Résultats de recherche pour « Pair Density Wave Instability »

A recent scanning tunneling microscopy (STM) experiment reports the observation of charge density wave (CDW) with period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately period 4a CDW that are commonly observed in the cuprates. Inspired by this work, we study a model where a bi-directional pair density wave (PDW) with period 8 is at play. This further divides into two classes, (1) where the PDW is a competing state of the d wave superconductor and can exist only near the vortex core where the d wave order is suppressed, and (2) where the PDW is the primary order, the so called mother state that persists with strong phase fluctuations to high temperature and high magnetic field and lies behind the pseudogap phenomenology. We study the charge density wave structures near the vortex core in these models. We emphasize the importance of the phase winding of the d-wave order parameter. The PDW can be pinned by the vortex core due to this winding and become static. Furthermore, the period 8 CDW inherits the properties of this winding, which gives rise to a special feature of the Fourier transform peak, namely, it is split in certain directions. There are also a line of zeros in the inverse Fourier transform of filtered data. We propose that these are key experimental signatures that can distinguish between the PDW-driven scenario from the more mundane option that the period 8 CDW is primary. We discuss the pros and cons of the options considered above. Finally we attempt to place the STM experiment in the broader context of pseudogap physics of underdoped cuprates and relate this observation to the unusual properties of X ray scattering data on CDW carried out to very high magnetic field.

The possibility of realizing pair density wave (PDW) phases, in which Cooper pairs have a finite momentum, presents an interesting challenge that has been studied in a wide variety of systems. In conventional superconductors, this is only possible when external fields lift the spin degeneracy of the Fermi surface, leading to pair formation at an incommensurate momentum. Here, we study a second possibility, potentially relevant to transition metal dichalcogenides, in which the Fermi surface consists of a pair of pockets centered at the $\ifmmode\pm\else\textpm\fi{}K$ points of the Brillouin zone as well as a central pocket at the $\mathrm{\ensuremath{\Gamma}}$ point. In the limit where these three pockets are identical, the pairing susceptibility has a logarithmic divergence at the nonzero wave vectors $\ifmmode\pm\else\textpm\fi{}\mathbf{K}$, allowing for a weak-coupling analysis of the PDW instability. We find that repulsive electronic interactions combine to yield effective attractive interactions in the singlet and triplet PDW channels, as long as the $\mathrm{\ensuremath{\Gamma}}$ pocket is present. Because these PDW channels decouple from the uniform superconducting channel, they can become the leading unconventional pairing instability of the system. Upon solving the linearized gap equations, we find that the PDW instability is robust against small trigonal warping of the $\ifmmode\pm\else\textpm\fi{}K$ pockets and small detuning between the $\mathrm{\ensuremath{\Gamma}}$ and $\ifmmode\pm\else\textpm\fi{}K$ pockets, which affect the PDW transition in a similar way as the Zeeman magnetic field affects the uniform superconducting transition. We also derive the Ginzburg-Landau free energy for the PDW gaps with momenta $\ifmmode\pm\else\textpm\fi{}\mathbf{K}$, analyzing the conditions for and consequences of the emergence of FF-type and LO-type PDW ground states. Our classification of the induced orders in each ground state reveals unusual phases, including an odd-frequency charge-$2e$ superconductor in the LO-type PDW.

We study electronic ordering instabilities of twisted bilayer graphene with $n=2$ electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using renormalization group method, we find $d$/$p$-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at $n=2$ and yields a single doubly-degenerate pocket upon doping to $n>2$. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations.

By analyzing simple models of fermions in lattice potentials we argue that the zero-temperature pairing instability of any ideal band-insulator occurs at a finite momentum. The resulting supersolid state is known as "pair density wave". The pairing momentum at the onset of instability is generally incommensurate as a result of phase-space restrictions and relative strengths of interband and intraband pairing. However, commensurate pairing occurs in the strong-coupling limit and becomes a Cooper-channel analogue of the Halperin-Rice exciton condensation instability in indirect bandgap semiconductors. The exceptional sensitivity of incommensurate pairing to quantum fluctuations can lead to a strongly-correlated insulating regime and a non-BCS transition, even in the case of weak coupling as shown by an exact renormalization group analysis.

We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the Euler-Bernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress and the Green-Lagrange strain. For all models, we consider linear constitutive relations in order to isolate the effect of finite motion. The proposed methodology, however, is applicable to problems that also exhibit material nonlinearity. For the rod model, we obtain the exact analytical explicit solution of the derived finite-deformation dispersion relation, and compare it with data obtained via numerical simulation of nonlinear wave motion in a finite rod. For the beam model, we obtain a solution by numerical root finding. The results allow us to quantify the deviation in the dispersion curves when exact large deformation is considered compared to following the assumption of infinitesimal deformation. We show that incorporation of finite deformation following the chosen definitions of stress and strain raises the frequency branches for both axial and flexural waves above the nominal values associated with linear motion. For the beam problem, only the inextensional planar motion model provides an accurate description of the finite-deformation response for both static deflection and wave dispersion. Our findings, which represent the first derivation of finite-strain, amplitude-dependent dispersion relations for any type of elastic media, draw attention to 1) the tangible effect of finite deformation on wave dispersion and consequently on the speed of sound in an elastic medium and 2) the importance of incorporating longitudinal-transverse motion coupling in nonlinear analysis of thin structures.

We investigate the nematic and loop-current-type orders that may arise as vestigial precursor phases in a model with an underlying pair-density wave (PDW) instability. We discuss how such a vestigial phase gives rise to a highly anisotropic stiffness for a coexisting single-component superconductor with low intrinsic stiffness, as is the case for the underdoped cuprate superconductors. Next, focusing on a regime with a mean-field PDW ground state with loop-current and nematic $xy$ (${\mathrm{B}}_{2g}$) order, we find a preemptive transition into low- and high-temperature vestigial phases with loop-current and nematic order corresponding to $xy$ (${\mathrm{B}}_{2g}$) and ${x}^{2}\ensuremath{-}{y}^{2}$ (${\mathrm{B}}_{1g}$) symmetry, respectively. Near the transition between the two phases, a state of soft nematic order emerges for which we expect that the nematic director is readily pinned away from the high-symmetry directions in the presence of an external field. Results are discussed in relation to findings in the cuprates, especially to the recently inferred highly anisotropic superconducting fluctuations [W\aa{}rdh et al., arXiv:2203.06769], giving additional evidence for an underlying ubiquitous PDW instability in these materials.

The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. These problems may exhibit oscillatory instabilities where eigenvalues detach from the edges of the continuous spectrum, so called edge bifurcations. A numerical framework, based on a fast robust shooting algorithm using exterior algebra is described. The complete algorithm is robust in the sense that it does not produce spurious unstable eigenvalues. The algorithm allows to locate exactly where the unstable discrete eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows for stable shooting along multi-dimensional stable and unstable manifolds. The method is illustrated by computing the stability and instability of gap solitary waves of a coupled mode model.

In this paper, the closed-form analytic solutions of two new Faraday's standing solitary waves due to the parametric resonance of liquid in a vessel vibrating vertically with a constant frequency are given for the first time. Using a model based on the symmetry of wave elevation and the linearized Boussinesq equation, we gain the closed-form wave elevations of the two kinds of non-monotonically decaying standing solitary waves with smooth crest and the even or odd symmetry. All of them have never been reported, to the best of our knowledge. Besides, they can well explain some experimental phenomena. All of these are helpful to deepen and enrich our understandings about standing solitary waves and Faraday's wave.

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations, and both intrachain and interchain repulsive interactions. We find a close proximity of spin-density- and charge-density-wave phases and singlet d-wave and triplet f-wave superconducting phases. There is a striking correspondence between our results and recent puzzling experimental findings in the Bechgaard salts, including the coexistence of spin-density-wave and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase.

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations, and both intrachain and interchain repulsive interactions. $d$-wave superconductivity, which dominates over the spin-density-wave (SDW) phase at large nesting deviations, becomes unstable to the benefit of a triplet $f$-wave phase for a weak repulsive interchain backscattering term ${g}_{1}^{\ensuremath{\perp}}>0$, despite the persistence of dominant SDW correlations in the normal state. Antiferromagnetism becomes unstable against the formation of a charge-density-wave state when ${g}_{1}^{\ensuremath{\perp}}$ exceeds some critical value. While these features persist when both Umklapp processes and interchain forward scattering $({g}_{2}^{\ensuremath{\perp}})$ are taken into account, the effect of ${g}_{2}^{\ensuremath{\perp}}$ alone is found to frustrate nearest-neighbor interchain $d$- and $f$-wave pairing and instead favor next-nearest-neighbor interchain singlet or triplet pairing. We argue that the close proximity of SDW and charge-density-wave phases, singlet $d$-wave, and triplet $f$-wave superconducting phases in the theoretical phase diagram provides a possible explanation for recent puzzling experimental findings in the Bechgaard salts, including the coexistence of SDW and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase.