Related papers: Zero-modes on orbifolds : magnetized orbifold mode…
We study strongly correlated fractional topological phases on a two-sphere threaded by a magnetic dipole field with globally vanishing flux. Solving the Dirac equation in this background produces spheroidal wavefunctions forming a highly…
We consider the strong field asymptotics for the occurrence of zero modes of certain Weyl-Dirac operators on $\mathbb{R}^3$. In particular we are interested in those operators $\mathcal{D}_{B}$ for which the associated magnetic field $B$ is…
In presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different…
Nodal-line semimetals with magnetic orders have been theoretically predicted and experimentally observed in only few compounds. We theoretically explore the electronic structure in bulk and boundary of such a magnetic nodal-line state by…
We extend the groundbreaking results of Gromov and Lawson on positive scalar curvature and the Dirac operator on complete Riemannian manifolds to Dirac operators defined along the leaves of foliations of non-compact complete Riemannian…
We explore Majorana zero modes bound to a vortex line in a three dimensional topological superconductor model, focusing our attention on the validity of the index theorem previously derived. We first solve the Bogoliubov-de Gennes equation…
Let M be a closed spin manifold of dimension congruent to 3 modulo 4. We give a simple proof of the fact that the space of metrics on M with invertible Dirac operator is either empty or it has infinitely many path components.
The interplay of time-reversal and $n$-fold rotation symmetries ($n=2,4,6$) is known to bring a new class of topological crystalline insulators (TCIs) having $n$ surface Dirac cones due to surface rotation anomaly. We show that the…
We prove that minimal Dirac operators on the half-line are self-modeling, which means that such an operator is determined by its arbitrary unitary copy uniquely up to a transformation (shape equivalence) which changes its potential by a…
We investigate elliptic operators with a symmetry that forces their index to vanish. We study the secondary index, defined modulo 2. We examine Callias-type operators with this symmetry on non-compact manifolds and establish mod 2 versions…
This paper presents some results concerning the size of magnetic fields that support zero modes for the three dimensional Dirac equation and related problems for spinor equations. It is a well known fact that for the Schr\"odinger in three…
We calculate the index of the Dirac operator defined on the q-deformed fuzzy sphere. The index of the Dirac operator is related to its net chiral zero modes and thus to the trace of the chirality operator. We show that for the q-deformed…
We analyze the zero-energy sector of the trigonal zigzag nanodisk and corner based on the Dirac theory of graphene. The zero-energy states are shown to be indexed by the edge momentum and grouped according to the irreducible representation…
We study the zero modes of the operator $H_f=D^*_fD_f$, with a Dirac type operator $D_f$, acting on the spinor bundle over a closed even dimensional Riemannian manifold $M$. The operator $D_f=D+ifI$ is a deformation of the Dirac operator…
We investigate the independent chiral zero modes on the orbifolds from the Atiyah-Segal-Singer fixed point theorem. The required information for this calculation includes the fixed points of the orbifold and the manner in which the spatial…
A way to identify the would-be zero-modes of staggered lattice fermions away from the continuum limit is presented. Our approach also identifies the chiralities of these modes, and their index is seen to be determined by gauge field…
We investigate the index of the Neuberger's Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting…
The q-deformed fuzzy sphere $S_{qF}^2(N)$ is the algebra of $(N+1)\times(N+1)$ dim. matrices, covariant with respect to the adjoint action of $\uq$ and in the limit $q\to 1$, it reduces to the fuzzy sphere $S_{F}^2(N)$. We construct the…
We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and analytical…
With time reversal symmetry a Dirac operator has vanishing index and Chern number. We show that we can nevertheless define a nontrivial Z$_2$ index as well as a corresponding topological invariant given by gauge field, which implies that…