scholarly journals Second-order bulk-boundary correspondence in rotationally symmetric topological superconductors from stacked Dirac Hamiltonians

2020 ◽  
Vol 101 (15) ◽  
Author(s):  
Elis Roberts ◽  
Jan Behrends ◽  
Benjamin Béri
Keyword(s):  
Second Order ◽  
Topological Superconductors ◽  
Boundary Correspondence ◽  
Rotationally Symmetric

scholarly journals Magnetic flux periodicity in second order topological superconductors

2020 ◽  
Vol 101 (12) ◽  
Author(s):  
Suman Jyoti De ◽  
Udit Khanna ◽  
Sumathi Rao
Keyword(s):  
Magnetic Flux ◽  
Second Order ◽  
Topological Superconductors

scholarly journals A fractional corner anomaly reveals higher-order topology

Science ◽  
2020 ◽  
Vol 368 (6495) ◽  
pp. 1114-1118 ◽  
Author(s):  
Christopher W. Peterson ◽  
Tianhe Li ◽  
Wladimir A. Benalcazar ◽  
Taylor L. Hughes ◽  
Gaurav Bahl
Keyword(s):  
Charge Density ◽  
Higher Order ◽  
Order Topology ◽  
Two Dimensional ◽  
Spectral Measurements ◽  
Fractional Charge ◽  
Boundary Correspondence ◽  
Rotationally Symmetric ◽  
Topological Crystalline Insulators ◽  
Gap States

Spectral measurements of boundary-localized topological modes are commonly used to identify topological insulators. For high-order insulators, these modes appear at boundaries of higher codimension, such as the corners of a two-dimensional material. Unfortunately, this spectroscopic approach is only viable if the energies of the topological modes lie within the bulk bandgap, which is not required for many topological crystalline insulators. The key topological feature in these insulators is instead fractional charge density arising from filled bulk bands, but measurements of such charge distributions have not been accessible to date. We experimentally measure boundary-localized fractional charge density in rotationally symmetric two-dimensional metamaterials and find one-fourth and one-third fractionalization. We then introduce a topological indicator that allows for the unambiguous identification of higher-order topology, even without in-gap states, and we demonstrate the associated higher-order bulk-boundary correspondence.

A Numerical Study of Rotationally Symmetric Flow of Second-Order Fluid

1973 ◽  
Vol 40 (3) ◽  
pp. 685-687 ◽  
Author(s):  
M. Balaram ◽  
B. R. Luthra
Keyword(s):  
Angular Velocity ◽  
Flow Parameter ◽  
Numerical Study ◽  
Wall Stress ◽  
Rotating Disk ◽  
Second Order ◽  
Symmetric Flow ◽  
Rotationally Symmetric ◽  
Tangential Wall ◽  
Rotationally Symmetric Flow

This is a numerical investigation of the steady flow produced by an infinite rotating disk when the second-order fluid at infinity is in a state of solid rotation. The flow field is determined when the fluid at infinity is rotating in the same sense as that of the disk. The use of this viscometric representation limits the result to weakly viscoelastic fluids. The numerical computations obtained indicate that the question of increased or decreased total (radial plus tangential) wall stresses due to the presence of elasticity depends on the flow parameter S(S > 1 or S < 1, indicate that the fluid at infinity having a faster or slower angular velocity compared with that of the disk). We found that the total wall stress is higher or lower when compared with a Newtonian fluid depending on S > 1 or S < 1, respectively. With increasing |α| (as the fluid becomes more non-Newtonian), the total wall stress is increased or decreased when S < 1 or S > 1.

scholarly journals Quadrupole spin polarization as signature of second-order topological superconductors

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Kirill Plekhanov ◽  
Niclas Müller ◽  
Yanick Volpez ◽  
Dante M. Kennes ◽  
Herbert Schoeller ◽  
...  
Keyword(s):  
Spin Polarization ◽  
Second Order ◽  
Quadrupole Spin ◽  
Topological Superconductors

Second-order treatment of the influence of space charge and external fields on rotationally symmetric finite-emittance relativistic beams of charged particles

1985 ◽  
Vol 63 (8) ◽  
pp. 1092-1097
Author(s):  
Giulio Bosi
Keyword(s):  
Magnetic Field ◽  
Space Charge ◽  
Charged Particles ◽  
External Electromagnetic Field ◽  
Second Order ◽  
Longitudinal Motion ◽  
Standard Geometry ◽  
Rotationally Symmetric ◽  
Longitudinal Effects ◽  
Suitable Generalization

The present paper reports a relativistic treatment of space-charge effects on rotationally symmetric beams of charged particles under the influence of an external electromagnetic field. The general form of a stationary distribution describing a homogeneous, monokinetic beam is suggested, and the details of a suitable generalization of the Kapchinskij–Vladimirskij distribution are fully developed. It is shown that if second-order terms, which mainly affect the longitudinal motion, are retained, the given distribution actually provides a parabolic charge density throughout a beam cross section while the longitudinal current density remains uniform, as is usually assumed. The relativistic version of the envelope equation, including the magnetic field, is also calculated and its classical limit is compared with an available equation applicable to a beam under the influence of merely an electric field. Emittance-dependent discrepancies, related to the longitudinal effects of the space charge, are detected. The standard geometry of a rotationally symmetric Pierce gun is finally revised to allow for the addition of an external magnetic field.

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