63,087 research outputs found
General response theory of topologically stable Fermi points and its implications for disordered cases
We develop a general response theory of gapless Fermi points with nontrivial
topological charges for gauge and nonlinear sigma fields, which asserts that
the topological character of the Fermi points is embodied as the terms with
discrete coefficients proportional to the corresponding topological charges.
Applying the theory to the effective non-linear sigma models for topological
Fermi points with disorders in the framework of replica approach, we derive
rigorously the Wess-Zumino terms with the topological charges being their
levels in the two complex symmetry classes of A and AIII. Intriguingly, two
nontrivial examples of quadratic Fermi points with the topological charge `2'
are respectively illustrated for the classes A and AIII. We also address a
qualitative connection of topological charges of Fermi points in the real
symmetry classes to the topological terms in the non-linear sigma models, based
on the one-to-one classification correspondence.Comment: 8 pages and 2 figures, revised version with appendi
Topological Classification and Stability of Fermi Surfaces
In the framework of the Cartan classification of Hamiltonians, a kind of
topological classification of Fermi surfaces is established in terms of
topological charges. The topological charge of a Fermi surface depends on its
codimension and the class to which its Hamiltonian belongs. It is revealed that
six types of topological charges exist, and they form two groups with respect
to the chiral symmetry, with each group consisting of one original charge and
two descendants. It is these nontrivial topological charges which lead to the
robust topological protection of the corresponding Fermi surfaces against
perturbations that preserve discrete symmetries.Comment: 5 pages, published version in PR
Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
A topology-intrinsic connection between the stabilities of Fermi surfaces
(FSs) and topological insulators/superconductors (TIs/TSCs) is revealed. In
particular, a one-to-one relation between the topological types of FSs and
TIs/TSCs is rigorously derived; combining it with a well-established
topological theory of FSs, we produce a complete table illustrating precisely
topological types of all TIs/TSCs, while a valid part of it was postulated
before. Moreover, we propose and prove a general index theorem that relates the
topological charge of FSs on the natural boundary of a strong TI/TSC to its
bulk topological number. Implications of the general index theorem on the
boundary quasi-particles are also addressed.Comment: 5 pages with Supplemental Material, more content is adde
- …