Approaching Disordered Quantum Dot Systems by Complex Networks with Spatial and Physical-Based Constraints

This paper focuses on modeling a disordered system of quantum dots (QDs) by using complex networks with spatial and physical-based constraints. The first constraint is that, although QDs (=nodes) are randomly distributed in a metric space, they have to fulfill the condition that there is a minimum inter-dot distance that cannot be violated (to minimize electron localization). The second constraint arises from our process of weighted link formation, which is consistent with the laws of quantum physics and statistics: it not only takes into account the overlap integrals but also Boltzmann factors to include the fact that an electron can hop from one QD to another with a different energy level. Boltzmann factors and coherence naturally arise from the Lindblad master equation. The weighted adjacency matrix leads to a Laplacian matrix and a time evolution operator that allows the computation of the electron probability distribution and quantum transport efficiency. The results suggest that there is an optimal inter-dot distance that helps reduce electron localization in QD clusters and make the wave function better extended. As a potential application, we provide recommendations for improving QD intermediate-band solar cells.

Download Full-text

Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links

Nanomaterials ◽

10.3390/nano11020375 ◽

2021 ◽

Vol 11 (2) ◽

pp. 375

Author(s):

Lucas Cuadra ◽

José Carlos Nieto-Borge

Keyword(s):

Time Evolution ◽

Evolution Operator ◽

Special Kind ◽

Laplacian Matrix ◽

Probability Amplitude ◽

Geometric Graphs ◽

Time Evolution Operator ◽

Random Geometric Graphs ◽

Link Weight ◽

Proposed Model

This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=nodes) involved. This naturally leads to a weighted adjacency matrix, a Laplacian matrix, and a time evolution operator that have meaning in Quantum Mechanics. The model prohibits the existence of long-range links (shortcuts) between distant nodes because the electron cannot tunnel between two QDs that are too far away in the array. The spatial network generated by the proposed model captures inner properties of the QD system, which cannot be deduced from the simple interactions of their isolated components. It predicts the system quantum state, its time evolution, and the emergence of quantum transport when the network becomes connected.

Download Full-text

Complexity growth in integrable and chaotic models

Journal of High Energy Physics ◽

10.1007/jhep07(2021)011 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Vijay Balasubramanian ◽

Matthew DeCross ◽

Arjun Kar ◽

Yue Li ◽

Onkar Parrikar

Keyword(s):

Time Evolution ◽

Evolution Operator ◽

Linear Growth ◽

Conjugate Points ◽

Majorana Fermions ◽

Time Evolution Operator ◽

Free Theory ◽

Group Manifold ◽

Geodesic Length ◽

Evolution Trajectory

Abstract We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($$ \sqrt{N} $$ N ), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(eN), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

Download Full-text

Temperature Dependence of Carrier Extraction Processes in GaSb/AlGaAs Quantum Nanostructure Intermediate-Band Solar Cells

Nanomaterials ◽

10.3390/nano11020344 ◽

2021 ◽

Vol 11 (2) ◽

pp. 344

Author(s):

Yasushi Shoji ◽

Ryo Tamaki ◽

Yoshitaka Okada

Keyword(s):

Solar Cells ◽

Molecular Beam ◽

Optical Excitation ◽

Material System ◽

Intermediate Band ◽

Temperature Characteristics ◽

Quantum Nanostructures ◽

Band Engineering ◽

Intermediate Band Solar Cells ◽

Carrier Extraction

From the viewpoint of band engineering, the use of GaSb quantum nanostructures is expected to lead to highly efficient intermediate-band solar cells (IBSCs). In IBSCs, current generation via two-step optical excitations through the intermediate band is the key to the operating principle. This mechanism requires the formation of a strong quantum confinement structure. Therefore, we focused on the material system with GaSb quantum nanostructures embedded in AlGaAs layers. However, studies involving crystal growth of GaSb quantum nanostructures on AlGaAs layers have rarely been reported. In our work, we fabricated GaSb quantum dots (QDs) and quantum rings (QRs) on AlGaAs layers via molecular-beam epitaxy. Using the Stranski–Krastanov growth mode, we demonstrated that lens-shaped GaSb QDs can be fabricated on AlGaAs layers. In addition, atomic force microscopy measurements revealed that GaSb QDs could be changed to QRs under irradiation with an As molecular beam even when they were deposited onto AlGaAs layers. We also investigated the suitability of GaSb/AlGaAs QDSCs and QRSCs for use in IBSCs by evaluating the temperature characteristics of their external quantum efficiency. For the GaSb/AlGaAs material system, the QDSC was found to have slightly better two-step optical excitation temperature characteristics than the QRSC.

Download Full-text