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Recent Advances in the Theory of Disordered Systems

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Prof. Dr. Aimin Guo

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Guest Editor

School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China
Interests: localization transition in disordered systems; quantum transport theory; spintronics; chirality-induced spin selectivity; 2D materials; topological insulators

Prof. Dr. Qiao Chen

E-Mail Website
Guest Editor

Department of Maths and Physics, Hunan Institute of Engineering, Xiangtan 411104, Hunan, China
Interests: Quantum transport theory; 2D materials; Majorana fermions; Electronic properties of low dimension systems; Spintronics

Special Issue Information

Dear Colleagues,

Since the pioneering proposal made by Philip Anderson about sixty-five years ago stated that diffusion vanishes in random lattices, Anderson localization has attracted extensive and ongoing interesting, where the disorder induced by, e.g., impurities gives rise to the localization of electronic wave functions. It was further confirmed by the scaling theory of localization which insists that all electronic states should be localized in non-interacting one- and two-dimensional disordered systems, and in contrast the electronic states in three-dimensional disordered systems could transform from metallic behavior to insulating behavior by increasing the disorder strength which is accompanied by the appearance of the mobility edge. This disorder-induced Anderson localization has been reported experimentally in many disordered media, ranging from light, microwaves, ultrasound, to cold atoms.

Indeed, the disorder is inevitable during the fabrication of materials and usually leads to the localization of wave functions. Until now, many intriguing phenomena have reported in disordered systems or quasiperiodic ones. For instance, all electronic states in the Aubry–Andre model could be metallic for small disorder strength and become insulating after surpassing a critical value of disorder strength. The disorder could, in some cases, enhance the charge transport ability of graphene.

This Special Issue is dedicated to reviewing recent developments, sharing new results, as well as opening new perspectives to the theory of disordered systems.

Prof. Dr. Aimin Guo
Prof. Dr. Qiao Chen
Guest Editors

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Keywords

anderson localization
localization transition
disordered systems
mobility edge
quantum transport
quasiperiodic systems
2D materials
1D systems
localization length
participation ratio

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Research

18 pages, 1034 KiB

Open AccessArticle

Computation of the Spatial Distribution of Charge-Carrier Density in Disordered Media

by Alexey V. Nenashev, Florian Gebhard, Klaus Meerholz and Sergei D. Baranovskii

Entropy 2024, 26(5), 356; https://doi.org/10.3390/e26050356 - 24 Apr 2024

Viewed by 249

Abstract

The space- and temperature-dependent electron distribution

n (r, T)

determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to

n (r, T)

in random potentials, while avoiding the time-consuming numerical solution of [...] Read more.

The space- and temperature-dependent electron distribution

n (r, T)

determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to

n (r, T)

in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present several numerical techniques targeted to fulfill this task. For a degenerate system with Fermi statistics, a numerical approach based on a matrix inversion and one based on a system of linear equations are developed. For a non-degenerate system with Boltzmann statistics, a numerical technique based on a universal low-pass filter and one based on random wave functions are introduced. The high accuracy of the approximate calculations are checked by comparison with the exact quantum-mechanical solutions. Full article

(This article belongs to the Special Issue Recent Advances in the Theory of Disordered Systems)

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9 pages, 597 KiB

Open AccessFeature PaperArticle

Topological Dimensions from Disorder and Quantum Mechanics?

by Ivan Horváth and Peter Markoš

Entropy 2023, 25(11), 1557; https://doi.org/10.3390/e25111557 - 17 Nov 2023

Cited by 4 | Viewed by 798

Abstract

We have recently shown that the critical Anderson electron in

D = 3

dimensions effectively occupies a spatial region of the infrared (IR) scaling dimension

d_{IR} \approx 8 / 3

. Here, we inquire about the dimensional substructure involved. We partition space [...] Read more.

We have recently shown that the critical Anderson electron in

D = 3

dimensions effectively occupies a spatial region of the infrared (IR) scaling dimension

d_{IR} \approx 8 / 3

. Here, we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probabilities, such that the points comprising a region are of similar relevance, and calculate the IR scaling dimension d of each. This allows us to infer the probability density

p (d)

for dimension d to be accessed by the electron. We find that

p (d)

has a strong peak at d very close to two. In fact, our data suggest that

p (d)

is non-zero on the interval

[d_{\min}, d_{\max}] \approx [4 / 3, 8 / 3]

and may develop a discrete part (

δ

-function) at

d = 2

in the infinite-volume limit. The latter invokes the possibility that a combination of quantum mechanics and pure disorder can lead to the emergence of integer (topological) dimensions. Although

d_{IR}

is based on effective counting, of which

p (d)

has no a priori knowledge,

d_{IR} \geq d_{\max}

is an exact feature of the ensuing formalism. A possible connection of our results to the recent findings of

d_{IR} \approx 2

in Dirac near-zero modes of thermal quantum chromodynamics is emphasized. Full article

(This article belongs to the Special Issue Recent Advances in the Theory of Disordered Systems)

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