arXiv subjects

Chris A. Marianetti

Publications and source records attributed to Chris A. Marianetti.

At least 37 records · Page 2Linked to original sources

arXiv2019

Off-shell effective energy theory: a unified treatment of the Hubbard model from d=1 to d=$\infty$

Here we propose an exact formalism, off-shell effective energy theory (OET), which provides a thermodynamic description of a generic quantum Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix; and there are dual realizations based on a given partitioning. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix ansatz, and we renormalize the CPE using a standard expansion of the ground state energy. We showcase the OET for the one band Hubbard model in d=1, 2, and $\infty$, using a partitioning between kinetic and potential energy, yielding two realizations denoted as $\mathcal{K}$ and $\mathcal{X}$. OET shows favorable agreement with exact or state-of-the-art results over all parameter space, and has a negligible computational cost. Physically, $\mathcal{K}$ describes the Fermi liquid, while $\mathcal{X}$ gives an analogous description of both the Luttinger liquid and the Mott insulator. Our approach should find broad applicability in lattice model Hamiltonians, in addition to real materials systems.

cond-mat.str-el↗

arXiv2019

A group theoretical approach to computing phonons and their interactions

Here we present four independent advances which facilitate the computation of phonons and their interactions from first-principles. First, we implement a group-theoretical approach to construct the order N Taylor series of a d-dimensional crystal purely in terms of space group irreducible derivatives (ID), which guarantees symmetry by construction and allows for a practical means of communicating and storing phonons and their interactions. Second, we prove that the smallest possible supercell which accommodates N given wavevectors in a d-dimensional crystal is determined using the Smith Normal Form of the matrix formed from the corresponding wavevectors; resulting in negligible computational cost to find said supercell, in addition to providing the maximum required multiplicity for uniform supercells at arbitrary N and d. Third, we develop a series of finite displacement methodologies to compute phonons and their interactions which exploit the first two developments: lone and bundled irreducible derivative (LID and BID) approaches. LID computes a single ID, or as few as possible, at a time in the smallest supercell possible, while BID exploits perturbative derivatives for some order less than N (e.g. Hellman-Feynman forces) in order to extract all ID in the smallest possible supercells using the fewest possible computations. Finally, we derive an equation for the order N-2 volume derivatives of the phonons in terms of the order N ID. Given that the former are easily computed, they can be used as a stringent, infinite ranged test of the ID. Our general framework is illustrated on graphene, yielding irreducible phonon interactions to fifth order. Additionally, we provide a cost analysis for the rock-salt structure at N=3, demonstrating a massive speedup compared to popular finite displacement methods in the literature.

physics.comp-ph↗

arXiv2017

Structural and metal-insulator transitions in rhenium based double perovskites via orbital ordering

Re-based double perovskites (DPs) exhibit a complex interplay of structural and metal-insulator transitions. Here we systematically study the ground state electronic and structural properties for a family of Re-based DPs $A_2B$ReO$_6$ ($A$=Sr, Ca and $B$=Cr, Fe), which are related by a common low energy Hamiltonian, using density functional theory + $U$ calculations. We show that the on-site interaction $U$ of Re induces orbital ordering (denoted COO), with each Re site having an occupied $d_{xy}$ orbital and a C-type alternation among $d_{xz}/d_{yz}$, resulting in an insulating state consistent with experimentally determined insulators Sr$_2$CrReO$_6$, Ca$_2$CrReO$_6$, and Ca$_2$FeReO$_6$. The threshold value of $U_{Re}$ for orbital ordering is reduced by inducing $E_g$ octahedral distortions of the same C-type wavelength (denoted COD), which serves as a structural signature of the orbital ordering; octahedral tilting also reduces the threshold. The COO, and the concomitant COD, are a spontaneously broken symmetry for the Sr based materials (i.e. $a^0a^0c^-$ tilt pattern), while not for the Ca based systems (i.e. $a^-a^-b^+$ tilt pattern). Spin-orbit coupling does not qualitatively change the physics of the COO/COD, but can induce relevant quantitative changes. We prove that a single set of $U_{Cr}$,$U_{Fe}$,$U_{Re}$ capture the experimentally observed metallic state in Sr$_2$FeReO$_6$ and insulating states in the other three systems. We predict that the COO is the origin of the insulating state in Sr$_2$CrReO$_6$, and that the concomitant COD may be experimentally observed at sufficiently low temperatures (ie. space group P$4_2/m$). Additionally, given our prescribed values of $U$, we show that the COO induced insulating state in Ca$_2$CrReO$_6$ will survive even if the COD amplitude is suppressed (e.g. due to thermal fluctuations).

cond-mat.str-el↗

arXiv2016

Compositional phase stability of strongly correlated electron materials within DFT+$U$

Predicting the compositional phase stability of strongly correlated electron materials is an outstanding challenge in condensed matter physics. In this work, we employ the DFT+U formalism to address the effects of local correlations due to transition metal d electrons on compositional phase stability in the prototype phase stable and separating materials LixCoO2 and olivine LixFePO4, respectively. We exploit a new spectral decomposition of the DFT+U total energy, revealing the distinct roles of the filling and ordering of the d orbital correlated subspace. The on-site interaction U drives both of these very different materials systems towards phase separation, stemming from enhanced ordering of the d orbital occupancies in the x=0 and x=1 species, whereas changes in the overall filling of the d shell contribute negligibly. We show that DFT+U formation energies are qualitatively consistent with experiments for phase stable LixCoO2, phase separating LixFePO4, and phase stable LixCoPO4. However, we find that charge ordering plays a critical role in the energetics at intermediate x, strongly dampening the tendency for the Hubbard U to drive phase separation. Most relevantly, the phase stability of Li1/2CoO2 within DFT+U is qualitatively incorrect without allowing charge ordering, which is problematic given that neither charge ordering nor the band gap that it induces are observed in experiment. We demonstrate that charge ordering arises from the correlated subspace interaction energy as opposed to the double counting. Additionally, we predict the Li order-disorder transition temperature for Li1/2CoO2, demonstrating that the unphysical charge ordering within DFT+U renders the method problematic, often producing unrealistically large results. Our findings motivate the need for other advanced techniques, such as DFT+DMFT, for total energies in strongly correlated materials.

cond-mat.str-el↗

arXiv2016

Pressure-resistant intermediate valence in Kondo insulator SmB6

Resonant x-ray emission spectroscopy (RXES) was used to determine the pressure dependence of the f-electron occupancy in the Kondo insulator SmB6. Applied pressure reduces the f-occupancy, but surprisingly, the material maintains a significant divalent character up to a pressure of at least 35 GPa. Thus, the closure of the resistive activation energy gap and onset of magnetic order are not driven by stabilization of an integer valent state. Over the entire pressure range, the material maintains a remarkably stable intermediate valence that can in principle support a nontrivial band structure.

cond-mat.str-el↗

arXiv2016

Electronic correlations in monolayer VS$_2$

The layered transition metal dichalcogenide vanadium disulfide (VS$_2$), which nominally has one electron in the $3d$ shell, is potent for strong correlation physics and is possibly another realization of an effective one-band model beyond the cuprates. Here monolayer VS$_2$ in both the trigonal prismatic and octahedral phases is investigated using density functional theory plus Hubbard $U$ (DFT+$U$) calculations. Trigonal prismatic VS$_2$ has an isolated low-energy band that emerges from a confluence of crystal field splitting and direct V--V hopping. Within spin density functional theory, ferromagnetism splits the isolated band of the trigonal prismatic structure, leading to a low-band-gap $S=1/2$ ferromagnetic Stoner insulator; the octahedral phase is higher in energy. Including the on-site interaction $U$ increases the band gap, leads to Mott insulating behavior, and for sufficiently high values stabilizes the ferromagnetic octahedral phase. The validity of DFT and DFT+$U$ for these two-dimensional materials with potential for strong electronic correlations is discussed. A clear benchmark is given by examining the experimentally observed charge density wave (CDW) in octahedral VS$_2$, for which DFT grossly overestimates the bond length differences compared to known experiments; the presence of CDWs is also probed for the trigonal prismatic phase. Finally, we investigate why only the octahedral phase has been observed in experiments and discuss the possibility of realizing the trigonal prismatic phase. Our work suggests trigonal prismatic VS$_2$ is a promising candidate for strongly correlated electron physics that, if realized, could be experimentally probed in an unprecedented fashion due to its monolayer nature.

cond-mat.str-el↗

arXiv2016

Influence of quantum confinement and strain on orbital polarization of four-layer LaNiO$_3$ superlattices: a DFT+DMFT study

Atomically precise superlattices involving transition metal oxides provide a unique opportunity to engineer correlated electron physics using strain (modulated by choice of substate) and quantum confinement (controlled by layer thickness). Here we use the combination of density functional theory and dynamical mean field theory (DFT+DMFT) to study Ni E$_g$ $d$-orbital polarization in strained LaNiO$_3$/LaAlO$_3$ superlattices consisting of four layers of nominally metallic NiO$_2$ and four layers of insulating AlO$_2$ separated by LaO layers. The layer-resolved orbital polarization is calculated as a function of strain and analyzed in terms of structural, quantum confinement, and correlation effects. The effect of strain is determined from the dependence of the results on the Ni-O bond-length ratio and the octahedral rotation angles; quantum confinement is studied by comparison to bulk calculations with similar degrees of strain; correlation effects are inferred by varying interaction parameters within our DFT+DMFT calculations. The calculated dependence of orbital polarization on strain in superlattices is qualitatively consistent with recent X-ray absorption spectroscopy and resonant reflectometry data. However, interesting differences of detail are found between theory and experiment. Under tensile strain, the two inequivalent Ni ions display orbital polarization similar to that calculated for strained bulk LaNiO$_3$ and observed in experiment. Compressive strain produces a larger dependence of orbital polarization on Ni position and even the inner Ni layer exhibits orbital polarization different from that calculated for strained bulk LaNiO$_3$.

cond-mat.str-el↗

arXiv2016

Applicability of DFT + U to U metal and U-Zr alloy

In the Letter [J. Nucl. Mater. 444, 356 (2014)] and Comment [Phys Rev B 90, 157101 (2014)], Soderlind et al. argue that 1) DFT based on GGA already models U metal and U-Zr alloy accurately, and 2) DFT + U models them worse than DFT according to results they calculate or select from our recent study [Phys. Rev. B 88, 235128 (2013)]. Here we demonstrate in response to 1) that previously neglected and more recent experimental data indicate that DFT, even when implemented in all-electron methods, does not model the bulk modulus and elastic constants of αU very accurately. Furthermore, Soderlind et al.'s claim that deficiency exists in our PAW calculation is unfounded and hence our results, including those that show DFT results compare unfavorably with experimental/computational references, are valid. We also demonstrate in response to 2) that Soderlind et al.'s arguments are unsound for three reasons. First, they focus on just the BCC phases γU and γ(U,Zr)--which at the ab initio modeling temperature of 0 K are unstable and hence difficult to model and benchmar--as primary subjects of examination; however it is results for the stable phases mostly neglected by Soderlind et al. that are the primary evidence of our argument. Second, they make unfounded generalization of DFT + U results at selected U eff values to argue that DFT + U in general gives wrong or unsatisfactory results. Third, some key points in Soderlind et al.'s criticisms of DFT + U are not well supported, including the claims that for γ(U,Zr) DFT + U at Ueff = 1.24 eV gives positive deviations from linear dependence of composition that are unprecedentedly large and partially negative enthalpies of mixing that are inconsistent with the existence of miscibility gap in the experimental phase diagram. We therefore maintain our conclusion that DFT + U can be of value for modeling U and U-Zr.

cond-mat.mtrl-sci↗

arXiv2015

New class of planar ferroelectric Mott insulators via first principles design

Inorganic perovskite oxide ferroelectrics have recently generated substantial interest for photovoltaic applications; however, existing materials suffer from excessive electronic band gaps and insufficient electric polarization. The recent resurgence of hybrid perovskite ferroelectrics addresses the aforementioned deficiencies, but they are highly unstable against environmental effects and an inorganic resolution may still be optimal. Here we use first-principles calculations to design a low band gap, planar ferroelectric by leveraging the complexity of layered double perovskite oxides AA$^\prime $BB$^\prime$O$_6$. We exploit A$\ne$A$^\prime$ size mismatch, a nominally empty $d$-shell on the B-site, and A cations bearing lone-pair electrons to achieve a large ferroelectric polarization. Additionally, B$^\prime\ne$B is chosen to achieve full charge transfer and a Mott susceptible filling on the B$^\prime$-site, yielding a low band gap. These principles are illustrated in BaBiCuVO$_6$, BaBiNiVO$_6$, BaLaCuVO$_6$, and PbLaCuVO$_6$, which could be realized in layer-by-layer growth. This new class of materials could lead to stable, high-efficiency photovoltaic.

cond-mat.mtrl-sci↗

arXiv2015

Density functional versus spin-density functional and the choice of correlated subspace in multi-variable effective action theories of electronic structure

Modern extensions of density functional theory such as the density functional theory plus U and the density functional theory plus dynamical mean-field theory require choices, including selection of variable (charge vs spin density) for the density functional and specification of the correlated subspace. This paper examines these issues in the context of the "plus U" extensions of density functional theory, in which additional correlations on specified correlated orbitals are treated using a Hartree-Fock approximation. Differences between using charge-only or spin-density-dependent exchange-correlation functionals and between Wannier and projector-based definitions of the correlated orbitals are considered on the formal level and in the context of the structural energetics of the rare earth nickelates. It is demonstrated that theories based on spin-dependent exchange-correlation functionals can lead to large and in some cases unphysical effective on-site exchange couplings. Wannier and projector-based definitions of the correlated orbitals lead to similar behavior near ambient pressure, but substantial differences are observed at large pressures. Implications for other beyond density functional methods such as the combination of density functional and dynamical mean field theory are discussed.

cond-mat.str-el↗

arXiv2015

Charge transfer across transition metal oxide interfaces: emergent conductance and new electronic structure

We perform density functional theory plus dynamical mean field theory calculations to investi- gate internal charge transfer in an artificial superlattice composed of alternating layers of vanadate and manganite perovskite and Ruddlesden-Popper structure materials. We show that the elec- tronegativity difference between vanadium and manganese causes moderate charge transfer from VO2 to MnO2 layers in both perovskite and Ruddlesden-Popper based superlattices, leading to hole doping of the VO2 layer and electron doping of the MnO2 layer. Comparison of the perovskite and Ruddlesden-Popper based heterostructures provides insights into the role of the apical oxy- gen. Our first principles simulations demonstrate that the combination of internal charge transfer and quantum confinement provided by heterostructuring is a powerful approach to engineering electronic structure and tailoring correlation effects in transition metal oxides.

cond-mat.mtrl-sci↗

arXiv2014

Density functional plus dynamical mean field theory of the metal-insulator transition in early transition metal oxides

The combination of density functional theory and single-site dynamical mean-field theory, using both Hartree and full continuous-time quantum Monte Carlo impurity solvers, is used to study the metal-insulator phase diagram of perovskite transition-metal oxides of the form $AB$O$_3$ with a rare-earth ion $A$=Sr, La, Y and transition metal $B$=Ti, V, Cr. The correlated subspace is constructed from atomiclike $d$ orbitals defined using maximally localized Wannier functions derived from the full $p$-$d$ manifold; for comparison, results obtained using a projector method are also given. Paramagnetic DFT+DMFT computations using full charge self-consistency along with the standard "fully localized limit" (FLL) double counting are shown to incorrectly predict that LaTiO$_3$, YTiO$_3$, LaVO$_3$ and SrMnO$_3$ are metals. A more general examination of the dependence of physical properties on the mean $p$-$d$ energy splitting, the occupancy of the correlated $d$ states, the double-counting correction, and the lattice structure demonstrates the importance of charge-transfer physics even in the early transition-metal oxides and elucidates the factors underlying the failure of the standard approximations. If the double counting is chosen to produce a $p$-$d$ splitting consistent with experimental spectra, single-site dynamical mean-field theory provides a reasonable account of the materials properties. The relation of the results to those obtained from "$d$-only" models in which the correlation problem is based on the frontier orbital $p$-$d$ antibonding bands is determined. It is found that if an effective interaction $U$ is properly chosen the $d$-only model provides a good account of the physics of the $d^1$ and $d^2$ materials.

cond-mat.str-el↗

arXiv2014

Total energy calculations using DFT+DMFT: computing the pressure phase diagram of the rare earth nickelates

A full implementation of the $ab$ $initio$ density functional plus dynamical mean field theory (DFT+DMFT) formalism to perform total energy calculations and structural relaxations is proposed and implemented. The method is applied to the structural and metal-insulator transitions of the rare earth nickelate perovskites as a function of rare earth ion, pressure, and temperature. In contrast to previous DFT and DFT+$U$ theories, the present method accounts for the experimentally observed structure of $La$NiO$_3$ and the insulating nature of the other perovskites, and quantitatively reproduces the metal-insulator and structural phase diagram in the plane of pressure and rare earth element. The temperature dependence of the energetics of the phase transformation indicates that the thermal transition is driven by phonon entropy effects.

cond-mat.str-el↗

arXiv2014

Computing total energies in complex materials using charge self-consistent DFT+DMFT

We have formulated and implemented a fully charge-self-consistent density functional theory plus dynamical mean field theory methodology which enables an efficient calculation of the total energy of realistic correlated electron systems. The density functional portion of the calculation uses a plane wave basis set within the projector augmented wave method enabling study of systems with large, complex unit cells. The dynamical mean field portion of the calculation is formulated using maximally localized Wannier functions, enabling a convenient implementation which is independent of the basis set used in the density functional portion of the calculation. The importance of using a correct double counting term is demonstrated. A generalized form of the standard double counting correction, which we refer to as the $U^\prime$ form, is described in detail and used. For comparison the density functional plus U method is implemented within the same framework including the generalized double counting. The formalism is validated via a calculation of the metal-insulator and structural phase diagrams of the rare-earth nickelate perovskites as functions of applied pressure and A-site rare-earth ions. The calculated density functional plus dynamical mean field results are found to be consistent with experiment. The density functional plus U method is shown to grossly overestimate the tendency for bond-disproportionation and insulating behavior.

cond-mat.str-el↗

arXiv2014

Selectively Localized Wannier Functions

Since the seminal work of Marzari and Vanderbilt, maximally localized Wannier functions have become widely used as a real-space representation of the electronic structure of periodic materials. In this paper we introduce selectively localized Wannier functions which extend the method of Marzari and Vanderbilt in two important ways. First, our method allows us to focus on localizing a subset of orbitals of interest. Second, our method allows us to fix centers of these orbitals, and ensure the preservation of the point-group symmetry. These characteristics are important when Wannier functions are used in methodologies that go beyond density functional theory by treating a local subspace of the Hamiltonian more effectively. Application of our method to GaAs, SrMnO$_3$, and Co demonstrates that selectively localized Wannier functions can offer improvements over the maximally localized Wannier function technique.

cond-mat.str-el↗

arXiv2014

Covalency and the metal-insulator transition in titanate and vanadate perovskites

A combination of density functional and dynamical mean-field theory is applied to the perovskites SrVO$_3$, LaTiO$_3$ and LaVO$_3$. We show that DFT+DMFT in conjunction with the standard fully localized-limit (FLL) double-counting predicts that LaTiO$_3$ and LaVO$_3$ are metals even though experimentally they are correlation-driven ("Mott") insulators. In addition, the FLL double counting implies a splitting between oxygen $p$ and transition metal $d$ levels which differs from experiment. Introducing into the theory an \textit{ad hoc} double counting correction which reproduces the experimentally measured insulating gap leads also to a $p$-$d$ splitting consistent with experiment if the on-site interaction $U$ is chosen in a relatively narrow range ($\sim 6\pm 1$ eV). The results indicate that these early transition metal oxides will serve as critical test for the formulation of a general \textit{ab initio} theory of correlated electron metals.

cond-mat.str-el↗

arXiv2014

A slave mode expansion for obtaining ab-initio interatomic potentials

Here we propose a new approach for performing a Taylor series expansion of the first-principles computed energy of a crystal as a function of the nuclear displacements. We enlarge the dimensionality of the existing displacement space and form new variables (ie. slave modes) which transform like irreducible representations of the space group and satisfy homogeneity of free space. Standard group theoretical techniques can then be applied to deduce the non-zero expansion coefficients a priori. At a given order, the translation group can be used to contract the products and eliminate terms which are not linearly independent, resulting in a final set of slave mode products. While the expansion coefficients can be computed in a variety of ways, we demonstrate that finite difference is effective up to fourth order. We demonstrate the power of the method in the strongly anharmonic system PbTe. All anharmonic terms within an octahedron are computed up to fourth order. A proper unitary transformation demonstrates that the vast majority of the anharmonicity can be attributed to just two terms, indicating that a minimal model of phonon interactions is achievable. The ability to straightforwardly generate polynomial potentials will allow precise simulations at length and time scales which were previously unrealizable.

cond-mat.mtrl-sci↗

arXiv2014

Three Dimensional Metallic and Two Dimensional Insulating Behavior in Tantalum Dichalcogenides

Using density functional theory with added on-site interactions (DFT+U), we study the electronic structure of bulk, monolayer, and bilayer of the layered transition-metal dichalcogenide $1T-TaS_2$. We show that a two-dimensional spin--$\frac{1}{2}$ Mott-phase exists for the monolayer in the charge-density wave state (CDW) and that such a phase is systematically destroyed by packing of the distorted layers leading to a one dimensional metal for bulk, CDW-distorted TaS$_2$. The latter finding is in contrast with previous DMFT predictions --disagreement we explain by the weak effective interaction felt by the electrons in the CDW state. Experimental observations of insulating behavior may arise from disorder due to stacking faults.

cond-mat.mtrl-sci↗