arXiv subjects

Andrew J. Millis

Publications and source records attributed to Andrew J. Millis.

At least 145 records · Page 8Linked to original sources

arXiv2016

Phase diagram of Sr$_{1-x}$Ba$_x$MnO$_3$ as a function of chemical doping, epitaxial strain and external pressure

We use \textit{ab initio} calculations to systematically study the phase diagram of multiferroic Sr$_{1-x}$Ba$_x$MnO$_3$ ($0 \leq x \leq 1$) as a function of chemical doping, epitaxial strain and external pressure. We find that by replacing Sr with Ba in cubic SrMnO$_3$ and imposing epitaxial strain, the material can be tuned to the vicinity of a first order transition between two multiferroic phases, one antiferromagnetic with a smaller polarization and one ferromagnetic with a larger polarization. A giant effective magneto-electric coupling and cross-field control (electric field control of magnetism or magnetic field control of polarization) can be achieved in the vicinity of the transition. The dependence of the theoretically computed transition point on the choice of exchange correlation functionals is determined and is found to be non-negligible. We also show that the perovskite structure of BaMnO$_3$ can be stabilized relative to its hexagonal polymorphs at pressures larger than 20 GPa.

cond-mat.mtrl-sci↗

arXiv2016

Hybrid quantum-classical approach to correlated materials

Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.

quant-ph↗

arXiv2016

Antisite defects at oxide interfaces

We use \textit{ab initio} calculations to estimate formation energies of cation (transition metal) antisite defects at oxide interfaces and to understand the basic physical effects that drive or suppress the formation of these defects. Antisite defects are found to be favored in systems with substantial charge transfer across the interface, while Jahn-Teller distortions and itinerant ferromagnetism can prevent antisite defects and help stabilize atomically sharp interfaces. Our results enable identification of classes of systems that may be more and less susceptible to the formation of antisite defects and motivate experimental studies and further theoretical calculations to elucidate the local structure and stability of oxide interface systems.

cond-mat.mtrl-sci↗

arXiv2016

The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation

The dynamical interplay between electron-electron interactions and electron-phonon coupling is investigated within the Anderson-Holstein model, a minimal model for open quantum systems that embody these effects. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. Both the particle-hole symmetric and the more generic particle-hole asymmetric cases are studied. The treatment is based on two complementary non-crossing approximations, the first of which is constructed around the weak-coupling limit and the second around the polaron limit. In general, the two methods disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The frameworks used here can form the starting point for numerically exact methods based on bold-line continuous-time quantum Monte Carlo algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.

cond-mat.str-el↗

arXiv2016

Charge transfer and electron-phonon coupling in monolayer FeSe on Nb doped SrTiO$_3$

Monolayer films of FeSe grown on SrTiO$_3$ substrates are electron doped relative to bulk and exhibit a significantly higher superconducting transition temperatures. We present density functional calculations and a modified Schottky model incorporating the strong paraelectricity of SrTiO$_3$ which demonstrate that the doping may be due to charge transfer from SrTiO$_3$ impurity bands driven by work function mismatch. Physically relevant levels of Nb doping are shown to lead to doping of the FeSe compatible with observation. The coupling of electrons in FeSe to polar phonons in the depletion regime of the SrTiO$_3$ is calculated. A $λ\sim 0.4$ is found; the coupling to long-wavelength phonons is found to be dominant.

cond-mat.supr-con↗

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↗

arXiv2015

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

cond-mat.str-el↗

arXiv2015

Photoinduced phase transitions in narrow-gap Mott insulators: the case of VO$_2$

We study the nonequilibrium dynamics of photoexcited electrons in the narrow-gap Mott insulator VO$_2$. The initial stages of relaxation are treated using a quantum Boltzmann equation methodology, which reveals a rapid ($\sim$ femtosecond time scale) relaxation to a pseudothermal state characterized by a few parameters that vary slowly in time. The long-time limit is then studied by a Hartree-Fock methodology, which reveals the possibility of nonequilibrium excitation to a new metastable $M_1$ metal phase that is qualitatively consistent with a recent experiment. The general physical picture of photoexcitation driving a correlated electron system to a new state that is not accessible in equilibrium may be applicable in similar materials.

cond-mat.str-el↗

arXiv2015

Spin-density functional theories and their $+U$ and $+J$ extensions: a comparative study of transition metals and transition metal oxides

Previous work on the physical content of exchange correlation functionals that depend on both charge and spin densities is extended to elemental transition metals and a wider range of perovskite transition metal oxides. A comparison of spectra and magnetic moments calculated using exchange correlation functionals depending on charge density only or on both charge and spin densities, as well as the $+U$ and $+J$ extensions of these methods confirms previous conclusions that the spin-dependent part of the exchange correlation functional provides an effective Hund's interaction acting on the transition metal $d$ orbitals. For the local spin density approximation and spin-dependent Perdew-Burke-Ernzerhof generalized gradient approximation, the effective Hund's exchange is found to be larger than 1 eV. The results indicate that at least as far as applications to transition metals and their oxides are concerned, $+U$, $+J$ and +dynamical mean field theory extensions of density functional theory should be based on exchange-correlation functionals of charge density only.

cond-mat.mtrl-sci↗

arXiv2015

Taming the dynamical sign problem in real-time evolution of quantum many-body problems

Current nonequilibrium Monte Carlo methods suffer from a dynamical sign problem that makes simulating real-time dynamics for long times exponentially hard. We propose a new `Inchworm Algorithm', based on iteratively reusing information obtained in previous steps to extend the propagation to longer times. The algorithm largely overcomes the dynamical sign problem, changing the scaling from exponential to quadratic. We use the method to solve the Anderson impurity model in the Kondo and mixed valence regimes, obtaining results both for quenches and for spin dynamics in the presence of an oscillatory magnetic field.

cond-mat.str-el↗

arXiv2015

Band Structure and Terahertz Optical Conductivity of Transition Metal Oxides: Theory and Application to CaRuO$_3$

Density functional plus dynamical mean field calculations are used to show that in transition metal oxides, rotational and tilting (GdFeO$_3$-type) distortions of the ideal cubic perovskite structure produce a multiplicity of low-energy optical transitions which affect the conductivity down to frequencies of the order of $1$ or $2$~mV (terahertz regime), mimicking non-Fermi-liquid effects even in systems with a strictly Fermi-liquid self-energy. For CaRuO$_3$, a material whose measured electromagnetic response in the terahertz frequency regime has been interpreted as evidence for non-Fermi-liquid physics, the combination of these band structure effects and a renormalized Fermi-liquid self-energy accounts for the low frequency optical response which had previously been regarded as a signature of exotic physics. Signatures of deviations from Fermi-liquid behavior at higher frequencies ($\sim 100$~meV) are discussed.

cond-mat.str-el↗

arXiv2015

Imaginary-time matrix product state impurity solver for dynamical mean-field theory

We present a new impurity solver for dynamical mean-field theory based on imaginary-time evolution of matrix product states. This converges the self-consistency loop on the imaginary-frequency axis and obtains real-frequency information in a final real-time evolution. Relative to computations on the real-frequency axis, required bath sizes are much smaller and less entanglement is generated, so much larger systems can be studied. The power of the method is demonstrated by solutions of a three band model in the single and two-site dynamical mean-field approximation. Technical issues are discussed, including details of the method, efficiency as compared to other matrix product state based impurity solvers, bath construction and its relation to real-frequency computations and the analytic continuation problem of quantum Monte Carlo, the choice of basis in dynamical cluster approximation, and perspectives for off-diagonal hybridization functions.

cond-mat.str-el↗

arXiv2015

Machine learning for many-body physics: efficient solution of dynamical mean-field theory

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both metallic and Mott insulator solutions can be predicted. The validity of the machine learning scheme is assessed by comparing predictions of full correlation functions, of quasi-particle weight and particle density to values directly computed. The results indicate that with modest further development, machine learning approach may be an attractive computational efficient option for real materials predictions for strongly correlated systems.

cond-mat.str-el↗

arXiv2015

Electronic correlations, magnetism and Hund's rule coupling in the ruthenium perovskites SrRuO$_3$ and CaRuO$_3$

A comparative density functional plus dynamical mean field theory study of the pseudocubic ruthenate materials CaRuO$_3$ and SrRuO$_3$ is presented. Phase diagrams are determined for both materials as a function of Hubbard repulsion $U$ and Hund's rule coupling $J$. Metallic and insulating phases are found, as are ferromagnetic and paramagnetic states. The locations of the relevant phase boundaries are determined. Based on the computed phase diagrams, Mott-dominated and Hund's dominated regimes of strong correlation are distinguished. Comparison of calculated properties to experiments indicates that the actual materials are in the Hund's coupling dominated region of the phase diagram so can be characterized as Hund's metals, in common with other members of the ruthenate family. Comparison of the phase diagrams for the two materials reveals the role played by rotational and tilt (GdFeO$_3$-type) distortions of the ideal perovskite structure. The presence of magnetism in SrRuO$_3$ and its absence in CaRuO$_3$ despite the larger mass and larger tilt/rotational distortion amplitude of CaRuO$_3$ can be understood in terms of density of states effects in the presence of strong Hund's coupling. Comparison of the calculated low-$T$ properties of CaRuO$_3$ to those of SrRuO$_3$ provides insight into the effects of magnetic order on the properties of a Hund's metal. The study provides a simultaneous description of magnetism and correlations and explicates the roles played by band theory and Hubbard and Hund's interactions.

cond-mat.str-el↗

arXiv2015

Metal-insulator transitions in GdTiO3/SrTiO3 superlattices

The density functional plus U method is used to obtain the electronic structure, lattice relaxation and metal-insulator phase diagram of superlattices consisting of $m$ layers of Gadolinium Titanate (GdTiO$_{3}$) alternating with $n$ layers of Strontium Titanate (SrTiO$_{3}$). Metallic phases occur when the number of SrTiO$_3$ layers is large or the interaction $U$ is small. In metallic phases, the mobile electrons are found in the SrTiO$_3$ layers, with near-interface electrons occupying $xy$-derived bands, while away from the interface the majority of electrons reside in $xz/yz$ bands. As the thickness of the SrTiO$_3$ layers decreases or the on-site interaction U increases a metal-insulator transition occurs. Two different insulating states are found. When the number of SrTiO$_{3}$ layers is larger than one, we find an insulating state with two sublattice charge and orbital ordering and associated Ti-O bond length disproportionations. When the number of SrTiO$_{3}$ units per layer is one, a different insulating phase occurs driven by orbital ordering within the quasi one-dimensional $xz/yz$ bonding bands connecting Ti atoms across the SrO layer. In this phase there is no sublattice charge ordering or bond disproportionation. The critical U for the single-layer insulator is $\sim$ 2.5 eV, much less than critical U $\sim$ 3.5 eV required to drive the metal-insulator transition when the number of SrTiO$_3$ is larger than one. Inconsistencies between the calculation and the experiment suggest that many-body correlations may be important. A local inversion symmetry breaking around Ti atoms suggests the possibility of in-plane ferroelectric polarization in the insulating phase.

cond-mat.str-el↗

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

Quasiparticle Properties of the Superconducting State of the Two Dimensional Hubbard Model

Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self energy of the two dimensional Hubbard model. From these the evolution of the superconducting gap and the momentum dependent photoemission and inverse photoemission spectra across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a `peak-dip-hump' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the "hump" feature is found to arise from a zero crossing of the real part of the electron self energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented.

cond-mat.str-el↗

arXiv2015

Strain Control of Electronic Phase in Rare Earth Nickelates

We use density functional plus $U$ methods to study the effects of a tensile or compressive substrate strain on the charge-ordered insulating phase of LuNiO$_3$. The numerical results are analyzed in terms of a Landau energy function, with octahedral rotational distortions of the perovskite structure included as a perturbation. Approximately 4% tensile or compressive strain leads to a first-order transition from an insulating structure with large amplitude breathing mode distortions of the NiO$_6$ octahedra to a metallic state in which breathing mode distortions are absent but Jahn-Teller distortions in which two Ni-O bonds become long and the other four become short are present. Compressive strain produces uniform Jahn-Teller order with the long axis aligned perpendicular to the substrate plane while tensile strain produces a staggered Jahn-Teller order in which the long bond lies in the plane and alternates between two nearly orthogonal in-plane directions forming a checkerboard pattern. In the absence of the breathing mode distortions and octahedral rotations, the tensile strain-induced transition to the staggered Jahn-Teller state would be of second order.

cond-mat.str-el↗