Geometrical approach and topological electron density in the p x + ip y superconductor
Abstract
We present an analysis on the geometrical and physical nature of the px + ipy superconductor on the square lattice, with an emphasis on the topological phase transition at half-filling. We develop a local topological marker from specific Dirac points within the Brillouin zone, which is introduced via the addition of two one-dimensional (1D) Z (Z2) invariants defined on the Bloch sphere. We relate this topological marker to the electron spectral function integrated on frequency through the local momentum-resolved electron density, which may be measured via Angle Resolved Photoemission Spectroscopy (ARPES), and show that it remains well-protected including temperature effects. Integrating on a small area around a specific point in momentum space associated to the measure uncertainty, this also reveals the Van Hove logarithmic profile of the density of states in the derivative of the local marker while preserving the topological information. Topological transitions correspond to a protected semi-metal. We analyse the real space representation of this topological marker from correlation functions. We present physical responses such as the topological superfluid density.
Related
- Unifying Plasticity in Ordered and Disordered Matter using Topological and Geometrical Descriptors
- A Topological\-Geometrical Descriptor (TGD) for Scalable and Interpretable Modeling of Two\-Dimensional Carbon Networks
- Dissipation-induced nonlocal phase-coherent transport in a topological superconductor
- Topological Superconducting Phases in a Strained Altermagnet-Superconductor Heterostructure
- Direct transition from a fractional Chern insulator to a topological superconductor
BibTeX
@misc{hur2026geometrical,
title = {{Geometrical approach and topological electron density in the p x + ip y superconductor}},
author = {Karyn Le Hur and Kabir Narayanan and Óscar Mañas Chambert},
howpublished = {HAL},
year = {2026},
month = sep,
eprint = {2608.09415},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05765947v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometrical approach and topological electron density in the p x + ip y superconductor
AU - Karyn Le Hur
AU - Kabir Narayanan
AU - Óscar Mañas Chambert
PY - 2026
DA - 2026/09/27
PB - HAL
UR - https://hal.science/hal-05765947v1
AB - We present an analysis on the geometrical and physical nature of the px + ipy superconductor on the square lattice, with an emphasis on the topological phase transition at half-filling. We develop a local topological marker from specific Dirac points within the Brillouin zone, which is introduced via the addition of two one-dimensional (1D) Z (Z2) invariants defined on the Bloch sphere. We relate this topological marker to the electron spectral function integrated on frequency through the local momentum-resolved electron density, which may be measured via Angle Resolved Photoemission Spectroscopy (ARPES), and show that it remains well-protected including temperature effects. Integrating on a small area around a specific point in momentum space associated to the measure uncertainty, this also reveals the Van Hove logarithmic profile of the density of states in the derivative of the local marker while preserving the topological information. Topological transitions correspond to a protected semi-metal. We analyse the real space representation of this topological marker from correlation functions. We present physical responses such as the topological superfluid density.
ER -