{"title":"Memory Function of a Three-Dimensional Holstein-Like System","authors":"Zoran Rukelj, Danko Radić, Ivan Kupčić","doi":"10.1007/s10948-025-06911-0","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate the zero-temperature electron–phonon memory function of a three-dimensional Holstein-like system with the free electron-like bands. The memory function is a complex function of the incoming photon energy, and it describes the effect of electron–phonon scattering in the dynamical conductivity. In the presented approach, memory function is of the second order in electron–phonon interaction with the amplitude connected to the internal energy scales of the electron–phonon system and with imaginary and real part being connected by Kramers-Kronig relations. A closed-form expression is provided for the imaginary part of the memory function in the case when finite bandwidth, Fermi energy, and optical phonon energy are comparable to one another with several of its features closely investigated. Similarly, we analyze the properties of the real part of the memory function in a closed form whose main features are traced back to the properties of the imaginary part.</p></div>","PeriodicalId":669,"journal":{"name":"Journal of Superconductivity and Novel Magnetism","volume":"38 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Superconductivity and Novel Magnetism","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10948-025-06911-0","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
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Abstract
We investigate the zero-temperature electron–phonon memory function of a three-dimensional Holstein-like system with the free electron-like bands. The memory function is a complex function of the incoming photon energy, and it describes the effect of electron–phonon scattering in the dynamical conductivity. In the presented approach, memory function is of the second order in electron–phonon interaction with the amplitude connected to the internal energy scales of the electron–phonon system and with imaginary and real part being connected by Kramers-Kronig relations. A closed-form expression is provided for the imaginary part of the memory function in the case when finite bandwidth, Fermi energy, and optical phonon energy are comparable to one another with several of its features closely investigated. Similarly, we analyze the properties of the real part of the memory function in a closed form whose main features are traced back to the properties of the imaginary part.
期刊介绍：
The Journal of Superconductivity and Novel Magnetism serves as the international forum for the most current research and ideas in these fields. This highly acclaimed journal publishes peer-reviewed original papers, conference proceedings and invited review articles that examine all aspects of the science and technology of superconductivity, including new materials, new mechanisms, basic and technological properties, new phenomena, and small- and large-scale applications. Novel magnetism, which is expanding rapidly, is also featured in the journal. The journal focuses on such areas as spintronics, magnetic semiconductors, properties of magnetic multilayers, magnetoresistive materials and structures, magnetic oxides, etc. Novel superconducting and magnetic materials are complex compounds, and the journal publishes articles related to all aspects their study, such as sample preparation, spectroscopy and transport properties as well as various applications.
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