1
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Alvertis AM, Williams-Young DB, Bruneval F, Neaton JB. Influence of Electronic Correlations on Electron-Phonon Interactions of Molecular Systems with the GW and Coupled Cluster Methods. J Chem Theory Comput 2024; 20:6175-6183. [PMID: 38954597 DOI: 10.1021/acs.jctc.4c00327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/04/2024]
Abstract
Electron-phonon interactions are of great importance to a variety of physical phenomena, and their accurate description is an important goal for first-principles calculations. Isolated examples of materials and molecular systems have emerged where electron-phonon coupling is enhanced over density functional theory (DFT) when using the Green's-function-based ab initio GW method, which provides a more accurate description of electronic correlations. It is, however, unclear how general this enhancement is and how employing high-end quantum chemistry methods, which further improve the description of electronic correlations, might further alter electron-phonon interactions over GW or DFT. Here, we address these questions by computing the renormalization of the highest occupied molecular orbital energies of Thiel's set of organic molecules by harmonic vibrations using DFT, GW, and equation-of-motion coupled-cluster calculations. We find that, depending on the amount of exact exchange included in the DFT starting point, GW can increase the magnitude of the electron-phonon coupling across Thiel's set of molecules by an average factor of 1.1-1.8 compared to the underlying DFT, while equation-of-motion coupled-cluster leads to an increase of 1.4-2. The electron-phonon coupling predicted with the ab initio GW method is generally in much closer agreement to coupled cluster values compared to DFT, establishing GW as a promising route for accurately computing electron-phonon phenomena in molecules and beyond at a much lower computational cost than higher-end quantum chemistry techniques.
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Affiliation(s)
- Antonios M Alvertis
- KBR, Inc., NASA Ames Research Center, Moffett Field, California 94035, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David B Williams-Young
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Fabien Bruneval
- Université Paris-Saclay, CEA, Service de Corrosion et de Comportement des Matériaux, SRMP, 91191 Gif-sur-Yvette, France
| | - Jeffrey B Neaton
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Physics, University of California Berkeley, Berkeley, California 94720, United States
- Kavli Energy NanoScience Institute at Berkeley, Berkeley, California 94720, United States
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2
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Ramasimha Varma A, Paul S, Itale A, Pable P, Tibrewala R, Dodal S, Yerunkar H, Bhaumik S, Shah V, Gururajan MP, Prasanna TRS. Electron-Phonon Interaction Contribution to the Total Energy of Group IV Semiconductor Polymorphs: Evaluation and Implications. ACS OMEGA 2023; 8:11251-11260. [PMID: 37008080 PMCID: PMC10061527 DOI: 10.1021/acsomega.2c08244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/29/2022] [Accepted: 02/28/2023] [Indexed: 06/19/2023]
Abstract
In density functional theory (DFT)-based total energy studies, the van der Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are included to obtain energy differences between polymorphs. We propose and compute a new correction term to the total energy, due to electron-phonon interactions (EPI). We rely on Allen's general formalism, which goes beyond the quasi-harmonic approximation (QHA), to include the free energy contributions due to quasiparticle interactions. We show that, for semiconductors and insulators, the EPI contributions to the free energies of electrons and phonons are the corresponding zero-point energy contributions. Using an approximate version of Allen's formalism in combination with the Allen-Heine theory for EPI corrections, we calculate the zero-point EPI corrections to the total energy for cubic and hexagonal polytypes of carbon, silicon and silicon carbide. The EPI corrections alter the energy differences between polytypes. In SiC polytypes, the EPI correction term is more sensitive to crystal structure than the vdW and ZPVE terms and is thus essential in determining their energy differences. It clearly establishes that the cubic SiC-3C is metastable and hexagonal SiC-4H is the stable polytype. Our results are consistent with the experimental results of Kleykamp. Our study enables the inclusion of EPI corrections as a separate term in the free energy expression. This opens the way to go beyond the QHA by including the contribution of EPI on all thermodynamic properties.
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Affiliation(s)
- Arjun
Varma Ramasimha Varma
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Shilpa Paul
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Anup Itale
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Pranav Pable
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Radhika Tibrewala
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Samruddhi Dodal
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Harshal Yerunkar
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Saurav Bhaumik
- Department
of Mathematics, Indian Institute of Technology
Bombay, Mumbai 400076, India
| | - Vaishali Shah
- Department
of Scientific Computing, Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India
| | | | - Tiramkudlu R. S. Prasanna
- Department
of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
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3
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Alvertis AM, Haber JB, Engel EA, Sharifzadeh S, Neaton JB. Phonon-Induced Localization of Excitons in Molecular Crystals from First Principles. PHYSICAL REVIEW LETTERS 2023; 130:086401. [PMID: 36898125 DOI: 10.1103/physrevlett.130.086401] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Revised: 01/20/2023] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular, how localized states form, the role of specific vibrations, and the relative importance of quantum and thermal nuclear fluctuations. Here, we present a first-principles study of these phenomena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons, exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory, the ab initio GW-Bethe-Salpeter equation approach, finite-difference, and path integral techniques. We find that for pentacene zero-point nuclear motion causes uniformly strong localization, with thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic effects drive temperature-dependent localization, and, while such effects prevent the emergence of highly delocalized excitons, we explore the conditions under which these might be realized.
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Affiliation(s)
- Antonios M Alvertis
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics, University of California Berkeley, Berkeley, 94720 California, USA
| | - Jonah B Haber
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics, University of California Berkeley, Berkeley, 94720 California, USA
| | - Edgar A Engel
- Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Sahar Sharifzadeh
- Division of Materials Science and Engineering, Boston University, Boston, 02215 Massachusetts, USA
- Department of Electrical and Computer Engineering, Boston University, Boston, 02215 Massachusetts, USA
| | - Jeffrey B Neaton
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics, University of California Berkeley, Berkeley, 94720 California, USA
- Kavli Energy NanoScience Institute at Berkeley, Berkeley, 94720 California, USA
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4
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Lin Z, Liu Y, Wang Z, Xu S, Chen S, Duan W, Monserrat B. Phonon-Limited Valley Polarization in Transition-Metal Dichalcogenides. PHYSICAL REVIEW LETTERS 2022; 129:027401. [PMID: 35867458 DOI: 10.1103/physrevlett.129.027401] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
The ability to selectively photoexcite at different Brillouin zone valleys forms the basis of valleytronics and other valley-related physics. Symmetry arguments combined with static lattice first-principles calculations suggest an ideal 100% valley polarization in transition-metal dichalcogenides under circularly polarized light. However, experimental reports of the valley polarization range from 32% to almost 100%. Possible explanations for this discrepancy include phonon-mediated transitions, which would place a fundamental limit to valley polarization, and defect-mediated transitions, which could, in principle, be reduced with cleaner samples. We explore the phonon-mediated fundamental limit by performing calculations of phonon-mediated optical absorption for circularly polarized light entirely from the first principles. We also use group theory to reveal the microscopic mechanisms behind the phonon-mediated excitations, discovering contributions from several individual phonon modes and from multiphonon processes. Overall, our calculations show that the phonon-limited valley polarization is around 70% at room temperature for state-of-the-art valleytronic materials including MoSe_{2}, MoS_{2}, WS_{2}, WSe_{2}, and MoTe_{2}. This fundamental limit implies that sufficiently pure transition-metal dichalcogenides are ideal candidates for valleytronics applications.
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Affiliation(s)
- Zuzhang Lin
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Yizhou Liu
- Department of Condensed Matter Physics, Weizmann Institute of Science, 7610001 Rehovot, Israel
| | - Zun Wang
- State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Shengnan Xu
- State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Siyu Chen
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Wenhui Duan
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
| | - Bartomeu Monserrat
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
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5
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Zacharias M, Kelires PC. Quantum Confinement of Electron-Phonon Coupling in Graphene Quantum Dots. J Phys Chem Lett 2021; 12:9940-9946. [PMID: 34614351 DOI: 10.1021/acs.jpclett.1c02899] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
On the basis of first-principles calculations and the special displacement method, we demonstrate the quantum confinement scaling law of the phonon-induced gap renormalization of graphene quantum dots (GQDs). We employ zigzag-edged GQDs with hydrogen passivation and embedded in hexagonal boron nitride. Our calculations for GQDs in the sub-10 nm region reveal strong quantum confinement of the zero-point renormalization ranging from 20 to 250 meV. To obtain these values we introduce a correction to the Allen-Heine theory of temperature-dependent energy levels that arises from the phonon-induced splitting of 2-fold degenerate edge states. This correction amounts to more than 50% of the gap renormalization. We also present momentum-resolved spectral functions of GQDs, which are not reported in previous contributions. Our results lay the foundation to systematically engineer temperature-dependent electronic structures of GQDs for applications in solar cells, electronic transport, and quantum computing devices.
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Affiliation(s)
- Marios Zacharias
- Research Unit for Nanostructured Materials Systems, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol, Cyprus
- Department of Mechanical and Materials Science Engineering, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol, Cyprus
| | - Pantelis C Kelires
- Research Unit for Nanostructured Materials Systems, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol, Cyprus
- Department of Mechanical and Materials Science Engineering, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol, Cyprus
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6
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Wang X, Berkelbach TC. Absorption Spectra of Solids from Periodic Equation-of-Motion Coupled-Cluster Theory. J Chem Theory Comput 2021; 17:6387-6394. [PMID: 34559525 DOI: 10.1021/acs.jctc.1c00692] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present ab initio absorption spectra of six three-dimensional semiconductors and insulators calculated using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The spectra are calculated efficiently by solving a system of linear equations at each frequency, giving access to an energy range of tens of electronvolts without explicit enumeration of excited states. We assess the impact of cost-saving approximations associated with Brillouin zone sampling, frozen orbitals, and the partitioned EOM-CCSD approximation. Although our most converged spectra exhibit line shapes that are in good agreement with experimental spectra, they are uniformly shifted to higher energies by about 1 eV, which is not explained by the remaining finite-size errors. We tentatively attribute this discrepancy to a combination of vibrational effects and the remaining electron correlation, i.e., triple excitations and above.
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Affiliation(s)
- Xiao Wang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Timothy C Berkelbach
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States.,Department of Chemistry, Columbia University, New York, New York 10027, United States
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7
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Park S, Wang H, Schultz T, Shin D, Ovsyannikov R, Zacharias M, Maksimov D, Meissner M, Hasegawa Y, Yamaguchi T, Kera S, Aljarb A, Hakami M, Li L, Tung V, Amsalem P, Rossi M, Koch N. Temperature-Dependent Electronic Ground-State Charge Transfer in van der Waals Heterostructures. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2008677. [PMID: 34032324 PMCID: PMC11468622 DOI: 10.1002/adma.202008677] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Revised: 04/03/2021] [Indexed: 06/12/2023]
Abstract
Electronic charge rearrangement between components of a heterostructure is the fundamental principle to reach the electronic ground state. It is acknowledged that the density of state distribution of the components governs the amount of charge transfer, but a notable dependence on temperature is not yet considered, particularly for weakly interacting systems. Here, it is experimentally observed that the amount of ground-state charge transfer in a van der Waals heterostructure formed by monolayer MoS2 sandwiched between graphite and a molecular electron acceptor layer increases by a factor of 3 when going from 7 K to room temperature. State-of-the-art electronic structure calculations of the full heterostructure that accounts for nuclear thermal fluctuations reveal intracomponent electron-phonon coupling and intercomponent electronic coupling as the key factors determining the amount of charge transfer. This conclusion is rationalized by a model applicable to multicomponent van der Waals heterostructures.
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Affiliation(s)
- Soohyung Park
- Advanced Analysis CenterKorea Institute of Science and Technology (KIST)Seoul02792South Korea
| | - Haiyuan Wang
- Fritz Haber Institute of the Max Planck Society14195BerlinGermany
- Chaire de Simulation à l'Echelle Atomique (CSEA)Ecole Polytechnique Fédérale de Lausanne (EPFL)LausanneCH‐1015Switzerland
| | - Thorsten Schultz
- Humboldt‐Universität zu BerlinInstitut für Physik and IRIS Adlershof12489BerlinGermany
- Helmholtz‐Zentrum für Materialien und Energie GmbH12489BerlinGermany
| | - Dongguen Shin
- Humboldt‐Universität zu BerlinInstitut für Physik and IRIS Adlershof12489BerlinGermany
| | | | - Marios Zacharias
- Fritz Haber Institute of the Max Planck Society14195BerlinGermany
- Department of Mechanical and Materials Science EngineeringCyprus University of TechnologyLimassol3603Cyprus
| | - Dmitrii Maksimov
- Fritz Haber Institute of the Max Planck Society14195BerlinGermany
- Max Planck Institute for the Structure and Dynamics of Matter22761HamburgGermany
| | | | | | | | - Satoshi Kera
- Institute for Molecular ScienceOkazaki444‐8585Japan
| | - Areej Aljarb
- Physical Sciences and EngineeringKing Abdullah University of Science and TechnologyThuwal23955‐6900Saudi Arabia
| | - Mariam Hakami
- Physical Sciences and EngineeringKing Abdullah University of Science and TechnologyThuwal23955‐6900Saudi Arabia
| | - Lain‐Jong Li
- Physical Sciences and EngineeringKing Abdullah University of Science and TechnologyThuwal23955‐6900Saudi Arabia
- Department of Mechanical EngineeringThe University of Hong KongPok Fu Lam RoadHong KongChina
| | - Vincent Tung
- Physical Sciences and EngineeringKing Abdullah University of Science and TechnologyThuwal23955‐6900Saudi Arabia
| | - Patrick Amsalem
- Humboldt‐Universität zu BerlinInstitut für Physik and IRIS Adlershof12489BerlinGermany
| | - Mariana Rossi
- Fritz Haber Institute of the Max Planck Society14195BerlinGermany
- Max Planck Institute for the Structure and Dynamics of Matter22761HamburgGermany
| | - Norbert Koch
- Humboldt‐Universität zu BerlinInstitut für Physik and IRIS Adlershof12489BerlinGermany
- Helmholtz‐Zentrum für Materialien und Energie GmbH12489BerlinGermany
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8
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Fidanyan K, Hamada I, Rossi M. Quantum Nuclei at Weakly Bonded Interfaces: The Case of Cyclohexane on Rh(111). ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000241] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Karen Fidanyan
- Fritz Haber Institute of the Max Planck Society Faradayweg 4‐6 Berlin 14195 Germany
- Max Planck Institute for the Structure and Dynamics of Matter Luruper Chaussee 149 Hamburg 22761 Germany
| | - Ikutaro Hamada
- Department of Precision Engineering Graduate School of Engineering Osaka University 2‐1 Yamadaoka Suita Osaka 565‐0871 Japan
| | - Mariana Rossi
- Fritz Haber Institute of the Max Planck Society Faradayweg 4‐6 Berlin 14195 Germany
- Max Planck Institute for the Structure and Dynamics of Matter Luruper Chaussee 149 Hamburg 22761 Germany
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9
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Gorelov V, Ceperley DM, Holzmann M, Pierleoni C. Electronic structure and optical properties of quantum crystals from first principles calculations in the Born–Oppenheimer approximation. J Chem Phys 2020; 153:234117. [DOI: 10.1063/5.0031843] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vitaly Gorelov
- Maison de la Simulation, CEA, CNRS, Univ. Paris-Sud, UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - David M. Ceperley
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Markus Holzmann
- Univ. Grenoble Alpes, CNRS, LPMMC, 3800 Grenoble, France
- Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France
| | - Carlo Pierleoni
- Maison de la Simulation, CEA, CNRS, Univ. Paris-Sud, UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
- Department of Physical and Chemical Sciences, University of L’Aquila, Via Vetoio 10, I-67010 L’Aquila, Italy
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10
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de Miguel R, Rubí JM. Statistical Mechanics at Strong Coupling: A Bridge between Landsberg's Energy Levels and Hill's Nanothermodynamics. NANOMATERIALS 2020; 10:nano10122471. [PMID: 33321739 PMCID: PMC7764728 DOI: 10.3390/nano10122471] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/21/2020] [Revised: 12/03/2020] [Accepted: 12/06/2020] [Indexed: 12/27/2022]
Abstract
We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill's nanothermodynamics.
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Affiliation(s)
- Rodrigo de Miguel
- Department of Teacher Education, Norwegian University of Science and Technology, 7491 Trondheim, Norway
- Correspondence: ; Tel.: +47-73412115
| | - J. Miguel Rubí
- Department of Condensed Matter Physics, University of Barcelona, 08007 Barcelona, Spain;
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11
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Gorelov V, Holzmann M, Ceperley DM, Pierleoni C. Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure. PHYSICAL REVIEW LETTERS 2020; 124:116401. [PMID: 32242714 DOI: 10.1103/physrevlett.124.116401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Accepted: 02/13/2020] [Indexed: 06/11/2023]
Abstract
We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical quantum Monte Carlo methods properly extended to quantum and thermal crystals, simulated by coupled electron ion Monte Carlo methods. Nuclear zero point effects cause a large reduction in the gap (∼2 eV). Depending on the structure, the fundamental indirect gap closes between 380 and 530 GPa for ideal crystals and 330-380 GPa for quantum crystals. Beyond this pressure the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ∼450-500 GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.
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Affiliation(s)
- Vitaly Gorelov
- Université Paris-Saclay, UVSQ, CNRS, CEA, Maison de la Simulation, 91191, Gif-sur-Yvette, France
| | - Markus Holzmann
- Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
- Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France
| | - David M Ceperley
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Carlo Pierleoni
- Université Paris-Saclay, UVSQ, CNRS, CEA, Maison de la Simulation, 91191, Gif-sur-Yvette, France
- Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio 10, I-67010 L'Aquila, Italy
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12
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Paleari F, P C Miranda H, Molina-Sánchez A, Wirtz L. Exciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride. PHYSICAL REVIEW LETTERS 2019; 122:187401. [PMID: 31144865 DOI: 10.1103/physrevlett.122.187401] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Revised: 02/05/2019] [Indexed: 06/09/2023]
Abstract
We present an ab initio method to calculate phonon-assisted absorption and emission spectra in the presence of strong excitonic effects. We apply the method to bulk hexagonal BN, which has an indirect band gap and is known for its strong luminescence in the UV range. We first analyze the excitons at the wave vector q[over ¯] of the indirect gap. The coupling of these excitons with the various phonon modes at q[over ¯] is expressed in terms of a product of the mean square displacement of the atoms and the second derivative of the optical response function with respect to atomic displacement along the phonon eigenvectors. The derivatives are calculated numerically with a finite difference scheme in a supercell commensurate with q[over ¯]. We use detailed balance arguments to obtain the intensity ratio between emission and absorption processes. Our results explain recent luminescence experiments and reveal the exciton-phonon coupling channels responsible for the emission lines.
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Affiliation(s)
- Fulvio Paleari
- Physics and Materials Science Research Unit, University of Luxembourg, 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg
| | - Henrique P C Miranda
- Physics and Materials Science Research Unit, University of Luxembourg, 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg
- Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des étoiles 8, bte L7.03.01, 1348, Louvain-la-Neuve, Belgium
| | - Alejandro Molina-Sánchez
- Institute of Materials Science (ICMUV), University of Valencia, Catedrático Beltrán 2, E-46980 Valencia, Spain
| | - Ludger Wirtz
- Physics and Materials Science Research Unit, University of Luxembourg, 162a avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg
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13
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Monserrat B. Electron-phonon coupling from finite differences. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:083001. [PMID: 29328057 DOI: 10.1088/1361-648x/aaa737] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.
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Affiliation(s)
- Bartomeu Monserrat
- Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019, United States of America. TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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14
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de Miguel R, Rubi JM. Finite Systems in a Heat Bath: Spectrum Perturbations and Thermodynamics. J Phys Chem B 2016; 120:9180-6. [DOI: 10.1021/acs.jpcb.6b05591] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Rodrigo de Miguel
- Section for Natural Science,
FLT Faculty, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - J. Miguel Rubi
- Departament de
Fisica Fonamental,
Facultat de Fisica, Universitat de Barcelona, 08029 Barcelona, Spain
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15
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Engel EA, Monserrat B, Needs RJ. Vibrational effects on surface energies and band gaps in hexagonal and cubic ice. J Chem Phys 2016; 145:044703. [DOI: 10.1063/1.4959283] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Edgar A. Engel
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Bartomeu Monserrat
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA
| | - Richard J. Needs
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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16
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Engel EA, Monserrat B, Needs RJ. Vibrational renormalisation of the electronic band gap in hexagonal and cubic ice. J Chem Phys 2015; 143:244708. [DOI: 10.1063/1.4938029] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Edgar A. Engel
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Bartomeu Monserrat
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA
| | - Richard J. Needs
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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17
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Poncé S, Gillet Y, Laflamme Janssen J, Marini A, Verstraete M, Gonze X. Temperature dependence of the electronic structure of semiconductors and insulators. J Chem Phys 2015; 143:102813. [PMID: 26374006 DOI: 10.1063/1.4927081] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.
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Affiliation(s)
- S Poncé
- European Theoretical Spectroscopy Facility and Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des étoiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium
| | - Y Gillet
- European Theoretical Spectroscopy Facility and Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des étoiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium
| | - J Laflamme Janssen
- European Theoretical Spectroscopy Facility and Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des étoiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium
| | - A Marini
- Consiglio Nazionale delle Ricerche (CNR), Via Salaria Km 29.3, CP 10, 00016 Monterotondo Stazione, Italy
| | - M Verstraete
- European Theoretical Spectroscopy Facility and Physique des matériaux et nanostructures, Université de Liège, Allée du 6 Août 17, B-4000 Liège, Belgium
| | - X Gonze
- European Theoretical Spectroscopy Facility and Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des étoiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium
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18
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Zacharias M, Patrick CE, Giustino F. Stochastic Approach to Phonon-Assisted Optical Absorption. PHYSICAL REVIEW LETTERS 2015; 115:177401. [PMID: 26551142 DOI: 10.1103/physrevlett.115.177401] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Indexed: 06/05/2023]
Abstract
We develop a first-principles theory of phonon-assisted optical absorption in semiconductors and insulators which incorporates the temperature dependence of the electronic structure. We show that the Hall-Bardeen-Blatt theory of indirect optical absorption and the Allen-Heine theory of temperature-dependent band structures can be derived from the present formalism by retaining only one-phonon processes. We demonstrate this method by calculating the optical absorption coefficient of silicon using an importance sampling Monte Carlo scheme, and we obtain temperature-dependent line shapes and band gaps in good agreement with experiment. The present approach opens the way to predictive calculations of the optical properties of solids at finite temperature.
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Affiliation(s)
- Marios Zacharias
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - Christopher E Patrick
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - Feliciano Giustino
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
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