Bogoliubov-De Gennes Formalism for Tracking Free Majoranas on Ultra Cold Fermi Gases

Extensión del formalismo de Bogoliubov-De Gennes para el rastreo de fermiones de Majorana libres en gases fermionicos ultrafríos

By: A. A. Pérez Losada, K. Rodríguez Ramírez, A. Argüelles,

Main Information

Volume:
Vol.51-N3 / 2018 - Ordinario
Section:
Quantum and Non-Linear Optics
Pages:
50313:1-9
DOI:
http://doi.org/10.7149/OPA.51.3.50313
Type:
Research papers / Trabajos de investigación
Language:
Spanish
Attachments:
Keywords:
Majorana fermions, dispersion relation, Bogoliubov-de Gennes Hamiltonian.

Fermiones de Majorana, redes o pticas, Hamiltoniano de Bogoliubov-de Gennes.
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Abstract

The collective excitations of a system, particularly at low temperatures, behave as quasi-particles with properties that may differ from their constituents. In particular, there are exotic excitations called Majorana fermions or zero-energy modes modes, which have the special characteristic of being their own antiparticle. In that sense, this work seeks tracing these excitations in an artificial arrangement of a nanowire simulated through a one-dimensional chain. In that direction, the Fourier transform is used with the purpose of bringing the Hamiltonian from position to momentum space. Subsequently, it is proposed to diagonalize the system using the Bogoliubov-de Gennes formalism. In this way, we obtain the phase diagram displaying the set of parameters for which zero energy modes are stabilized.


Las excitaciones colectivas de un sistema, en particular a bajas temperaturas, se comportan como cuasi-partículas con propiedades que pueden diferir de las partículas constituyentes. En particular existen excitaciones exóticas llamadas fermiones de Majorana o modos de borde de energía cero, las cuales tienen la característica especial de ser su propia antipartícula y por tanto son modos de energía cero. En ese sentido, este trabajo busca rastrear dichas excitaciones en un arreglo artificial de un nanohilo, simulando este a través de una cadena unidimensional de a tomos fermionicos ultrafríos. En esa dirección, se usa la transformada de Fourier con el propósito de llevar el Hamiltoniano del sistema desde el espacio de posición al espacio de momento y posteriormente, diagonalizar el sistema desde el formalismo de Bogoliubov-de Gennes. De esta manera, se consigue realizar el diagrama de transición de fase del sistema, donde se muestra el conjunto de parámetros para los cuales se estabilizan dichos modos de energía nula.

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