scholarly journals Topological semimetals carrying arbitrary Hopf numbers: Fermi surface topologies of a Hopf link, Solomon's knot, trefoil knot, and other linked nodal varieties

2017 ◽  
Vol 96 (4) ◽  
Author(s):  
Motohiko Ezawa
Keyword(s):  
Fermi Surface ◽  
Trefoil Knot ◽  
Topological Semimetals ◽  
Hopf Link

scholarly journals ALMOST POSITIVE LINKS HAVE NEGATIVE SIGNATURE

2010 ◽  
Vol 19 (02) ◽  
pp. 187-289 ◽  
Author(s):  
JÓZEF H. PRZYTYCKI ◽  
KOUKI TANIYAMA
Keyword(s):  
Partial Answer ◽  
Link Diagram ◽  
Link Diagrams ◽  
Left Handed ◽  
Trefoil Knot ◽  
Trivial Link ◽  
Hopf Link

We analyze properties of links which have diagrams with a small number of negative crossings. We show that if a nontrivial link has a diagram with all crossings positive except possibly one, then the signature of the link is negative. If a link diagram has two negative crossings, we show that the signature of the link is nonpositive with the exception of the left-handed Hopf link (possibly, with extra trivial components). We also characterize those links which have signature zero and diagrams with two negative crossings. In particular, we show that if a nontrivial knot has a diagram with two negative crossings then the signature of the knot is negative, unless the knot is a twist knot with negative clasp. We completely determine all trivial link diagrams with two or fewer negative crossings. For a knot diagram with three negative crossings, the signature of the knot is nonpositive except for the left-handed trefoil knot. These results generalize those of Rudolph, Cochran, Gompf, Traczyk and Przytycki, solve [27, Conjecture 5], and give a partial answer to [3, Problem 2.8] about knots dominating the trefoil knot or the trivial knot. We also describe all unknotting number one positive knots.

scholarly journals REGULAR PROJECTIONS OF GRAPHS WITH AT MOST THREE DOUBLE POINTS

2010 ◽  
Vol 19 (07) ◽  
pp. 917-933
Author(s):  
YOUNGSIK HUH ◽  
RYO NIKKUNI
Keyword(s):  
Planar Graph ◽  
Natural Projection ◽  
Double Points ◽  
Trefoil Knot ◽  
Generic Immersion ◽  
Hopf Link

A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. In this paper, we show that if a generic immersion of a planar graph is knotted then the number of double points of the immersion is more than or equal to three. To prove this, we also show that an embedding of a graph obtained from a generic immersion of the graph (does not need to be planar) with at most three double points is totally free if it contains neither a Hopf link nor a trefoil knot.

Angular magnetoresistance oscillations and the shape of the Fermi surface in ?(ET)2IBr2

1992 ◽  
Vol 2 (1) ◽  
pp. 89-99 ◽  
Author(s):  
M. V. Kartsovnik ◽  
V. N. Laukhin ◽  
S. I. Pesotskii ◽  
I. F. Schegolev ◽  
V. M. Yakovenko
Keyword(s):  
Fermi Surface ◽  
Magnetoresistance Oscillations

Fermi-surface reconstruction close to a pressure-induced metal-insulator transition

2004 ◽  
Vol 114 ◽  
pp. 277-281 ◽  
Author(s):  
J. Wosnitza ◽  
J. Hagel ◽  
O. Stockert ◽  
C. Pfleiderer ◽  
J. A. Schlueter ◽  
...  
Keyword(s):  
Fermi Surface ◽  
Surface Reconstruction ◽  
Insulator Transition ◽  
Metal Insulator Transition ◽  
Metal Insulator ◽  
Fermi Surface Reconstruction

The fermi surface of lead

1962 ◽  
Author(s):  
James Robert Anderson
Keyword(s):  
Fermi Surface

scholarly journals Linear and nonlinear optical responses in the chiral multifold semimetal RhSi

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Zhuoliang Ni ◽  
B. Xu ◽  
M.-Á. Sánchez-Martínez ◽  
Y. Zhang ◽  
K. Manna ◽  
...  
Keyword(s):  
Nonlinear Optical ◽  
Chemical Potential ◽  
Technological Development ◽  
Optical Responses ◽  
Chiral Magnetic Effect ◽  
Hole Band ◽  
Linear And Nonlinear ◽  
Characteristic Features ◽  
Topological Semimetals ◽  
Terahertz Emission Spectroscopy

AbstractChiral topological semimetals are materials that break both inversion and mirror symmetries. They host interesting phenomena such as the quantized circular photogalvanic effect (CPGE) and the chiral magnetic effect. In this work, we report a comprehensive theoretical and experimental analysis of the linear and nonlinear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions. We show that the characteristic features of the optical conductivity, which display two distinct quasi-linear regimes above and below 0.4 eV, can be linked to excitations of different kinds of multifold fermions. The characteristic features of the CPGE, which displays a sign change at 0.4 eV and a large non-quantized response peak of around 160 μA/V2 at 0.7 eV, are explained by assuming that the chemical potential crosses a flat hole band at the Brillouin zone center. Our theory predicts that, in order to observe a quantized CPGE in RhSi, it is necessary to increase the chemical potential as well as the quasiparticle lifetime. More broadly, our methodology, especially the development of the broadband terahertz emission spectroscopy, could be widely applied to study photogalvanic effects in noncentrosymmetric materials and in topological insulators in a contact-less way and accelerate the technological development of efficient infrared detectors based on topological semimetals.

scholarly journals Fermi surface of the skutterudite CoSb3 : Quantum oscillations and band-structure calculations

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
M. Naumann ◽  
P. Mokhtari ◽  
Z. Medvecka ◽  
F. Arnold ◽  
M. Pillaca ◽  
...  
Keyword(s):  
Band Structure ◽  
Fermi Surface ◽  
Quantum Oscillations ◽  
Band Structure Calculations ◽  
Structure Calculations
Sign in / Sign up

Export Citation Format

Share Document