Mean-field approximation of the Hubbard model expressed in a many-body basis

The effective independent-particle (mean-field) approximation of the Hubbard Hamiltonian is described in a many-body basis to develop a formal comparison with the exact diagonalization of the full Hubbard model, using small atomic chain as test systems. This allows for the development of an intuitive understanding of the shortcomings of the mean-field approximation and of how critical correlation effects are missed in this popular approach. The description in the many-body basis highlights a potential ambiguity related to the definition of the density of states. Specifically, satellite peaks are shown to emerge in the mean-field approximation, in departure from the common belief that they characterize correlation effects. The scheme emphasizes the importance of correlation and how different many-body corrections can improve the mean-field description. The pedagogical treatment is expected to make it possible for researchers to acquire an improved understanding of many-body effects as found in various areas related to electronic properties of molecules and solids, which is highly relevant to current efforts in quantum information and quantum computing

Robust correlated magnetic moments in end-modified graphene nanoribbons

We conduct a theoretical examination of the electronic and magnetic characteristics of end-modified 7-atom wide armchair graphene nanoribbons (AGNRs). Our investigation is performed within the framework of a single-band Hubbard model, beyond a mean-field approximation. First, we carry out a comprehensive comparison of various approaches for accommodating di-hydrogenation configurations at the AGNR ends. We demonstrate that the application of an on-site potential to the modified carbon atom, coupled with the addition of an electron, replicates phenomena such as the experimentally observed reduction of the bulk-states (BS) gap. These results for the density of states (DOS) and electronic densities align closely with those obtained through a method explicitly designed to account for the orbital properties of hydrogen atoms. Furthermore, our study enables a clear differentiation between magnetic moments already described in a mean-field (MF) approach, which are spatially confined to the same sites as the topological end-states (ES), and correlation-induced magnetic moments, which exhibit localization along all edges of the AGNRs. Notably, we show the robustness of these correlation-induced magnetic moments relative to end modifications, within the scope of the method we employ.</p

Semi-empirical many-body formalism of optical absorption in nanosystems and molecules

A computationally efficient Green’s function approach is developed to evaluate the optical properties of nanostructures within a semi-empirical Hubbard model. A GW formalism is applied on top of a tight-binding and mean-field approach. The use of the GW approximation includes key parts of the many-body physics that govern the optical response of nanostructures and molecules subjected to an external electromagnetic field and that is not included in the mean-field approximation. Such description of the electron-electron correlation yields computed spectra that compare significantly better with experiment for a subset of polycyclic aromatic hydrocarbons (PAHs) considered for illustrative purpose. More generally, the method is applicable to any structure whose electronic properties can be described in first approximation within a mean-field approach and is amenable for high-throughput studies aimed at screening materials with desired optical properties

Correlation effects on topological end-states in finite-size graphene nanoribbons in the GW approximation

Finite size armchair graphene nanoribbons (GNR) of different families are theoretically studied using the Hubbard model in both mean-field and GW approximations, including spin correlation effects. It is shown that correlation primarily affect the properties of topological end states of the nanoribbons. A representative structure of each of the three GNR families is considered but the 7-atom width nanoribbon is studied in detail and compared to experimental results, showing a clear improvement when correlations are included. Using on numerically computed local density of states, spin-polarized measurements in scanning tunneling microscopy are also suggested to help distinguish and highlight correlation effects

Conductive metal oxide and hafnium oxide bilayer ReRAM:an ab initio study

We perform generalized gradient approximation (GGA) simulations of interfaces between two Conductive Metal-Oxides (CMO, namely TaO and TiO) and cubic hafnium oxide ($HfO_2$) in the context of bilayer Resistive Random Access Memory (ReRAM) devices. We simulate filamentary conduction in $HfO_2$ by creating an atomically thin O atom vacancy path inside $HfO_2$. We show that this atomically thin filament leads to a great reduction of the resistance of the structures. Moreover, we explore the possibility of the influence of O excess inside the CMO on the global resistance of the device and confirm the induced modulation. We also shed the light on two possible causes for the observed increas in the resistance when O atoms are inserted inside the CMO. Eventually, we push forward key differences between devices with TaO and TiO as CMO. We show that structures with TaO are more stable in general and lead to a behaviour implying only low and high resistance (two well separated levels) while structures with TiO allows for intermediate resistances

Semi-empirical many-body formalism of optical absorption in nanosystems and molecules

A computationally efficient Green's function approach is developed to evaluate the optical properties of nanostructures using a GW formalism applied on top of a tight-binding and mean-field Hubbard model. The use of the GW approximation includes key parts of the many-body physics that govern the optical response of nanostructures and molecules subjected to an external electromagnetic field. Such description of the electron-electron correlation yields data that are in significantly improved agreement with experiments performed on a subset of polycyclic aromatic hydrocarbons (PAHs) considered for illustrative purpose. More generally, the method is applicable to any structure whose electronic properties can be described in first approximation within a mean-field approach and is amenable for high-throughput studies aimed at screening materials with desired optical properties

Robust correlated magnetic moments in end-modified graphene nanoribbons

We conduct a theoretical examination of the electronic and magnetic characteristics of end-modified 7-atom wide armchair graphene nanoribbons (AGNRs). Our investigation is performed within the framework of a single-band Hubbard model, beyond a mean-field approximation. First, we carry out a comprehensive comparison of various approaches for accommodating di-hydrogenation configurations at the AGNR ends. We demonstrate that the application of an on-site potential to the modified carbon atom, coupled with the addition of an electron, replicates phenomena such as the experimentally observed reduction in the bulk-states (BS) gap. These results for the density of states (DOS) and electronic densities align closely with those obtained through a method explicitly designed to account for the orbital properties of hydrogen atoms. Furthermore, our study enables a clear differentiation between mean-field (MF) magnetic moments, which are spatially confined to the same sites as the topological end-states (ES), and correlation-induced magnetic moments, which exhibit localization along all edges of the AGNRs. Notably, we find the robustness of these correlation-induced magnetic moments relative to end modifications, within the scope of the method we employ

Conductive metal oxide and hafnium oxide bilayer ReRAM: an ab initio study

We perform generalized gradient approximation (GGA) simulations of interfaces between two Conductive Metal-Oxides (CMO, namely TaO and TiO) and cubic hafnium oxide ($HfO_2$) in the context of bilayer Resistive Random Access Memory (ReRAM) devices. We simulate filamentary conduction in $HfO_2$ by creating an atomically thin O atom vacancy path inside $HfO_2$. We show that this atomically thin filament leads to a great reduction of the resistance of the structures. Moreover, we explore the possibility of the influence of O excess inside the CMO on the global resistance of the device and confirm the induced modulation. We also shed the light on two possible causes for the observed increas in the resistance when O atoms are inserted inside the CMO. Eventually, we push forward key differences between devices with TaO and TiO as CMO. We show that structures with TaO are more stable in general and lead to a behaviour implying only low and high resistance (two well separated levels) while structures with TiO allows for intermediate resistances