TY - JOUR

T1 - Understanding excitons using spherical geometry

AU - Loos, Pierre François

PY - 2012/5/21

Y1 - 2012/5/21

N2 - Using spherical geometry, we introduce a novel model to study excitons confined in a three-dimensional space, which offers unparalleled mathematical simplicity while retaining much of the key physics. This new model consists of an exciton trapped on the 3-sphere (i.e. the surface of a four-dimensional ball), and provides a unified treatment of Frenkel and Wannier-Mott excitons. Moreover, we show that one can determine, for particular values of the dielectric constant ε, the closed-form expression of the exact wave function. We use the exact wave function of the lowest bound state for ε=2 to introduce an intermediate regime which gives satisfactory agreement with the exact results for a wide range of ε values.

AB - Using spherical geometry, we introduce a novel model to study excitons confined in a three-dimensional space, which offers unparalleled mathematical simplicity while retaining much of the key physics. This new model consists of an exciton trapped on the 3-sphere (i.e. the surface of a four-dimensional ball), and provides a unified treatment of Frenkel and Wannier-Mott excitons. Moreover, we show that one can determine, for particular values of the dielectric constant ε, the closed-form expression of the exact wave function. We use the exact wave function of the lowest bound state for ε=2 to introduce an intermediate regime which gives satisfactory agreement with the exact results for a wide range of ε values.

KW - Exact solution

KW - Exciton

KW - Frenkel exciton

KW - Spherical geometry

KW - Wannier-Mott exciton

UR - http://www.scopus.com/inward/record.url?scp=84861190390&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2012.05.010

DO - 10.1016/j.physleta.2012.05.010

M3 - Article

SN - 0375-9601

VL - 376

SP - 1997

EP - 2000

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 26-27

ER -