mireabulletinRussian Technological JournalRussian Technological Journal2782-32102500-316XRTU MIREA10.32362/2500-316X-2026-14-4-106-115TTKFOCmireabulletin-1621Research ArticleМИКРО- И НАНОЭЛЕКТРОНИКА. ФИЗИКА КОНДЕНСИРОВАННОГО СОСТОЯНИЯMICRO- AND NANOELECTRONICS. CONDENSED MATTER PHYSICSМоделирование фотоэмиссии двухжидкостной системы носителей заряда, формирующейся при сильном электрон-фононном взаимодействииPhotoemission modeling of a two-liquid charge-carrier system formed at strong electron–phonon couplinghttps://orcid.org/0000-0002-0546-8740ДоронкинаС. В.DoronkinaS. V.

Доронкина Станислава Валерьевна, к.ф.-м.н., старший преподаватель, кафедра высшей математики 3, Институт перспективных технологий и индустриального программирования

Scopus Author ID 57219795495

119454, Москва, пр-т Вернадского, д. 78

Stanislava V. Doronkina, Cand. Sci. (Phys.-Math.), Senior Lecturer, Higher Mathematics Department 3, Institute for Advanced Technologies and Industrial Programming, 

78, Vernadskogo pr., Moscow, 119454

doronkina@mirea.ruhttps://orcid.org/0009-0004-9940-3842БабаянцА. С.BabayantsA. S.

Бабаянц Анастасия Станиславовна, студент, физический факультет

344006, Ростов-на-Дону, ул. Большая Садовая, д. 105/42

Anastasia S. Babayants, Student, Physics Faculty

105/42, Bolshaya Sadovaya ul., Rostov-on-Don, 344006

9aababayanz@gmail.comhttps://orcid.org/0009-0006-7927-2157ЛисицаИ. В.LisitsaI. V.

Лисица Иван Васильевич, ассистент, кафедра медицинской физики, математики и информационных технологий

344022, Ростовна-Дону, пер. Нахичеванский, д. 29

Ivan V. Lisitsa, Assistant, Department of Medical Physics, Mathematics, and Information Technology

29, Nakhichevanskii per., Rostov-on-Don, 344022

https://orcid.org/0000-0001-7262-8292МясниковаА. Э.MyasnikovaA. E.

Мясникова Анна Эдуардовна, д.ф.-м.н., доцент, профессор кафедры теоретической и вычислительной физики

Scopus Author ID 6602715354

344006, Ростов-на-Дону, ул. Большая Садовая, д. 105/42

Anna E. Myasnikova, Dr. Sci. (Phys.-Math.), Professor, Department of Theoretical and Computational Physics

105/42, Bolshaya Sadovaya ul., Rostov-on-Don, 344006

myasnikova67@yandex.ruМИРЭА Российский технологический университетРоссияMIREA Russian Technological UniversityRussian FederationЮжный федеральный университетРоссияSouthern Federal UniversityRussian FederationРостовский государственный медицинский университетРоссияRostov State Medical UniversityRussian Federation202608082026144106115Copyright © Доронкина С.В., Бабаянц А.С., Лисица И.В., Мясникова А.Э., 20262026Доронкина С.В., Бабаянц А.С., Лисица И.В., Мясникова А.Э.Doronkina S.V., Babayants A.S., Lisitsa I.V., Myasnikova A.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.rtj-mirea.ru/jour/article/view/1621Цели

Цели. С целью объяснения природы «водопадов», наблюдаемых в фотоэмиссионных спектрах купратных высокотемпературных сверхпроводников, в работе выполнен расчет фотоэмиссионных спектров с угловым разрешением систем с сильным электрон-фононным взаимодействием (ЭФВ) и законом дисперсии, характерным для купратов, и произведено сравнение полученного спектра с результатами экспериментов на сверхпроводящих купратах.

Методы

Методы. Фотоэмиссионные спектры рассчитаны на основе золотого правила Ферми при использовании энергии связи биполярона и полярона, энергии поля поляризации и волновых функции носителей заряда в них, полученных в рамках двукомпонентной модели, включающей жидкость биполяронов большого радиуса и ферми-жидкость делокализованных носителей заряда. Ранее было показано, что такая двухжидкостная система образует основное и слабо возбужденные состояния систем с сильным фрёлиховским ЭФВ. 

Результаты

Результаты. Рассчитаны спектры фотоэмиссионной спектроскопии с угловым разрешением от систем с сильным ЭФВ и купратоподобной дисперсией при использовании параметров двухжидкостной системы носителей заряда, полученных минимизацией свободной энергии системы. Полученные спектры демонстрируют особенности, наблюдаемые в экспериментальных спектрах купратных сверхпроводников с соответствующим уровнем допирования, что позволяет разобраться в физических причинах этих особенностей. 

Выводы

Выводы. В использованной для расчета модели различная энергетическая цена релаксации системы после фотоэмиссии из автолокализованного и делокализованного состояний, которые при дальнодействующем сильном ЭФВ сосуществуют и делят импульсное пространство в соответствии с принципом Паули, приводит к возникновению «водопадов» в спектрах ARPES[1] в нодальном направлении. Высота «водопада» определяется различием в энергетической стоимости релаксации. Волновой вектор «водопада» связан с равновесным размером биполяронов при данном уровне допирования и температуре соотношением неопределенностей, изменение его величины с допированием согласуется с наблюдаемым в экспериментальных спектрах.

Objectives

Objectives. The nature of the “waterfalls” observed in the photoemission spectra of cuprate high-temperature superconductors is explained by calculating the angle-resolved photoemission spectra of systems with significant electron–phonon interaction and dispersion law characteristic of cuprates. The resulting spectrum is compared with the results of experiments on superconducting cuprates.

Methods

Methods. Photoemission spectra obtained within a two-component model, comprising a liquid of large-radius bipolarons and a Fermi liquid of delocalized charge carriers, are calculated based on Fermi’s golden rule using the bipolaron and polaron binding energies, polarization field energy, and wave functions of charge carriers in them. The approach is based on previous findings that such a two-liquid system forms the ground and weakly excited states of systems with strong Fröhlich electron–phonon interaction.

Results

Results. Angle-resolved photoemission spectra of systems with strong electron–phonon interaction and cupratelike dispersion were calculated using the parameters of a two-fluid charge-carrier system, which were obtained by minimizing the free energy of the system. Features of the resulting spectra observed in the experimental spectra of cuprate superconductors with the corresponding doping level provide a basis to analyze their physical causes. 

Conclusions

Conclusions. The model used for the calculations is characterized by different energies of relaxation following the photoemission from the self-trapped state and delocalized state, which coexist and divide the momentum space in accordance with the Pauli exclusion principle under long-range strong electron–phonon interaction. This energy difference, which leads to the formation of so-called waterfalls in the angle-resolved photoemission spectra (ARPES spectra) in the nodal direction, also determines their heights. The wave vector of the waterfall is associated with the equilibrium size of bipolarons at given doping level and temperature by the uncertainty principle, as well as the change in this wave vector with varying doping level that agrees with the phenomena observed in the experimental spectra.

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The authors declare that there are no conflicts of interest present.