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Systems composed of several multi-layer compounds have been extremely useful in tailoring different quantum physical properties of nanomaterials. This is very much true when it comes to semiconductor materials and, in particular, to heterostructures and heterojunctions. The formalism of a position-dependent effective mass has proved to be a very efficient tool in those cases where quantum wells emerge either in one or two dimensions. In this work, we use a variety of mathematical theorems, as well as numerical computations, to study different scenarios pertaining to choices of a specific piecewise constant effective mass for a particle that causes its energy eigenvalues to reach an extremum. These results are relevant when it comes to practical technological applications such as modifying the optical energy gap between the first excited state and the ground state energy of the system. At the end of our contribution, we also question the physical validity of some approximations for systems with particles that possess a position-dependent mass especially for those cases in which the mass distribution is divergent.
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This content will become publicly available on February 26, 2026
The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterization
The concept of ‘effective mass’ is frequently used for the simplification of complex lumped parameter systems (discrete dynamical systems) as well as materials that have complicated microstructural features. From the perspective of wave propagation, it is claimed that for some bodies described as metamaterials, the corresponding ‘effective mass’ can be frequency dependent, negative or it may not even be a scalar quantity. The procedure has even led some authors to suggest that Newton’s second law needs to be modified within the context of classical continuum mechanics. Such absurd physical conclusions are a consequence of appealing to the notion of ‘effective mass’ with a preconception for the constitutive structure of the metamaterial and using a correct mathematical procedure. We show that such unreasonable physical conclusions would not arise if we were to use the appropriate ‘effective constitutive relation’ for the metamaterial, rather than use the concept of ‘effective mass’ with an incorrect predetermined constitutive relation.
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- Award ID(s):
- 2307562
- PAR ID:
- 10613937
- Publisher / Repository:
- MMS_25
- Date Published:
- Journal Name:
- Mathematics and mechanics of solids
- ISSN:
- 1741-3028
- Page Range / eLocation ID:
- https://doi.org/10.1177/10812865241308
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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