Quantum phase transitions in the noncommutative Dirac Oscillator

Abstract

We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the non-commutative plane. It is shown that the effect of non-commutativity is twofold: $i$) momentum non commuting coordinates simply shift the critical value ($B_{\text{cr}}$) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); $ii$) non-commutativity in the space coordinates induces a new critical value of the magnetic field, $B_{\text{cr}}^{\ast }$, where there is a second quantum phase transition (right-left), --this critical point disappears in the commutative limit--. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetisation of the system. Possible applications to the physics of silicene and graphene are briefly discussed.

26 pages, two figures. Editorial improvements, few references added. Version accepted by Physical Review A

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Cited by in corpus (14)

• On the Dirac oscillator in a spinning cosmic string spacetime in external magnetic fields: Investigation of energy spectrum and connection with the condensed matter physics
• Quantum phase transitions of the Dirac oscillator in a minimal length scenario
• Thermodynamics of Quantum Phase Transitions of a Dirac oscillator in a homogenous magnetic field
• Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
• PT phase transition in a (2+1)-d relativistic system
• Angular momentum quantum backflow in the noncommutative plane
• Fermionic fields in a four-dimensional Bonnor-Melvin-Lambda space-time
• Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time
• Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
• Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
• Quantum phase transitions of the Dirac oscillator in the Anti-Snyder model
• Non-Commutativity effects in the Dirac equation in crossed electric and magnetic fields
• Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space