Origin of the Stokes shift: A geometrical model of exciton spectra in 2D semiconductors

Abstract

We consider the optical absorption and emission spectra of excitons in two-dimensional semiconductors disordered through interface fluctuations. These spectra show a universal behavior exemplified by the fact that the offset of the spectral peaks (the Stokes shift) is proportional to their linewidths over a range of at least 2 orders of magnitude. We introduce a topographical theory of the exciton spectra which models such behavior in terms of statistical properties of a Gaussian random function. The coefficient of proportionality between the Stokes shift and the exciton absorption linewidth is found to be 7 = 2/\/67r In 2 = 0.553 by analysis and 0.6 by experiment.

Condensed ground states of frustrated Bose-Hubbard models

“…The gauge transformation affects the Fourier transform of the density operator (21), and therefore the expansion image (20). There is no inconsistency with general principles of gauge invariance.…”

“…Then, one finds the eigenvalues of ρ ij . For "simple" BECs, 41 the spectrum has one eigenvalue which is of order N , 21 and which is therefore much larger than all others for large N (the thermodynamic limit). Denoting this largest eigenvalue λ 0 , the condensate density n c and condensate fraction x c for average density n are defined by 21…”

“…In conventional condensed systems, one looks for the maximum eigenvalue of the single particle density matrix of the groundstate. 21 However, here the condensed states are (pinned) vortex lattices, and therefore break translational symmetry. As a result, one expects a degeneracy of the spectrum in the thermodynamic limit.…”

Theory of the excitonic lineshape in low-dimensional structures with rough interfaces

“…Zimmermann [9] has treated the effect of layer-thickness variations in more detail by solving a Schrodinger equation. The problem of inhomogeneous broadening and Stokes shift is treated classically by Yang et al [3]. There exist earlier works on the quantum mechanical treatment of disorder where exact solutions for certain one-dimensional problems were found [10].…”

“…Even in high-quality samples the interfaces are far from perfect [2]. In quantum wells, the fluctuations of the thickness lead to a strong inhomogeneous broadening, compared to bulk semiconductors [2,3]. In quantum-well wires, opposite tendencies can be observed, depending on the method of fabrication [4][5][6].…”