TY - JOUR

T1 - Quantum states in disordered media. I. Low-pass filter approach

AU - Gebhard, F.

AU - Nenashev, A. V.

AU - Meerholz, K.

AU - Baranovskii, S. D.

N1 - A.V.N. thanks the Faculty of Physics of the Philipps Universität Marburg for the kind hospitality during his research stay. S.D.B. and K.M. acknowledge financial support by the Deutsche Forschungsgemeinschaft (Research Training Group “TIDE,” Grant No. RTG2591) as well as by the key profile area “Quantum Matter and Materials (QM2)” at the University of Cologne. K.M. further acknowledges support by the DFG through the project ASTRAL (Grant No. ME1246-42). Публикация для корректировки.

PY - 2023

Y1 - 2023

N2 - The current burst in research activities on disordered semiconductors calls for the development of appropriate theoretical tools that reveal the features of electron states in random potentials while avoiding the time-consuming numerical solution of the Schrödinger equation. Among various approaches suggested so far, the low-pass filter approach of Halperin and Lax (HL) and the so-called localization landscape technique (LLT) have received most recognition in the community. We prove that the HL approach becomes equivalent to the LLT for the specific case of a Lorentzian filter when applied to the Schrödinger equation with a constant mass. Advantageously, the low-pass filter approach allows further optimization beyond the Lorentzian shape. We propose the global HL filter as optimal filter with only a single length scale, namely, the size of the localized wave packets. As an application, we design an optimized potential landscape for a (semi)classical calculation of the number of strongly localized states that faithfully reproduce the exact solution for a random white-noise potential in one dimension.

AB - The current burst in research activities on disordered semiconductors calls for the development of appropriate theoretical tools that reveal the features of electron states in random potentials while avoiding the time-consuming numerical solution of the Schrödinger equation. Among various approaches suggested so far, the low-pass filter approach of Halperin and Lax (HL) and the so-called localization landscape technique (LLT) have received most recognition in the community. We prove that the HL approach becomes equivalent to the LLT for the specific case of a Lorentzian filter when applied to the Schrödinger equation with a constant mass. Advantageously, the low-pass filter approach allows further optimization beyond the Lorentzian shape. We propose the global HL filter as optimal filter with only a single length scale, namely, the size of the localized wave packets. As an application, we design an optimized potential landscape for a (semi)classical calculation of the number of strongly localized states that faithfully reproduce the exact solution for a random white-noise potential in one dimension.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85144774873&origin=inward&txGid=cfb79ba71a2fbcfa4f0a88f796e56b0a

UR - https://www.mendeley.com/catalogue/e6e9aa34-139e-3865-a86e-db6202a93c39/

U2 - 10.1103/PhysRevB.107.064206

DO - 10.1103/PhysRevB.107.064206

M3 - Article

VL - 107

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 6

M1 - 064206

ER -