A. López, B. Montañes, Ernesto Antonio Medina Dagger
We analyze the scenario of modulating the potential strength of bound atoms in an optical honeycomb lattice patterned by an electric field to emulate uniaxial strain. This modulation can be achieved by a combination of the strength of the patterned electric field and gauge vector effects using the Floquet approach. We show that such a modulation allows one to follow through a topological transition between a semi-metal and a band insulator, when two non-equivalent K points merge as a function of the electric field strength. We explicitly compute the wavefunctions for the moving K points and the Chern numbers up to the transition. Anisotropic effective masses and the insulating gap are described close to the semimetal-insulator transition.
{"title":"Merging of Dirac points through uniaxial modulation on an optical lattice","authors":"A. López, B. Montañes, Ernesto Antonio Medina Dagger","doi":"10.5488/CMP.26.13503","DOIUrl":"https://doi.org/10.5488/CMP.26.13503","url":null,"abstract":"We analyze the scenario of modulating the potential strength of bound atoms in an optical honeycomb lattice patterned by an electric field to emulate uniaxial strain. This modulation can be achieved by a combination of the strength of the patterned electric field and gauge vector effects using the Floquet approach. We show that such a modulation allows one to follow through a topological transition between a semi-metal and a band insulator, when two non-equivalent K points merge as a function of the electric field strength. We explicitly compute the wavefunctions for the moving K points and the Chern numbers up to the transition. Anisotropic effective masses and the insulating gap are described close to the semimetal-insulator transition.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73418823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the three-dimensional site-diluted Ising model with power-law correlated defects and study the critical behavior of the second-moment correlation length and the magnetic susceptibility in the high-temperature phase. By comparing, for various defect correlation strengths, the extracted critical exponents ν and γ with the results of our previous finite-size scaling study, we consolidate the exponent estimates.
{"title":"Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects","authors":"S. Kazmin, W. Janke","doi":"10.5488/CMP.26.13201","DOIUrl":"https://doi.org/10.5488/CMP.26.13201","url":null,"abstract":"We consider the three-dimensional site-diluted Ising model with power-law correlated defects and study the critical behavior of the second-moment correlation length and the magnetic susceptibility in the high-temperature phase. By comparing, for various defect correlation strengths, the extracted critical exponents ν and γ with the results of our previous finite-size scaling study, we consolidate the exponent estimates.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91318666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss the possibility of defining an emergent local temperature in extended quantum many-body systems evolving out of equilibrium. For the most simple case of free-fermionic systems, we give an explicit formula for the effective temperature in the case of, not necessarily unitary, Gaussian preserving dynamics. In this framework, we consider the hopping fermions on a one-dimensional lattice submitted to randomly distributed projective measurements of the local occupation numbers. We show from the average over many quantum trajectories that the effective temperature relaxes exponentially towards infinity.
{"title":"Some speculations about local thermalization of nonequilibrium extended quantum systems","authors":"Máximo Coppola, D. Karevski","doi":"10.5488/CMP.26.13502","DOIUrl":"https://doi.org/10.5488/CMP.26.13502","url":null,"abstract":"We discuss the possibility of defining an emergent local temperature in extended quantum many-body systems evolving out of equilibrium. For the most simple case of free-fermionic systems, we give an explicit formula for the effective temperature in the case of, not necessarily unitary, Gaussian preserving dynamics. In this framework, we consider the hopping fermions on a one-dimensional lattice submitted to randomly distributed projective measurements of the local occupation numbers. We show from the average over many quantum trajectories that the effective temperature relaxes exponentially towards infinity.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81910973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is well known that the Dresselhaus spin-orbit coupling (SOC) in semiconductor two dimensional electron gases (2DEGs) possesses both linear and cubic in momentum contributions. Nevertheless, the latter is usually neglected in most theoretical studies. However, recent Kerr rotation experiments have revealed a significant enhancement of the cubic Dresselhaus interaction by increasing the drift velocities in 2DEGs hosted in GaAs quantum wells. Here, we present a study of the optical spin Hall conductivity in 2DEGs under the simultaneous presence of Rashba and (linear plus cubic) Dresselhaus SOC. The work was done within the Kubo formalism in linear response. We show that the coexistence of the Rashba and cubic Dresselhaus SOC in 2DEGs promotes a strong anisotropy of the band spin splitting which in turn leads to a very characteristic frequency dependence of the spin Hall conductivity. We find that the spin Hall conductivity response could be very sensible to sizeable cubic-Dresselhaus coupling strength. This may be of relevance for the optical control of spin currents in 2DEGs with non-negligible cubic-Dresselhaus SOC.
{"title":"Impact of the p-cubic Dresselhaus term on the spin Hall effect","authors":"E. Santana-Suárez, F. Mireles","doi":"10.5488/CMP.26.13504","DOIUrl":"https://doi.org/10.5488/CMP.26.13504","url":null,"abstract":"It is well known that the Dresselhaus spin-orbit coupling (SOC) in semiconductor two dimensional electron gases (2DEGs) possesses both linear and cubic in momentum contributions. Nevertheless, the latter is usually neglected in most theoretical studies. However, recent Kerr rotation experiments have revealed a significant enhancement of the cubic Dresselhaus interaction by increasing the drift velocities in 2DEGs hosted in GaAs quantum wells. Here, we present a study of the optical spin Hall conductivity in 2DEGs under the simultaneous presence of Rashba and (linear plus cubic) Dresselhaus SOC. The work was done within the Kubo formalism in linear response. We show that the coexistence of the Rashba and cubic Dresselhaus SOC in 2DEGs promotes a strong anisotropy of the band spin splitting which in turn leads to a very characteristic frequency dependence of the spin Hall conductivity. We find that the spin Hall conductivity response could be very sensible to sizeable cubic-Dresselhaus coupling strength. This may be of relevance for the optical control of spin currents in 2DEGs with non-negligible cubic-Dresselhaus SOC.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83462040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the interplay between a Kekulé patterned distortion in monolayer graphene and a monochromatic laser irradiation, focusing in the long wavelength approximation of its Landau level structure. Exploiting the symmetries of the system, we calculate in the static regime an exact analytical solution for the energy spectrum and its eigenstates, which in turn allows us to find close expressions for the polarizations in the valley and pseudospin degrees of freedom. We find that due to the valley-momentum coupling, the valley polarization exhibits a distinct magnetic response for the two K-valley components. Owing to that, the introduction of the radiation field mixes the Landau levels, and it is shown that by tuning the system to resonance leads to a larger valley-polarization response as compared to the non-resonant scenario.
{"title":"Interplay of Kekulé distortions and laser fields in graphene","authors":"A. López, F. Mireles","doi":"10.5488/CMP.26.13505","DOIUrl":"https://doi.org/10.5488/CMP.26.13505","url":null,"abstract":"We study the interplay between a Kekulé patterned distortion in monolayer graphene and a monochromatic laser irradiation, focusing in the long wavelength approximation of its Landau level structure. Exploiting the symmetries of the system, we calculate in the static regime an exact analytical solution for the energy spectrum and its eigenstates, which in turn allows us to find close expressions for the polarizations in the valley and pseudospin degrees of freedom. We find that due to the valley-momentum coupling, the valley polarization exhibits a distinct magnetic response for the two K-valley components. Owing to that, the introduction of the radiation field mixes the Landau levels, and it is shown that by tuning the system to resonance leads to a larger valley-polarization response as compared to the non-resonant scenario.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87036445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. de Pádua Santos, F. Moraes, F. Santos, S. Fumeron
Topological defects in elastic media may be described by a geometric field akin to three-dimensional gravity. From this point of view, disclinations are line defects of zero width corresponding to a singularity of the curvature in an otherwise flat background. On the other hand, in two dimensions, the Frank free energy of a nematic liquid crystal may be interpreted as an Abelian Higgs Lagrangian. In this work, we construct an Abelian Higgs model coupled to ``gravity'' for the nematic phase, with the perspective of finding more realistic disclinations. That is, a cylindrically symmetric line defect of finite radius, invariant under translations along its axis. Numerical analysis of the equations of motion indeed yield a +1 winding number ``thick'' disclination. The defect is described jointly by the gauge and the Higgs fields, that compose the director field, and the background geometry. Away from the defect, the geometry is conical, associated to a dihedral deficit angle. The gauge field, confined to the defect, gives a structure to the disclination while the Higgs field, outside, represents the nematic order.
{"title":"An Abelian Higgs model for disclinations in nematics","authors":"A. de Pádua Santos, F. Moraes, F. Santos, S. Fumeron","doi":"10.5488/CMP.26.13506","DOIUrl":"https://doi.org/10.5488/CMP.26.13506","url":null,"abstract":"Topological defects in elastic media may be described by a geometric field akin to three-dimensional gravity. From this point of view, disclinations are line defects of zero width corresponding to a singularity of the curvature in an otherwise flat background. On the other hand, in two dimensions, the Frank free energy of a nematic liquid crystal may be interpreted as an Abelian Higgs Lagrangian. In this work, we construct an Abelian Higgs model coupled to ``gravity'' for the nematic phase, with the perspective of finding more realistic disclinations. That is, a cylindrically symmetric line defect of finite radius, invariant under translations along its axis. Numerical analysis of the equations of motion indeed yield a +1 winding number ``thick'' disclination. The defect is described jointly by the gauge and the Higgs fields, that compose the director field, and the background geometry. Away from the defect, the geometry is conical, associated to a dihedral deficit angle. The gauge field, confined to the defect, gives a structure to the disclination while the Higgs field, outside, represents the nematic order.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88852232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a shell model (SM) for potassium dihydrogen phosphate (KDP) which is fitted to ab initio (AI) results that include nonlocal van der Waals corrections. The SM is comprehensively tested by comparing results of structural, vibrational and ferroelectric properties with AI and experimental data. The relaxed structural parameters are in very good agreement with the AI results and the available experimental data. The Γ-point phonons and the total phonon densities of states (DOSs) in the ferroelectric and paraelectric phases calculated with the developed SM are in good overall agreement with the corresponding AI and experimental data. We also compute the effective Debye temperature as a function of T which shows good accordance with the corresponding AI and experimental results. Classical molecular dynamics (MD) simulations obtained with the developed SM show a FE-PE phase transition at ≈ 360 K in remarkable agreement with ab initio MD calculations.
{"title":"Shell-model and first-principles calculations of vibrational, structural and ferroelectric properties of KH2PO4","authors":"R. Menchón, F. Torresi, J. Lasave, S. Koval","doi":"10.5488/CMP.25.43709","DOIUrl":"https://doi.org/10.5488/CMP.25.43709","url":null,"abstract":"We develop a shell model (SM) for potassium dihydrogen phosphate (KDP) which is fitted to ab initio (AI) results that include nonlocal van der Waals corrections. The SM is comprehensively tested by comparing results of structural, vibrational and ferroelectric properties with AI and experimental data. The relaxed structural parameters are in very good agreement with the AI results and the available experimental data. The Γ-point phonons and the total phonon densities of states (DOSs) in the ferroelectric and paraelectric phases calculated with the developed SM are in good overall agreement with the corresponding AI and experimental data. We also compute the effective Debye temperature as a function of T which shows good accordance with the corresponding AI and experimental results. Classical molecular dynamics (MD) simulations obtained with the developed SM show a FE-PE phase transition at ≈ 360 K in remarkable agreement with ab initio MD calculations.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75909524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As a continuation of the previously published work [Velychko O. V., Stasyuk I. V., Phase Transitions, 2019, 92, 420], a phenomenological framework for the relaxation dynamics of quantum lattice model with multi-well potentials is given in the case of deformed Sn2P2S6 ferroelectric lattice. The framework is based on the combination of statistical equilibrium theory and irreversible thermodynamics. In order to study these dynamics in a connected way we assume that the dipole ordering or polarization (η) and volume deformation (u) can be treated as fluxes and forces in the sense of Onsager theory. From the linear relations between the forces and fluxes, the rate equations are derived and characterized by two relaxation times (τS , τF) which describe the irreversible process near the equilibrium states. The behaviors of τS and τF in the vicinity of ferroelectric phase transitions are studied.
作为先前发表的工作的延续[Velychko O. V.， Stasyuk I. V.， Phase Transitions, 2019, 92,420]，给出了Sn2P2S6铁电晶格变形情况下具有多阱势的量子晶格模型弛化动力学的现象学框架。该框架是基于统计平衡理论和不可逆热力学的结合。为了以一种联系的方式研究这些动力学，我们假设偶极有序或极化(η)和体积变形(u)可以在Onsager理论的意义上被视为通量和力。从力与通量的线性关系出发，导出了速率方程，并用两个松弛时间(τS， τF)来描述接近平衡状态的不可逆过程。研究了铁电相变附近τS和τF的行为。
{"title":"Slow and fast relaxation times of quantum lattice model with local multi-well potentials: phenomenological dynamics for Sn2P2S6 ferroelectric crystals","authors":"R. Erdem, S. Özüm, N. Güçlü","doi":"10.5488/CMP.25.43707","DOIUrl":"https://doi.org/10.5488/CMP.25.43707","url":null,"abstract":"As a continuation of the previously published work [Velychko O. V., Stasyuk I. V., Phase Transitions, 2019, 92, 420], a phenomenological framework for the relaxation dynamics of quantum lattice model with multi-well potentials is given in the case of deformed Sn2P2S6 ferroelectric lattice. The framework is based on the combination of statistical equilibrium theory and irreversible thermodynamics. In order to study these dynamics in a connected way we assume that the dipole ordering or polarization (η) and volume deformation (u) can be treated as fluxes and forces in the sense of Onsager theory. From the linear relations between the forces and fluxes, the rate equations are derived and characterized by two relaxation times (τS , τF) which describe the irreversible process near the equilibrium states. The behaviors of τS and τF in the vicinity of ferroelectric phase transitions are studied.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88810682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Path integral Monte Carlo (PIMC) simulations with very simple models were used in order to unveil the physics behind the isotope effects in H-bonded ferroelectrics. First, we studied geometrical effects in the H-bonds caused by deuteration with a general three-site model based on a back-to-back double Morse potential plus a Morse potential between oxygens, fitted to explain different general features for a wide set of H-bonded compounds. Our model results show the Ubbelohde or geometrical effect (GE), i.e., the expansion of the H-bond with deuteration, in agreement to what is observed in H-bonded ferroelectrics with short H-bonds. Moreover, adjusting the potential parameters to ab initio results, we have developed a 1D model which considers the bilinear proton-proton interaction in mean-field to study nuclear quantum effects that give rise to the GE in KDP crystals. PIMC simulations reveal that protons tunnel more efficiently than deuterons along the 1D chain, giving rise to a strong attraction center that pulls the oxygens together. This mechanism, which is based on the correlation between tunneling and geometrial modifications of the H-bonds, leads to a strong GE in the ordered phase of the chain at low temperature which is in good agreement with the experimental data.
{"title":"Path integral Monte Carlo simulations of the geometrical effects in KDP crystals","authors":"F. Torresi, J. Lasave, S. Koval","doi":"10.5488/CMP.25.43708","DOIUrl":"https://doi.org/10.5488/CMP.25.43708","url":null,"abstract":"Path integral Monte Carlo (PIMC) simulations with very simple models were used in order to unveil the physics behind the isotope effects in H-bonded ferroelectrics. First, we studied geometrical effects in the H-bonds caused by deuteration with a general three-site model based on a back-to-back double Morse potential plus a Morse potential between oxygens, fitted to explain different general features for a wide set of H-bonded compounds. Our model results show the Ubbelohde or geometrical effect (GE), i.e., the expansion of the H-bond with deuteration, in agreement to what is observed in H-bonded ferroelectrics with short H-bonds. Moreover, adjusting the potential parameters to ab initio results, we have developed a 1D model which considers the bilinear proton-proton interaction in mean-field to study nuclear quantum effects that give rise to the GE in KDP crystals. PIMC simulations reveal that protons tunnel more efficiently than deuterons along the 1D chain, giving rise to a strong attraction center that pulls the oxygens together. This mechanism, which is based on the correlation between tunneling and geometrial modifications of the H-bonds, leads to a strong GE in the ordered phase of the chain at low temperature which is in good agreement with the experimental data.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88681858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the temperature dependence of dielectric permittivity along the polar axis for ferroelectric ammonium fluoroberyllate (AFB) crystal in the vicinity of its phase transition points. The experimental data within incommensurately modulated phase of AFB is compared with the predictions of phenomenological models known from the literature: the Curie-Weiss (CW) law, the generalized Curie-Weiss (GCW) law, and the models by Levanyuk and Sannikov (LS) and by Prelovšek, Levstik and Filipič (PLF) suggested for improper ferroelectrics. It is shown that the LS approach describes the temperature behavior of the dielectric permittivity for the AFB crystal better than the CW, GWC and PLF models. The main physical reasons of this situation are elucidated.
{"title":"Temperature dependence of dielectric permittivity in incommensurately modulated phase of ammonium fluoroberyllate","authors":"B. Horon, O. Kushnir, P. Shchepanskyi, V. Stadnyk","doi":"10.5488/CMP.25.43704","DOIUrl":"https://doi.org/10.5488/CMP.25.43704","url":null,"abstract":"We study the temperature dependence of dielectric permittivity along the polar axis for ferroelectric ammonium fluoroberyllate (AFB) crystal in the vicinity of its phase transition points. The experimental data within incommensurately modulated phase of AFB is compared with the predictions of phenomenological models known from the literature: the Curie-Weiss (CW) law, the generalized Curie-Weiss (GCW) law, and the models by Levanyuk and Sannikov (LS) and by Prelovšek, Levstik and Filipič (PLF) suggested for improper ferroelectrics. It is shown that the LS approach describes the temperature behavior of the dielectric permittivity for the AFB crystal better than the CW, GWC and PLF models. The main physical reasons of this situation are elucidated.","PeriodicalId":10528,"journal":{"name":"Condensed Matter Physics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91276378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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