{6+x} is discussed. In the charge channel, we identify a well-defined collective mode at small momentum transfer with strong anisotropic amplitude depending on the direction of momentum transfer, which is associated with the broken symmetry due to nematic ordering.

Magnetic penetration depth of MgB 2

The low temperature behaviour of the magnetic penetration depth λ( T) provides a useful probe of the low lying excitations in superconductors and hence of the anisotropy of the superconducting energy gap. In this paper, we will present measurements of the penetration depth in the Meissner state of both single crystal and polycrystalline samples of MgB 2, using a very low field RF technique. λ( T) shows a clear exponential temperature dependence T/ T c≲0.2, strongly indicating that this material is fully gapped. Detailed fits to the superfluid density over the full temperature range of our measurements (1> T/ T c>0.04) gives strong support for the existence of two distinct superconducting gaps, Δ s=29 K and Δ b =75 K, in agreement with recent theoretical predictions and other probes.

Higgs Boson in Superconductors

Superfluid helium, describable by a two-component order parameter, exhibits only the Bogolubov mode with energy →0 at long wavelengths, while aLorentz-invariant theory with a two-component order parameter exhibits a finite energy mode at long wavelengths (the Higgs boson), besides the above mass-less mode. The mass-less mode moves to high energies if it couples to electromagnetic fields (the Anderson-Higgs mechanism). Superconductors, on the other hand have been theoretically and experimentally shown to exhibit both modes. This occurs because the excitations in superconductors have an (approximate) particle-hole symmetry and therefore show a similarity to Lorentz-invariant theories.

D-Wave superconductors and quantum computers

Quantum algorithms promise enormous speed up in dealing with certain problem classes, but only in large enough quantum computers (about thousand qubits). Therefore the scalability of solid state devices make solid-state-based qubit prototypes an attractive choice. On the other side, it is difficult to preserve quantum coherence in such devices, in the presence of macroscopic number of degrees of freedom. The coherent ground state and suppression of low-energy excitations in superconductors could help solve the problems. Recent experiments on several mesoscopic qubit prototypes, using conventional superconductors, demonstrated coherent quantum behavior. Here I review the current results on qubit prototypes based on high- T c superconductors, and discuss the open questions and the further directions of research.

Macroscopic excitations in superconductors

Flux creep due to the motion of macroscopic quantum excitations is decribed with a macroscopic approach. The quantities characterizing the flux creep, calculated by means of the presented theory, have the same order of magnitude as those extracted from experiments. The dependence of the magnetic moment relaxation rate on time, temperature, and magnetic field is derived and compared with experimental data. The nonlinear dependence of the magnetic moment on the logarithm of time is obtained. The characteristic energy barrier depends very strongly on the magnetic field penetration depth and can become small even away from the critical temperature. The finiteness of the sample causes the linear dependence of the electric field on the current density (Ohm’s law) for sufficiently small current densities.

Collective excitations in superconductors: From Bardeen-Cooper-Schrieffer theory to Bose condensation.

We study the collective excitations of a system with local attractive interactions as a function of the coupling strength. The two-particle excitations are obtained in the random-phase approximation. For the strong-coupling limit we reproduce the excitation spectrum of a hard-core Bose gas, while in the weak-coupling limit we obtained a spectrum consistent with the BCS picture. The evolution of the excitation spectrum from the weak- to the strong-coupling limits is continuous. We briefly discuss the effect of these excitations in the thermodynamic properties of the system.

Collective excitations in superconductors with structural transition

In this paper we have found new low-frequency collective excitations in superconductors with structural transformation. The connection between our results and the experiments on Raman scattering in 2H-NbSe 2 cDw- superconductor is discussed.

Dielectric response functions in the problem of longitudinal collective mode excitation in superconductors

General methods of the electrodynamics of media with spatial and frequency dispersion are used to develop a formalism for the dielectric functions of the response of a superconducting metal to electromagnetic perturbations. The transformation of electromagnetic waves into long-wave oscillations of the longitudinal field in a superconductor is investigated. The temperature and frequency dependences of the collective mode contribution to the superconductor surface impedance are found. Resonant excitation of a collective mode in superconducting samples of finite size is predicted, which may result in selective transparency of superconducting films.

Cooper coupling of electrons in strong high-frequency fields

Abstract Kinetics equations have been obtained for electronic excitations in superconductors exposed to a longitudinal high-frequency sound and a uniform high-frequency electromagnetic field. It is shown that the equations determining the nonequilibrium energy gap of a superconductor contain not only the nonequilibrium distribution function of quasiparticles, but also the explicit external pumping.

Collective excitations in superconductors belowTc

Fluctuations of tunneling currents through Josephson junctions are investigated for clean superconductors in the vicinity below ${T}_{c}$. The collective quasiparticle excitations, leading to a maximum in the structure function of the order-parameter phase, also affect the longitudinal dielectric function $\ensuremath{\epsilon}$. A minimum in $\mathrm{Im}(\frac{1}{\ensuremath{\epsilon}})$ is the counterpart to the phase maximum. It is also present in dirty samples, but disappears in the gapless case. The longitudinal ultrasonic spectrum is discussed for clean and dirty probes. Besides the ordinary sound one finds a second maximum in the spectrum on account of the collective motion of the electrons below ${T}_{c}$.

Coherent behavior of two interacting Dayem bridges

Two superconducting thin-film microbridges (Dayem bridges) fabricated in the same tin or indium film and situated only a few micrometers apart can have their Josephson frequencies locked to each other when their dc voltages are approximately matched (independent of their relative sign). We have in a number of cases studied the results of such an interaction in the current-voltage characteristics and in the total emitted Josephson radiation. The threshold for observing a mutual locking depends on the quality of the Dayem bridges as well as on the distance between the two bridges. For tin we have so far obtained coherent behavior for two Dayem bridges at a distance of up to 12 µm. For indium the corresponding distance was 3.5 µm. A tentative model of the interaction is proposed. This model includes the suggestion of a propagating current/branch imbalance excitation in superconductors.

Collective excitations in superconductors

The excitations connected with quantum condensation of a fermion gas are calculated quantitatively along the lines of a previous paper. We find exact agreement with earlier results: excitations of the phonon type in the absence of Coulomb interaction, strong indications for their nonexistence in the presence of this interaction.

Phonon linewidths measured by neutron scattering

Two Brookhaven experimenters, John D. Axe and Gen Shirane, have used inelastic neutron scattering to detect the influence of the superconducting energy gap upon phonon lifetimes in Nb3Sn. Speaking at the January meeting of the American Physical Society in New York, Axe said their results yield estimates of the superconducting energy gap and the size and anisotropy of the electron‐phonon coupling. Axe and Shirane feel that their method of using inelastic neutron scattering will be useful in studying lowlying electron excitations in superconductors.

Nonequilibrium excitations in superconductors in high-frequency fields

Nonequilibrium excitations in superconductors in high-frequency fields