Z2index for gapless fermionic modes in the vortex core of three-dimensional paired Dirac fermions

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

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Study of Tip Vortex Cavitation Inception Using Navier-Stokes Computation and Bubble Dynamics Model

Journal of Fluids Engineering ◽

10.1115/1.2822002 ◽

1999 ◽

Vol 121 (1) ◽

pp. 198-204 ◽

Cited By ~ 12

Author(s):

Chao-Tsung Hsiao ◽

Laura L. Pauley

Keyword(s):

Vortex Core ◽

Bubble Dynamics ◽

Three Dimensional ◽

Window Size ◽

Tip Vortex ◽

Navier Stokes ◽

Cavitation Inception ◽

Flow Effects ◽

Bubble Sizes ◽

Real Flow

The Rayleigh-Plesset bubble dynamics equation coupled with the bubble motion equation developed by Johnson and Hsieh was applied to study the real flow effects on the prediction of cavitation inception in tip vortex flows. A three-dimensional steady-state tip vortex flow obtained from a Reynolds-Averaged Navier-Stokes computation was used as a prescribed flow field through which the bubble was passively convected. A “window of opportunity” through which a candidate bubble must pass in order to be drawn into the tip-vortex core and cavitate was determined for different initial bubble sizes. It was found that bubbles with larger initial size can be entrained into the tip-vortex core from a larger window size and also had a higher cavitation inception number.

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Spin wave mediated unidirectional vortex core reversal by two orthogonal monopolar field pulses: The essential role of three-dimensional magnetization dynamics

Journal of Applied Physics ◽

10.1063/1.4948354 ◽

2016 ◽

Vol 119 (17) ◽

pp. 173901 ◽

Cited By ~ 7

Author(s):

Matthias Noske ◽

Hermann Stoll ◽

Manfred Fähnle ◽

Ajay Gangwar ◽

Georg Woltersdorf ◽

...

Keyword(s):

Spin Wave ◽

Vortex Core ◽

Essential Role ◽

Three Dimensional ◽

Magnetization Dynamics

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Three-Dimensional Charge Density Wave and Surface-Dependent Vortex-Core States in a Kagome Superconductor CsV3Sb5

Physical Review X ◽

10.1103/physrevx.11.031026 ◽

2021 ◽

Vol 11 (3) ◽

Author(s):

Zuowei Liang ◽

Xingyuan Hou ◽

Fan Zhang ◽

Wanru Ma ◽

Ping Wu ◽

...

Keyword(s):

Charge Density ◽

Vortex Core ◽

Charge Density Wave ◽

Density Wave ◽

Three Dimensional

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Physics of Tip Clearance Flow in Turbomachinery (Keynote Paper)

Volume 2: Symposia and General Papers, Parts A and B ◽

10.1115/fedsm2002-31184 ◽

2002 ◽

Cited By ~ 5

Author(s):

Masahiro Inoue ◽

Masato Furukawa

Keyword(s):

Flow Field ◽

Physical Interpretation ◽

Vortex Core ◽

Vortical Structure ◽

Three Dimensional ◽

Axial Flow ◽

Tip Clearance ◽

Tip Clearance Flow ◽

Clearance Flow ◽

Flow Phenomena

In a recent advanced aerodynamic design of turbomachinery, the physical interpretation of three-dimensional flow field obtained by a numerical simulation is important for iterative modifications of the blade or impeller geometry. This paper describes an approach to the physical interpretation of the tip clearance flow in turbomachinery. First, typical flow phenomena of the tip clearance flow are outlined for axial and radial compressors, pumps and turbines to help comprehensive understanding of the tip clearance flow. Then, a vortex-core identification method which enables to extract the vortical structure from the complicated flow field is introduced, since elucidation of the vortical structure is essential to the physical interpretation of the tip clearance flow. By use of the vortex-core identification, some interesting phenomena of the tip clearance flows are interpreted, especially focussing on axial flow compressors.

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Destabilization of a vortex by acoustic waves

Journal of Fluid Mechanics ◽

10.1017/s0022112000008612 ◽

2000 ◽

Vol 414 ◽

pp. 315-337 ◽

Cited By ~ 5

Author(s):

STÉPHANE LEBLANC

Keyword(s):

Stability Analysis ◽

Vortex Core ◽

Acoustic Waves ◽

Periodic Potential ◽

Three Dimensional ◽

Basic Flow ◽

Almost Periodic ◽

The Core ◽

Parametric Resonances ◽

Time Periodic

The linear stability of a circular vortex interacting with two plane acoustic waves propagating in opposite directions is investigated. When the wavelength is large compared to the size of the vortex, the core is subjected to time-periodic compressions and strains. A stability analysis is performed with the geometrical optics approximation, which considers short-wavelength perturbations evolving along the trajectories of the basic flow. On the vortex core, the problem is reduced to a single Hill–Schrödinger equation with periodic or almost-periodic potential, the solution to which grows exponentially when parametric resonances occur. On interacting with the acoustic waves, the circular vortex is thus unstable to three-dimensional perturbations.

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RENORMALIZATION AMBIGUITIES AND GAUGE SYMMETRY IN CHERN–SIMONS THEORIES

Modern Physics Letters A ◽

10.1142/s0217732398000577 ◽

1998 ◽

Vol 13 (07) ◽

pp. 511-525

Author(s):

J. L. LÓPEZ

Keyword(s):

Effective Action ◽

Three Dimensional ◽

Gauge Coupling ◽

Simons Theory ◽

Radiative Corrections ◽

Dirac Fermions ◽

Coupling Constant ◽

Effective Constant ◽

Chern Simons ◽

Chern Simons Theory

The universality of radiative corrections to the gauge coupling constant k of the Chern–Simons theory is studied in a very general regularization scheme in the background gauge formalism. The effective constant k eff induced by radiative corrections can be any real number depending on the balance between the ultraviolet behavior of scalar and pseudoscalar terms in the regularized action. This ambiguity of the effective action is related to the ambiguity in the parity anomaly of three-dimensional Dirac fermions. The effective action also contains a non-analytic term in the gauge field with the same coefficient and opposite gauge transformation in such a way that the effective action is gauge-invariant. The results open the possibility of a connection with non-rational two-dimensional conformal theories for non-integer values of k eff .

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Self-similar behaviour of a rotor wake vortex core

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.636 ◽

2014 ◽

Vol 740 ◽

Cited By ~ 9

Author(s):

Mohamed Ali ◽

Malek Abid

Keyword(s):

Vortex Core ◽

Scaling Laws ◽

Stokes Equations ◽

Three Dimensional ◽

Azimuthal Velocity ◽

Reynolds Numbers ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Rotating Blade ◽

Self Similar

AbstractWe report a self-similar behaviour of solutions (obtained numerically) of the Navier–Stokes equations behind a single-blade rotor. That is, the helical vortex core in the wake of a rotating blade is self-similar as a function of its age. Profiles of vorticity and azimuthal velocity in the vortex core are characterized, their similarity variables are identified and scaling laws of these variables are given. Solutions of incompressible three-dimensional Navier–Stokes equations for Reynolds numbers up to $Re= 2000$ are considered.

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Magnetoinfrared Spectroscopy of Landau Levels and Zeeman Splitting of Three-Dimensional Massless Dirac Fermions inZrTe5

Physical Review Letters ◽

10.1103/physrevlett.115.176404 ◽

2015 ◽

Vol 115 (17) ◽

Cited By ~ 113

Author(s):

R. Y. Chen ◽

Z. G. Chen ◽

X.-Y. Song ◽

J. A. Schneeloch ◽

G. D. Gu ◽

...

Keyword(s):

Three Dimensional ◽

Zeeman Splitting ◽

Landau Levels ◽

Dirac Fermions

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Transient Growth of Three-Dimensional Vortex Perturbations During Near-Parallel Collision With a Circular Cylinder

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2006-98116 ◽

2006 ◽

Author(s):

X. Liu ◽

J. S. Marshall

Keyword(s):

Circular Cylinder ◽

Vortex Core ◽

Computational Study ◽

Three Dimensional ◽

The Body ◽

Transient Growth ◽

Two Dimensional ◽

Three Dimensional Flow ◽

Dimensional Flow ◽

Flow Features

A computational study is reported that examines the transient growth of three-dimensional flow features for nominally parallel vortex-cylinder interaction problems. We consider a helical vortex with small-amplitude perturbations that is advected onto a circular cylinder whose axis is parallel to the nominal vortex axis. The study assesses the applicability of the two-dimensional flow assumption for parallel vortex-body interaction problems in which the body impinges on the vortex core. The computations are performed using an unstructured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is quantified by use of a proper-orthogonal decomposition of the Fourier-transformed velocity and vorticity fields in the cylinder azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical waves on the vortex core, and the results for cylinder force are compared to the two-dimensional results. The degree of perturbation amplification as the vortex approaches the cylinder is quantified and shown to be mostly dependent on the dominant axial wavenumber of the perturbation. The perturbation amplification is observed to be greatest for perturbations with axial wavelength of about 1.5 times the cylinder diameter.

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