arXiv subjects

Richard M. Martin

Publications and source records attributed to Richard M. Martin.

At least 19 recordsLinked to original sources

arXiv2026

Electronic Structure of Epitaxial Films of the Bilayer Strontium Ruthenate: Sr$_{3}$Ru$_2$O$_{7}$

We report a combined study of the low-energy electronic band structure of epitaxial Sr$_3$Ru$_2$O$_7$ films using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT). To investigate the effects of substrate dependence on the band structure, Sr$_3$Ru$_2$O$_7$ thin films are epitaxially grown on SrTiO$_3$ (STO) and (LaAlO$_{3}$)$_{0.3}$(Sr$_{2}$TaAlO$_{6}$)$_{0.7}$ (LSAT) substrates using molecular beam epitaxy. The measured and calculated Fermi-surfaces clearly show substantial changes in the Fermi surface topologies that originate from the underlying strain states. The compressively strained film grown on LSAT exhibits Fermi-surface features consistent with an orthorhombic-like symmetry; and the tensile-strained film grown on STO features a tetragonal-like surface symmetry. In addition, the ARPES data for both films indicate weakly dispersive spectral features within $\sim15~\text{meV}$ below the Fermi level. These observations underscore the strong sensitivity of the electronic structure of Sr$_3$Ru$_2$O$_7$ to epitaxial strain and establish a foundation for future efforts to tune correlated phases in this bilayer ruthenate.

cond-mat.str-el↗

arXiv2025

Energy density and stress fields in quantum systems

There has been an enduring interest and controversy about whether or not one can define physically meaningful energy density and stress fields, $e(\bf{r})$ and $σ_{αβ}(\bf{r})$, since the two forms of the kinetic energy, $\frac{1}{2}|\nabla Ψ|^2$ and $-\frac{1}{2}Ψ\nabla^2 Ψ$, lead to different densities, and analogous issues arise for interactions. This paper considers the ground state of a system of many interacting particles in an external potential, and presents a resolution in steps. 1) For the kinetic energy all effects of exchange and correlation are shown to be unique functions of position $\bf{r}$; all issues of non-uniqueness involve only the density $n(\bf{r})$ and are equivalent to an effective single-particle problem with wavefunction $s(\bf{r}) = \sqrt{n(\bf{r})/N}$. 2) Interactions can be considered as potentials acting on particles or interaction fields, e.g., the Maxwell form in terms of electric fields. In each case, there is a mean field part that is a function of the density and a part due to correlation that is uniquely defined. 3) The final results follow from the nature of energy and stress. Because the energy determines the ground state itself through the variational principle, the kinetic energy must involve $-\frac{1}{2}s\nabla^2 s$ and interactions in terms of potentials. This leads to density functional theory interpreted as energy density $e(\bf{r})$ equilibrated to minimize fluctuations with the same chemical potential at all points $\bf{r}$. However, stress is related to forces, and the only acceptable expressions for the stress field involve the combination $\frac{1}{2}[s\nabla^2 s - |\nabla s|^2]$, and Coulomb interactions in terms of electric fields. Together these results lead to well-defined formulations of energy density and stress fields that are physically motivated and based on a clear set of arguments.

cond-mat.mtrl-sci↗

arXiv2025

Optical bounds on many-electron localization

We establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length $\ell$ (the quantum fluctuations in polarization), electric susceptibility $χ$, and optical gap $E_{\rm G}$. All-electron and valence-only versions of the bounds are given, and the latter are found to be more informative. The bounds on $\ell$ are particularly interesting, as they provide reasonably tight estimates for an ellusive ground-state property - the average localization length of valence electrons - from tabulated experimental data: electron density, high-frequency dielectric constant, and optical gap. The localization lengths estimated in this way for several materials follow simple chemical trends, especially for the alkali halides. We also illustrate our findings via analytically solvable harmonic oscillator models, which reveal an intriguing connection to the physics of long-ranged van der Waals forces.

cond-mat.mtrl-sci↗

arXiv2025

Layer-dependent spin-resolved electronic structure of ferromagnetic triple-layered ruthenate Sr$_4$Ru$_3$O$_{10}$

High-resolution angle- and spin-resolved photoemission spectroscopy (ARPES) of the triple-layered ruthenate Sr$_4$Ru$_3$O$_{10}$ reveals features of the electronic structure that extend our understanding of the layered strontium ruthenates. The spectra near the Fermi energy are very different from the non-magnetic analogues Sr$_2$RuO$_4$ and Sr$_3$Ru$_2$O$_7$ with distinct Fermi surfaces for wide electron-like minority spin bands around the zone center and narrow hole-like majority spin Fermi surface contours around the zone corners. The most dramatic results are two narrow spectral peaks $\sim$30 meV below the Fermi-level, a spin-minority hole-like band at the Brillouin zone center, and a spin-majority saddle-band van Hove singularity at the zone edge, which exhibits almost 100\% spin-polarization at low temperature, and a strong temperature dependent coherence-incoherence crossover attributed to Hund metal correlations. Quantitative comparison of the ARPES to spin-polarized density functional theory (DFT) calculations identify the specific antibonding and nonbonding orbital origins of the narrow bands, with a prediction of different spatial localization in the central and outer layers. This is shown to be consistent with experimental ARPES multi-zone matrix element intensity variations, and implicates outer-layer-specific control of the in-plane metamagnetism. The renormalization of the bands relative to the mean-field DFT, the demonstration of spin-polarized oxygen bands, and of spin-minority and spin-majority band-crossing hybridization, provide a more complete picture of the magnetism which displays aspects of both delocalized and local moment behavior.

cond-mat.str-el↗

arXiv2022

Electronic Structure and Magnetism of the Triple-layered Ruthenate Sr$_{4}$Ru$_{3}$O$_{10}$

We report electronic band structure calculations for Sr$_{4}$Ru$_{3}$O$_{10}$ that displays both ferromagnetic and metamagnetic behavior. The density functional calculations find the ground state to be ferromagnetic in agreement with the experiment and we find that the inclusion of Coulomb Hubbard interaction U applied to the Ru 4d states has dramatic effects on the Fermi surface, which reveal the role of Coulomb interactions and correlated many-body physics. The minority spin bands are mainly empty with Fermi surfaces in the outer areas of the Brillouin zone away from the $Γ$ point with bands that disperse steeply upward. The majority spin bands are full or nearly fully occupied and form narrow bands near the Fermi energy around the $Γ$ point, which could be the electronic origin of the metamagnetism. The results are in qualitative agreement with recent angle resolved photoemission spectroscopy (ARPES) experiments and show the need for a combined theoretical study and experimental ARPES investigation with better energy resolution to reveal the nature of the narrow bands close to the Fermi-level, which is critical for understanding the exotic magnetic properties observed in this material.

cond-mat.str-el↗

arXiv2018

Associating Growth in Infancy and Cognitive Performance in Early Childhood: A functional data analysis approach

Physical growth traits can be naturally represented by continuous functions. In a large dataset of infancy growth patterns, we develop a practical approach to infer statistical associations between growth-trajectories and IQ performance in early childhood. The main objective of this study is to show how to assess physical growth curves and detect if particular infancy growth patterns are associated with differences in IQ (Full-scale WASI scores) in later ages using a semi-parametric functional response model. Additionally, we investigate the association between different growth measurements in terms of their cross-correlation with each other, their correlation with later IQ, as well as their time-varying dynamics. This analysis framework can easily incorporate or learn population information in a non-parametric way, rendering the existence of prior population charts partially redundant.

stat.AP↗

arXiv2018

QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org .

physics.comp-ph↗

arXiv2010

Energy density in density functional theory: Application to crystalline defects and surfaces

We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.

cond-mat.mtrl-sci↗

arXiv2010

Electrical conductivity of high-pressure liquid hydrogen by quantum Monte Carlo methods

We compute the electrical conductivity for liquid hydrogen at high pressure using quantum Monte Carlo. The method uses Coupled Electron-Ion Monte Carlo to generate configurations of liquid hydrogen. For each configuration correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give AC electrical conductivity directly. The extrapolated DC conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transition at high pressure. Our results are in good agreement with shock-wave data.

cond-mat.str-el↗

arXiv2008

On the Origin of the 2DEG Carrier Density at the LaAlO$_3$/SrTiO$_3$ Interface

Transport measurements of the two-dimensional electron gas (2DEG) at the LaAlO$_3$/SrTiO$_3$ interface have found a density of carriers much lower than expected from the "polar catastrophe" arguments. From a detail density-functional study, we suggest how this discrepancy may be reconciled. We find that electrons occupy multiple subbands at the interface leading to a rich array of transport properties. Some electrons are confined to a single interfacial layer and susceptible to localization, while others with small masses and extended over several layers are expected to contribute to transport.

cond-mat.mtrl-sci↗

arXiv2008

Spin resolved energy parametrization of a quasi-one-dimensional electron gas

By carrying out extensive lattice regularized diffusion Monte Carlo calculations, we study the spin and density dependence of the ground state energy for a quasi-one-dimensional electron gas, with harmonic transverse confinement and long-range $1/r$ interactions. We present a parametrization of the exchange-correlation energy suitable for spin density functional calculations, which fulfills exact low and high density limits.

cond-mat.str-el↗

arXiv2008

Renormalization factor and effective mass of the two-dimensional electron gas

We calculate the momentum distribution of the Fermi liquid phase of the homogeneous, two-dimensional electron gas. We show that, close to the Fermi surface, the momentum distribution of a finite system with $N$ electrons approaches its thermodynamic limit slowly, with leading order corrections scaling as $N^{-1/4}$. These corrections dominate the extrapolation of the renormalization factor, $Z$, and the single particle effective mass, $m^*$, to the infinite system size. We show how convergence can be improved analytically. In the range $1 \le r_s \le 10$, we get a lower renormalization factor $Z$ and a higher effective mass, $m^*>m$, compared to the perturbative RPA values.

cond-mat.str-el↗

arXiv2008

Molecular hydrogen adsorbed on benzene: insights from a quantum Monte Carlo study

We present a quantum Monte Carlo study of the hydrogen-benzene system where binding is very weak. We demonstrate that the binding is well described at both variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) levels by a Jastrow correlated single determinant geminal wave function with an optimized compact basis set that includes diffuse orbitals. Agreement between VMC and fixed-node DMC binding energies is found to be within 0.18 mHa, suggesting the calculations are well-converged with respect to the basis. Essentially the same binding is also found in independent DMC calculations using a different trial wave function of a more conventional Slater-Jastrow form, supporting our conclusion that the binding energy is accurate and includes all effects of correlation. We compare with empirical models and previous calculations, and we discuss the physical mechanisms of the interaction, the role of diffuse basis functions, and the charge redistribution in the bond.

cond-mat.mtrl-sci↗

arXiv2008

Efficient method to calculate total energies of large nanoclusters

We present an approach to calculate total energies of nanoclusters based on first principles estimates. For very large clusters the total energy can be separated into surface, edge and corner energies, in addition to bulk contributions. Using this separation and estimating these with direct, first principles calculations, together with the relevant chemical potentials, we have calculated the total energies of Cu and CdSe tetrahedrons containing a large number of atoms. In our work we consider polyhedral clusters so that in addition our work provides direct information on relaxation. For Cu the effects are very small and the clusters vary uniformly from very small to very large sizes. For CdSe there are important variations in surface and edge structures for specific sizes; nevertheless, the approach can be used to extrapolate to large non-stoichiometric clusters with polar surfaces.

cond-mat.mtrl-sci↗

arXiv2007

Disorder Enhanced Spin Polarization in Diluted Magnetic Semiconductors

We present a theoretical study of diluted magnetic semiconductors that includes spin-orbit coupling within a realistic host band structure and treats explicitly the effects of disorder due to randomly substituted Mn ions. While spin-orbit coupling reduces the spin polarization by mixing different spin states in the valence bands, we find that disorder from Mn ions enhances the spin polarization due to formation of ferromagnetic impurity clusters and impurity bound states. The disorder leads to large effects on the hole carriers which form impurity bands as well as hybridizing with the valence band. For Mn doping 0.01 < x < 0.04, the system is metallic with a large effective mass and low mobility.

cond-mat.dis-nn↗

arXiv2006

Electron-Phonon Interactions in C$_{28}$-derived Molecular Solids

We present {\it ab initio} density-functional calculations of molecular solids formed from C$_{28}$-derived closed-shell fullerenes. Solid C$_{28}$H$_4$ is found to bind weakly and exhibits many of the electronic structure features of solid C$_{60}$ with an enhanced electron-phonon interaction potential. We show that chemical doping of this structure is feasible, albeit more restrictive than its C$_{60}$ counterpart, with an estimated superconducting transition temperature exceeding those of the alkali-doped C$_{60}$ solids.

cond-mat.supr-con↗

arXiv2006

The Finite Size Error in Many-body Simulations with long-Ranged Interactions

We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. Finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.

cond-mat.other↗

arXiv2004

Jahn-Teller Distortion and Ferromagnetism in the Dilute Magnetic Semiconductors GaN:Mn

Using first-principles total-energy methods, we investigate Jahn-Teller distortions in III-V dilute magnetic semiconductors, GaAs:Mn and GaN:Mn in the cubic zinc blende structure. The results for an isolated Mn impurity on a Ga site show that there is no appreciable effect in GaAs, whereas, in GaN there is a Jahn-Teller effect in which the symmetry around the impurity changes from T$_{d}$ to D$_{2d}$ or to C$_{2v}$. The large effect in GaN occurs because of the localized d$^4$ character, which is further enhanced by the distortion. The lower symmetry should be detectable experimentally in cubic GaN with low Mn concentration, and should be affected by charge compensation (reductions of holes and conversion of Mn ions to d$^5$ with no Jahn-Teller effect). Jahn-Teller effect is greatly reduced because the symmetry at each Mn site is lowered due to the Mn-Mn interaction. The tendency toward ferromagnetism is found to be stronger in GaN:Mn than in GaAs:Mn and to be only slightly reduced by charge compensation.

cond-mat.mtrl-sci↗