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Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping

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arxiv 2401.13864 v2 pith:HYC67B4C submitted 2024-01-25 cond-mat.mes-hall hep-thmath-phmath.MPnlin.SI

Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping

Francisco Correa , Luis Inzunza , V\'it Jakubsk\'y This is my paper
classification cond-mat.mes-hall hep-thmath-phmath.MPnlin.SI
keywords quantumzero-energygrapheneinvariancelorentzianmodelshapestates
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Confining Dirac fermions in graphene by electrostatic fields is a challenging task. Electric quantum dots created by a scanning tunneling microscope (STM) tip can trap zero-energy quasi-particles. The Lorentzian quantum well provides a faithful, exactly solvable, approximation to such a potential, hosting zero-energy bound states for certain values of the coupling constant. We show that in this critical configuration, the system can be related to the free particle model by means of a supersymmetric transformation. The revealed shape invariance of the model greatly simplifies the calculation of the zero modes and naturally explains the degeneracy of the zero energy.

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