Long-range Phase Coherence Research Articles

Emergence of long-range phase coherence in nonlocal fluids of light

The emergence of long-range phase coherence among random nonlinear waves is a fascinating effect that characterizes fundamental phenomena such as the condensation of nonlinear waves and the related manifestation of superfluidity of certain turbulent flows. Here we report a previously unrecognized phenomenon of spontaneous emergence of long-range phase coherence among incoherent waves interacting through a nonlocal nonlinearity. The theory reveals that the establishment of long-range phase coherence constitutes a generic property of a conservative (Hamiltonian) system of highly nonlocal random waves that evolve in the strongly nonlinear regime. Aside from phase coherence, the field exhibits intensity fluctuations whose coherence length is shown to increase in a dramatic way during the evolution of the system. The analysis can be transposed to the temporal domain, revealing the emergence of temporal phase coherence among incoherent waves propagating in nonlinear materials featured by a noninstantaneous nonlinear response.

Local resilience of the 1T−TiSe2 charge density wave to Ti self-doping

In Ti-intercalated self-doped $1T$-TiSe$_2$ crystals, the charge density wave (CDW) superstructure induces two nonequivalent sites for Ti dopants. Recently, it has been shown that increasing Ti doping dramatically influences the CDW by breaking it into phase-shifted domains. Here, we report scanning tunneling microscopy and spectroscopy experiments that reveal a dopant-site dependence of the CDW gap. Supported by density functional theory, we demonstrate that the loss of the longrange phase coherence introduces an imbalance in the intercalated-Ti site distribution and restrains the CDW gap closure. This local resilient behavior of the $1T$-TiSe$_2$ CDW reveals a novel mechanism between CDW and defects in mutual influence.

Destroying Coherence in High-Temperature Superconductors with Current Flow

The loss of single-particle coherence going from the superconducting state to the normal state in underdoped cuprates is a dramatic effect that has yet to be understood. Here, we address this issue by performing angle resolved photoemission spectroscopy (ARPES) measurements in the presence of a transport current. We find that the loss of coherence is associated with the development of an onset in the resistance, in that well before the midpoint of the transition is reached, the sharp peaks in the ARPES spectra are completely suppressed. Since the resistance onset is a signature of phase fluctuations, this implies that the loss of single-particle coherence is connected with the loss of long-range phase coherence.

Macroscopic character of composite high-temperature superconducting wires

The "d-wave" symmetry of the superconducting order in the cuprate high temperature superconductors is a well established fact, and one which identifies them as "unconventional." However, in macroscopic contexts -- including many potential applications ({\it i.e.} superconducting "wires") -- the material is a composite of randomly oriented superconducting grains in a metallic matrix, in which Josephson coupling between grains mediates the onset of long-range phase coherence. Here, we analyze the physics at length scales large compared to the size of such grains, and in particular the macroscopic character of the long-range order that emerges. While XY-glass order and macroscopic d-wave superconductivity may be possible, we show that under many circumstances -- especially when the d-wave superconducting grains are embedded in a metallic matrix -- the most likely order has global s-wave symmetry.

Long-Range Phase Coherence in Double-Barrier Magnetic Tunnel Junctions with a Large Thick Metallic Quantum Well

Double-barrier heterostructures are model systems for the study of electron tunneling and discrete energy levels in a quantum well (QW). Until now resonant tunneling phenomena in metallic QWs have been observed for limited thicknesses (1-2 nm) under which electron phase coherence is conserved. In the present study we show evidence of QW resonance states in Fe QWs up to 12 nm thick and at room temperature in fully epitaxial double MgAlO_{x} barrier magnetic tunnel junctions. The electron phase coherence displayed in this QW is of unprecedented quality because of a homogenous interface phase shift due to the small lattice mismatch at the Fe-MgAlO_{x} interface. The physical understanding of the critical role of interface strain on QW phase coherence will greatly promote the development of spin-dependent quantum resonant tunneling applications.

Emergence of coherence in the charge-density wave state of 2H-NbSe2.

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature Tcdw. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at Tcdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states.

Unconventional superconductivity in ultrathin superconducting NbN films studied by scanning tunneling spectroscopy

Using scanning tunneling spectroscopy, we address the problem of the superconductor-insulator phase transition in homogeneously disordered ultrathin (2--15 nm) films of NbN. Samples thicker than 8 nm, for which the Ioffe-Regel parameter ${k}_{F}l\ensuremath{\ge}5.6$, manifest a conventional superconductivity: a spatially homogeneous BCS-like gap, vanishing at the critical temperature, and a disordered vortex lattice in magnetic field. Upon thickness reduction, however, while ${k}_{F}l$ lowers, the STS reveals striking deviations from the BCS scenario, among which a progressive decrease of the coherence peak height and small spatial inhomogeneities. In addition, the gap below ${T}_{C}$ develops on a spectral background, which becomes more and more ``V-shaped'' approaching the localization. The thinnest film (2.16 nm), while not being exactly at the superconductor-insulator transition (SIT) (${T}_{C}\ensuremath{\approx}0.4{T}_{C}^{\mathrm{bulk}}$), showed unconventional signatures such as the vanishing of the coherence peaks and the absence of vortices. This behavior suggests a weakening of long-range phase coherence, when approaching the SIT in this quasi-2D limit.

Quantum simulation of dynamical maps with trapped ions

Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to chaos. Quantum mechanical counterparts show intriguing phenomena such as dynamical localization on the single particle level. Here we extend the concept of dynamical maps to an open-system, many-particle context: We experimentally explore the stroboscopic dynamics of a complex many-body spin model by means of a universal quantum simulator using up to five ions. In particular, we generate long-range phase coherence of spin by an iteration of purely dissipative quantum maps. We also demonstrate the characteristics of competition between combined coherent and dissipative non-equilibrium evolution. This opens the door for studying many-particle non-equilibrium physics and associated dynamical phase transitions with no immediate counterpart in equilibrium condensed matter systems. An error detection and reduction toolbox that facilitates the faithful quantum simulation of larger systems is developed as a first step in this direction.

Multiple quantum criticality in a two-dimensional superconductor

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Superconductivity in the pseudogap region of Bi2Sr1.4La0.6CuO6+δfrom angular-dependent torque measurements

We show in-plane and out-of-plane angular dependent torque data on underdoped Bi${}_{2}$Sr${}_{1.4}$La${}_{0.6}$CuO${}_{6+\ensuremath{\delta}}$ single crystals. We find that the superconducting signal persists well into the normal state, at least up to twice the zero-field superconducting transition temperature ${T}_{c0}$. The superconductivity is highly anisotropic below ${T}_{c0}$, while its anisotropy decreases significantly just above ${T}_{c0}$. In this latter $T$ regime the Cooper pairs lose their long-range phase coherence.

On the possible key experiments to show the singlet-to-triplet conversion of the Cooper pairs by the use of a SFCO-method

The problem of electron pairing above Meissner expel arose when high-Tc superconductive (HTS) materials were discovered. And scientists are admitting know that there is need to consider 2 processes for HTS: electron pairing and long-range phase coherence among Cooper pairs (pair condensation) – separately and independently each other. Otherwise, it is admitted, that in HTS electrons become paired above Meissner expel (above T0, starting from Tc) & start forming SC-condensate only at T0, while in low-Tc SC materials (LTS) the pairing and pair condensation start simultaneously (T0 = Tc). But, since discovery of HTS new data appeared and importance of some earlier data was recognized, indicating analogy among the HTS and LTS in connection with these 2 processes. Here we show that there are no differences among these materials regarding the said processes: electron pairing and pair condensation are separate & independent even in LTS. Difference is in a temperature scale. For LTS these processes run in a narrow range (∼30mK), while in HTS the scale is longer (for YBaCuO, more than 3K). This is the reason why separation of Tc from T0 in LTS is so hard so far. The problem is still open also due to lack of methods for "nonperturbative" study of the beginnings of SC transition in clean (tiny) objects with small signal. Analysis of data permits to conclude that becomes urgent sensitive study of the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity in heavy-fermion materials that have layered electronic structure. And, the SFCO method may stand key tool for sensitive study of the pair formation in FFLO state. Such a study may show singlet-to-triplet conversion of Cooper pairs. It may also allow separating the ideal conducting (R = 0) & ideal diamagnetic (B = 0) states, which are important for true interpretation of a real nature of superconductivity.

Probing phase coherence in solid helium using torsional oscillators of different path lengths

Long-range phase coherence is a critical signature of macroscopic quantum phenomena. To date, nonclassical rotational inertia (NCRI) of solid helium has been reported only in samples with physical dimension of at most 5 cm. We have investigated solid helium in longer path-length torsional oscillators. Samples of length ranging from 6 to 100 cm were grown inside toroids and in self-connected long capillaries. NCRI of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ were found in cells with path length of 6 and 9 cm. In cells with path length of 30 and 100 cm, NCRI, if it exists, is less than $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, respectively.

ASPECTS OF LOCALIZATION ACROSS THE 2D SUPERCONDUCTOR-INSULATOR TRANSITION

It is well known that the metal-insulator transition in two dimensions for non-interacting fermions takes place at infinitesimal disorder. In contrast, the superconductor-to-insulator transition takes place at a finite critical disorder (on the order of Vc ~ 2t), where V is the typical width of the distribution of random site energies and t is the hopping scale. In this article we compare the localization/delocalization properties of one and two particles. Whereas the metal-insulator transition is a consequence of single-particle Anderson localization, the superconductor-insulator transition (SIT) is due to pair localization – or, alternatively, fluctuations of the phase conjugate to pair density. The central question we address is how superconductivity emerges from localized single-particle states. We address this question using inhomogeneous mean field theory and quantum Monte Carlo techniques and make several testable predictions for local spectroscopic probes across the SIT. We show that with increasing disorder, the system forms superconducting blobs on the scale of the coherence length embedded in an insulating matrix. In the superconducting state, the phases on the different blobs are coherent across the system whereas in the insulator long-range phase coherence is disrupted by quantum fluctuations. As a consequence of this emergent granularity, we show that the single-particle energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT despite a robust single-particle gap.

Modeling of superconducting stripe phases in high-Tc cuprates

Even before the experimental discovery of spin- and charge-stripe order in La2−x−yNdySrxCuO4 and La2−xBaxCuO4 at x = 1/8, stripe formation was predicted from theoretical considerations. Nevertheless, a consistent description of the complex coexistence of stripe order with superconductivity has remained a challenge. Here we introduce a Hartree–Fock decoupling scheme that unifies previous approaches and allows for a detailed analysis of the competition between antiferromagnetism and superconductivity in real and momentum space. We identify two distinct parameter regimes, where spin-stripe order coexists with either one- or two-dimensional superconductivity; experiments on different striped cuprates are compatible with either the former or the latter regime. We argue that the cuprates at x = 1/8 fall into an intermediate coupling regime with a crossover to long-range phase coherence between individual superconducting stripes.

Origin of the magnetic field induced changes of the transverse plasma mode in the c-axis infrared response of underdoped Y Ba2Cu3O7−δ

We report on results of our theoretical study of magnetic field induced changes of the c-axis infrared response of bilayer cuprate superconductors using the phenomenological multilayer model involving the conductivity of the spacing layers and that of the bilayer units. For H perpendicular to the planes, the local conductivities have been expressed in terms of a two-fluid approximation—as weighted averages of the superconducting state ones and the normal state ones representing contributions of the vortex cores, the weight of the latter increasing linearly with the field. This allows us to reproduce and interpret the fast decrease with increasing H of the well known 400 cm−1 peak (transverse plasma mode) in the c-axis conductivity, observed by LaForge and co-workers. For the local conductivities of underdoped Y Ba2Cu3O7−δ with Tc = 58 K reported by Dubroka and co-workers and the fraction of the normal state (T ≈ Tc) component given by (μ0H/25 T), the computed field induced changes of the reflectivity are in quantitative agreement with the data. This suggests that the response at H = 0 and T ≈ Tc is close to that at H = 25 T < Hc2 and T ≪ Tc, in accord with theories attributing the above Tc state to that of a superconductor lacking long-range phase coherence. Also discussed are changes of the response induced by H parallel to the CuO2 planes.

Quantum phase transition in an array of coupled dissipative cavities

The features of superfluid-Mott insulator phase transition in the array of dissipative nonlinear cavities are analyzed. We show analytically that the coupling to the bath can be reduced to renormalizing the eigenmodes of atom-cavity system. This gives rise to a localizing effect and drives the system into mixed states. For the superfluid state, a dynamical instability will lead to a sweeping to a localized state of photons. For the Mott state, a dissipation-induced fluctuation will suppress the restoring of long-range phase coherence driven by interaction.

The Meissner effect in a strongly underdoped cuprate above its critical temperature

The Meissner effect and associated perfect 'bulk' diamagnetism together with zero resistance and gap opening are characteristic features of the superconducting state. In the pseudogap state of cuprates, unusual diamagnetic signals and anomalous proximity effects have been detected, but a Meissner effect has never been observed. Here we probe the local diamagnetic response in the normal state of an underdoped La1.94Sr0.06CuO4 layer (Tc′≤5 K), which is brought into close contact with two nearly optimally doped La1.84Sr0.16CuO4 layers (Tc≈32 K). We show that the entire 'barrier' layer of thickness, much larger than the typical c axis coherence lengths of cuprates, exhibits a Meissner effect at temperatures above Tc′ but below Tc. The temperature dependence of the effective penetration depth and superfluid density in different layers indicates that superfluidity with long-range phase coherence is induced in the underdoped layer by the proximity to optimally doped layers, but this induced order is sensitive to thermal excitation.

Helical-mode magnetostatic resonances in small ferrite particles and singularmetamaterials

Small ferrite-disk particles with magnetostatic (magneto-dipole) oscillations arecharacterized by the topological-phase states—the vortex states. In a recently publishedpaper (Kamenetskii et al 2010 Phys. Rev. A 81 053823), it was shown that such magneticvortices act as traps, providing purely subwavelength confinement of electromagnetic fields.The symmetry properties of magnetostatic-vortex ferrite disks allow one to proposenew-type subwavelength microwave structures. In this paper it is demonstrated that theunique topological properties of the fields in a ferrite disk are intimately related to thesymmetry breaking effects of magnetostatic oscillations. This analysis is based onpostulates about a physical meaning of the magnetostatic-potential function as a complex scalar wavefunction, which presumes a long-range phase coherence inmagnetic dipole–dipole interactions. The proper solutions are found based on an analysis ofmagnetostatic-wave propagation in a helical coordinate system. It is shown that while acomposition of two helical waves may acquire a geometrical phase over-running of2π during a period, every separate helical wave has a dynamical phase over-running ofπ and so behaves as a double-valued function. This results in the appearance of helical-modemagnetostatic resonances in quasi-2D ferrite disks. The solutions give magnetostatic-wavepower-flow-density vortices with cores at the disk center and azimuthally running waves ofmagnetization. The near fields of magnetostatic-vortex ferrite-disk particles arecharacterized by space–time symmetry violation. For incident electromagnetic waves, suchparticles, with sizes much less than the free-space electromagnetic wavelength, appear aslocal singular regions. From the properties of a composition of magnetostatic-vortexferrite-disk particles, one may propose novel metamaterials—singular metamaterials.

Particle-hole mixing driven by the superconducting fluctuations

Development of the STM and ARPES spectroscopy enabled to reach the resolution sufficient for probing the particle-hole entanglement in superconducting materials, even above the critical temperature Tc. On a quantitative level one can characterize such entanglement in terms of the Bogoliubov angle which determines to what extent the particles and holes constitute the effective quasiparticles. In classical superconductors, where the phase transition is related to formation of the Cooper pairs almost simultaneously accompanied by onset of their long-range phase coherence, the Bogoliubov angle is slanted (due to finite particle-hole mixing) all the way up to Tc. In the high temperature superconductors and in superfluid ultracold fermion atoms near the Feshbach resonance the situation is different because the preformed pairs can exist above Tc albeit loosing coherence due to the strong quantum fluctuations. We discuss a generic temperature dependence of the Bogoliubov angle in such pseudogap state indicating a novel, non-BCS behavior. For analysis we use the two-component model describing the pairs coexisting with single fermions and study selfconsistently their feedback effects by the similarity transformation originating from the renormalization group approach.

Diamagnetism and Cooper pairing aboveTcin cuprates

In the cuprate superconductors, Nernst and torque magnetization experiments have provided evidence that the disappearance of the Meissner effect at $T_c$ is caused by the loss of long-range phase coherence, rather than the vanishing of the pair condensate. Here we report a series of torque magnetization measurements on single crystals of $\mathrm{La_{2-x}Sr_xCuO_4}$ (LSCO), $\mathrm{Bi_2Sr_{2-y}La_yCuO_6}$ (Bi 2201), $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ (Bi 2212) and optimal $\mathrm{YBa_2Cu_3O_7}$. Some of the measurements were taken to fields as high as 45 T. Focusing on the magnetization above $T_c$, we show that the diamagnetic term $M_d$ appears at an onset temperature $T^M_{onset}$ high above $T_c$. We construct the phase diagram of both LSCO and Bi 2201 and show that $T^M_{onset}$ agrees with the onset temperature of the vortex Nernst signal $T^{\nu}_{onset}$. Our results provide thermodynamic evidence against a recent proposal that the high-temperature Nernst signal in LSCO arises from a quasiparticle contribution in a charge-ordered state.