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We re-examine direct CP violation in the quasi-two-body $D\to V\!P$ decays and study CP asymmetries in three-body $D$ decays proceeding through intermediate vector resonances within the framework of the topological amplitude approach for tree amplitudes and the QCD factorization approach for penguin amplitudes. Using the same mechanism of incorporating long-distance penguin-exchange amplitude induced from final-state rescattering that nicely accounts for the CP asymmetry difference between $D^0\to K^+K^-$ and $\pi^+\pi^-$ modes, we find that CP asymmetry can also occur at the per mille level in many of the $D\to V\!P$ channels or otherwise be negligibly small. We point out six golden modes which have sufficiently large branching fractions and direct CP violation of order $10^{-3}$. In particular, the direct CP asymmetry difference $\Delta a_{CP}^{V\!P}$ between $D^0\to K^+K^{*-}$ and $\pi^+\rho^-$ is predicted to be $(-1.61\pm0.33)\times 10^{-3}$, very similar to the counterpart in the $P\!P$ sector. Besides, we find a positive and large CP asymmetry of order $10^{-3}$ in $D^0\to K_S K^{*0}$, an example of the asymmetry induced at the tree level. We take into account the flavor-singlet QCD-penguin contributions to calculate their effects on the modes such as $D\to\pi\phi$ and $D\to \eta \phi$. We compare our results with the other approach in detail. For three-body $D$ decays, we perform the Dalitz plot analysis of those decays mediated by several vector resonances with the same mass but different electric charges. Local CP asymmetry varies in magnitude and sign from region to region and can reach the percent level in certain local regions of phase space due to interference., Comment: 36 pages, 5 figures, 5 reference added, published version in PRD

We propose a logical qubit based on the Blume-Capel model: a higher spin generalization of the Ising chain and which allows for an on-site anisotropy preserving rotational invariance around the Ising axis. We show that such a spin-3/2 Blume-Capel model can also support localized Majorana bound states at the ends of the chain. Inspired by known braiding protocols of these Majorana bound states, upon appropriate manipulation of the system parameters, we demonstrate a set of universal gate operations which act on qubits encoded in the doubly degenerate ground states of the chain., Comment: 7 pages, 4 figures

In this computational work based on density functional theory we study the electronic and electron transport properties of asymmetric multi-layer MoSSe junctions, known as Janus junctions. Focusing on 4-layer systems, we investigate the influence of electric field, electrostatic doping, strain, and interlayer stacking on the electronic structure. We discover that a metal to semiconductor transition can be induced by an out-of-plane electric field. The critical electric field for such a transition can be reduced by in-plane biaxial compressive strain. Due to an intrinsic electric field, a 4-layer MoSSe can rectify out-of-plane electric current. The rectifying ratio reaches 34.1 in a model junction Zr/4-layer MoSSe/Zr. This ratio can be further enhanced by increasing the number of MoSSe layers. In addition, we show a drastic sudden vertical compression of 4-layer MoSSe due to in-plane biaxial tensile strain, indicating a second phase transition. Furthermore, an odd-even effect on electron transmission at the Fermi energy for Zr/$n$-layer MoSSe/Zr junctions with $n=1, \, 2,\, 3, \,\dots,\, 10$ is observed. These findings reveal the richness of physics in this asymmetric system and strongly suggest that the properties of 4-layer MoSSe are highly tunable, thus providing a guide to future experiments relating materials research and nanoelectronics.

We study gate field effects on the Mn$_{12}$O$_{12}$(COOH)$_{16}$(H$_2$O)$_4$ | graphene | GaAs heterostructure via first-principles calculations. We find that under moderate doping levels electrons can be added to but not taken from the single-molecule magnet Mn$_{12}$O$_{12}$(COOH)$_{16}$(H$_2$O)$_4$ (Mn$_{12}$). The magnetic anisotropy energy (MAE) of Mn$_{12}$ decreases as the electron doping level increases, due to electron transfer from graphene to Mn$_{12}$ and change in the band alignment between Mn$_{12}$ and graphene. At an electron doping level of $-5.00 \times 10^{13}\, \textrm{cm}^{-2}$, the MAE decreases by about 18% compared with zero doping. The band alignment between graphene and GaAs is more sensitive to electron doping than to hole doping since the valence band of GaAs is close to the Fermi level. The GaAs substrate induces a small bandgap in the supported graphene under the zero gate field and a nearly strain-free configuration. Finally, we propose a vertical tunnel junction for probing the gate dependence of MAE via electron transport measurements.

It is customary to apply the so-called narrow width approximation $\Gamma(B\to RP_3\to P_1P_2P_3)=\Gamma(B\to RP_3)Br(R\to P_1P_2)$ to extract the branching fraction of the quasi-two-body decay $B\to RP_3$, with $R$ and $P_3$ being an intermediate resonant state and a pseudoscalar meson, respectively. However, the above factorization is valid only in the zero width limit. We consider a correction parameter $\eta_R$ from finite width effects. Our main results are: (i) We present a general framework for computing $\eta_R$ and show that it can be expressed in terms of the normalized differential rate and determined by its value at the resonance. (ii) We introduce a form factor $F(s_{12},m_R)$ for the strong coupling involved in the $R(m_{12})\to P_1P_2$ decay when $m_{12}$ is away from $m_R$. We find that off-shell effects are small in vector meson productions, but prominent in the $K_2^*(1430)$, $\sigma/f_0(500)$ and $K_0^*(1430)$ resonances. (iii) We evaluate $\eta_R$ in the theoretical framework of QCD factorization (QCDF) and in the experimental parameterization (EXPP) for three-body decay amplitudes. In general, $\eta_R^{\rm QCDF}$ and $\eta_R^{\rm EXPP}$ are similar for vector mesons, but different for tensor and scalar resonances. A study of the differential rates enables us to understand the origin of their differences. (iv) Finite-width corrections to $Br(B^-\to RP)_{\rm NWA}$ obtained in the narrow width approximation are generally small, less than 10\%, but they are prominent in $B^-\to\sigma/f_0(500)\pi^-$ and $B^-\to \overline K_0^{*0}(1430)\pi^-$ decays. The EXPP of the normalized differential rates should be contrasted with the theoretical predictions from QCDF calculation as the latter properly takes into account the energy dependence in weak decay amplitudes., Comment: 44 pages, 8 figures, typos corrected, references updated and added, accepted by PRD

For three-body hadron decays mediated by intermediate resonances with large widths, we show how to properly extract the quasi-two-body decay rates for a meaningful comparison with the corresponding theoretical estimates, using several $B$ decays as explicit examples. We compute the correction factor from finite width effects in the QCD factorization approach, and make a comparison with that using the experimental parameterization in which the momentum dependence in the weak dynamics is absent. Although the difference is generally less than $10\%$ for tensor and vector resonances, it can be as large as $(25-40)\%$ for scalar resonances. Our finding can in fact be applied to general quasi-two-body decays., Comment: 5 pages, 2 figures, title changed, version to appear in Phys. Lett. B

This work builds a bridge between density functional theory (DFT) and model interpretations of Anderson's superexchange theory by constructing a $f$-$d$-$p$ model with DFT Wannier functions to enable a direct quantum many-body solution within an embedding approach. When applied to long-range magnetic interactions in a Mn-Ce magnetic molecule, we are able to obtain numerical insights about double exchange and superexchange interactions. Direct metal-metal charge transfer processes are generally weak in this molecule, which leads to small contributions from double exchange interactions. For long-range interactions, Mn-Ce charge transfer is not significant compared to Ce-O charge transfer. The unusual superexchange between Mn atoms with different valence states is identified as the dominant mechanism. This procedure opens a path for quantitative understanding of different exchange interactions in complex magnetic systems, including molecular magnets, transition metal organic frameworks, and other solid materials., Comment: 6 pages, 5 figures

We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework, and a self-consistent scheme is proposed for solving the exact density functional theory. We apply the theory to structurally-disordered systems, symmetric and asymmetric Hubbard dimers, and the corresponding lattice models. The single fermion excitation spectra show a persistent gap due to the fermionic-entanglement-induced pairing condensate. For disordered systems, the density of states at the edge of the gap diverges in the thermodynamic limit, suggesting a topologically ordered phase. A sharp resonance is predicted as the gap is not dependent on the temperature of the system. For the symmetric Hubbard model, the gap for both half-filling and doped case suggests that the quantum phase transition between the antiferromagnetic and superconducting phases is continuous.

The factorized form of unitary coupled cluster theory (UCC) is a promising wave-function ansatz for the variational quantum eigensolver algorithm. Here, we present a quantum inspired algorithm for UCC based on an exact operator identity for the individual UCC factors. We implement this algorithm for calculations of the H$_{10}$ linear chain and the H$_2$O molecule with single and double $\zeta$ basis sets to provide insights about UCC as a wave-function ansatz. We find that as an electronic structure method, UCC could potentially be valuable for strongly correlated systems, for which conventional coupled cluster theory has difficulties. On quantum computers, the factorized form of UCC can also serve as an initial state preparation method for the quantum phase-estimation algorithm, since it yields higher overlap with the ground state than many other common variational ansatzes. This classical algorithm for UCC also enables widespread testing of the technique, which will be useful for benchmarking quantum computations., Comment: 26 pages 7 figures version 2 Sept.23rd 2020

We present in this work a study of tree-dominated charmless three-body decays of $B$ mesons, $B^-\to K^+K^-\pi^-$ and $B^-\to\pi^+\pi^-\pi^-$, within the factorization approach. The main results are: (i) There are two distinct sources of nonresonant contributions: one arises from the $b\to u$ tree transition and the other from the nonresonant matrix element of scalar densities $\langle M_1M_2|\bar q_1 q_2|0\rangle^{\rm NR}$. It turns out that even for tree-dominated three-body decays, dominant nonresonant contributions originate from the penguin diagram rather than from the $b\to u$ tree process, as implied by the large nonresonant component observed recently in the $\pi^- K^+$ system which accounts for one third of the $B^-\to K^+K^-\pi^-$ rate. (ii) The calculated branching fraction of $B^-\to f_2(1270)\pi^-\to K^+K^-\pi^-$ is smaller than the LHCb by a factor of $\sim 7$ in its central value, but the predicted $\B(B^-\to f_2(1270)\pi^-\to\pi^+\pi^-\pi^-)$ is consistent with the data. Branching fractions of $B^-\to f_2(1270)\pi^-$ extracted from the LHCb measurements of these two processes also differ by a factor of seven! Therefore, it is likely that the $f_2(1270)$ contribution to $B^-\to K^+K^-\pi^-$ is largely overestimated experimentally. Including $1/m_b$ power corrections from penguin annihilation inferred from QCD factorization (QCDF), a sizable CP asymmetry of 32\% in the $f_2(1270)$ component agrees with experiment. (iii) A fraction of 5\% for the $\rho(1450)$ component in $B^-\to\pi^+\pi^-\pi^-$ is in accordance with the theoretical expectation. However, a large fraction of 30\% in $B^-\to K^+K^-\pi^-$ is entirely unexpected. This issue needs to be clarified in the future., Comment: 40 pages and 5 figures, discussions added on p.5 and p.9, version to appear in PRD

This review article provides a bird's-eye view of what first-principles based methods can contribute to next-generation device design and simulation. After a brief overview of methods and capabilities in the area, we focus on published work by our group since 2015 and current work on $\textrm{CrI}_3$. We introduce both single- and dual-gate models in the framework of density functional theory and the constrained random phase approximation in estimating the Hubbard $U$ for 2D systems vs. their 3D counterparts. A wide range of systems, including graphene-based heterogeneous systems, transition metal dichalcogenides, and topological insulators, and a rich array of physical phenomena, including the macroscopic origin of polarization, field effects on magnetic order, interface state resonance induced peak in transmission coefficients, spin filtration, etc., are covered. For $\textrm{CrI}_3$ we present our new results on bilayer systems such as the interplay between stacking and magnetic order, pressure dependence, and electric field induced magnetic phase transitions. We find that a bare bilayer $\textrm{CrI}_3$, graphene$\,|\,$bilayer $\textrm{CrI}_3\,|\,$graphene, $h$-BN$\,|\,$bilayer $\textrm{CrI}_3\,|\,h$-BN, and $h$-BN$\,|\,$bilayer $\textrm{CrI}_3\,|\,$graphene all have a different response at high field, while small field the difference is small except for graphene$\,|\,$bilayer $\textrm{CrI}_3\,|\,$graphene. We conclude with discussion of some ongoing work and work planned in the near future, with the inclusion of further method development and applications.

Magic-angle twisted bilayer graphene (MATBG) is notable as a highly tunable platform for investigating strongly correlated phenomena such as high-$T_c$ superconductivity and quantum spin liquids, due to easy control of doping level through gating and sensitive dependence of the magic angle on hydrostatic pressure. Experimental observations of correlated insulating states, unconventional superconductivity and ferromagnetism in MATBG indicate that this system exhibits rich exotic phases. In this work, using density functional theory calculations in conjunction with the effective screening medium method, we find the MATBG under pressure at a twisting angle of $2.88\unicode{xb0}$ and simulate how its electronic states evolve when doping level and out-of-plane electric field are gate-tuned. Our calculations show that, at doping levels between two electrons and four holes per moir\'{e} unit cell, a ferromagnetic solution with spin density localized at AA stacking sites is lower in energy than the nonmagnetic solution. The magnetic moment of this ferromagnetic state decreases with both electron and hole doping and vanishes at four electrons/holes doped per moir\'{e} unit cell. Hybridization between the flat bands at the Fermi level and the surrounding dispersive bands can take place at finite doping. Moreover, upon increasing the out-of-plane electric field at zero doping, a transition from the ferromagnetic state to the nonmagnetic one is seen. We also analyze the interlayer bonding character due to the flat bands via Wannier functions. Finally, we report trivial band topology of the flat bands in the ferromagnetic state at a certain doping level.

The decay amplitude of $B^+\to \pi^+\pi^-\pi^+$ in the Dalitz plot has been analyzed by the LHCb using three different approaches for the $S$-wave component. It was found that the mode with $\sigma$ (or $f_0(500)$) exhibited a CP asymmetry of 15\% in the isobar model, whereas the $f_2(1270)$ mode had a 40\% asymmetry. On the contrary, CP asymmetry for the dominant quasi-two-body decay $B^-\to\rho^0\pi^-$ was found to be consistent with zero in all three approaches, while all the existing theoretical predictions lead to a negative CP asymmetry ranging from $-7\%$ to $-45\%$. We show that the nearly vanishing CP violation in $B^-\to\rho^0\pi^-$ is understandable in the framework of QCD factorization (QCDF). It arises from the $1/m_b$ power corrections to the penguin amplitudes due to penguin annihilations and to the color-suppressed tree amplitude due to hard spectator interactions. Penguin annihilation and hard spectator interactions contribute destructively to $A_{CP}(B^-\to\rho^0\pi^-)$ to render it consistent with zero. The branching fraction and CP asymmetry in $B^-\to\sigma/f_0(500)\pi^-$ are investigated in QCDF with results in agreement with experiment., Comment: 11 pages

The hadronic two-body weak decays of the doubly charmed baryons $\Xi_{cc}^{++}, \Xi_{cc}^+$ and $\Omega_{cc}^+$ are studied in this work. To estimate the nonfactorizable contributions, we work in the pole model for the $P$-wave amplitudes and current algebra for $S$-wave ones. For the $\Xi_{cc}^{++}\to \Xi_c^+\pi^+$ mode, we find a large destructive interference between factorizable and nonfactorizable contributions for both $S$- and $P$-wave amplitudes. Our prediction of $\sim 0.70\%$ for its branching fraction is smaller than the earlier estimates in which nonfactorizable effects were not considered, but agrees nicely with the result based on an entirely different approach, namely, the covariant confined quark model. On the contrary, a large constructive interference was found in the $P$-wave amplitude by Dhir and Sharma, leading to a branching fraction of order $(7-16)\%$. Using the current results for the absolute branching fractions of $(\Lambda_c^+,\Xi_c^+)\to p K^-\pi^+$ and the LHCb measurement of $\Xi_{cc}^{++}\to\Xi_c^+\pi^+$ relative to $\Xi_{cc}^{++}\to\Lambda_c^+ K^- \pi^+\pi^+$, we obtain $\B(\Xi_{cc}^{++}\to\Xi_c^+\pi^+)_{\rm expt}\approx (1.83\pm1.01)\%$ after employing the latest prediction of $\B(\Xi_{cc}^{++}\to\Sigma_c^{++}\overline{K}^{*0})$. Our prediction of $\mathcal{B}(\Xi_{cc}^{++}\to\Xi_c^+\pi^+)\approx 0.7\%$ is thus consistent with the experimental value but in the lower end. It is important to pin down the branching fraction of this mode in future study. Factorizable and nonfactorizable $S$-wave amplitudes interfere constructively in $\Xi_{cc}^+\to\Xi_c^0\pi^+$. Its large branching fraction of order 4\% may enable experimentalists to search for the $\Xi_{cc}^+$ through this mode. That is, the $\Xi_{cc}^+$ is reconstructed through the $\Xi_{cc}^+\to\Xi_c^0\pi^+$ followed by the decay chain $\Xi_c^0\to \Xi^-\pi^+\to p\pi^-\pi^-\pi^+$., Comment: 25 pages, 1 figure, version accepted by PRD

Exchange coupling constants ($J$) are fundamental to the understanding of spin spectra of magnetic systems. Here we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. $J$ values calculated from CC in this fashion converge smoothly towards the FCI result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary EOM-CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.

In light of the potential use of single-molecule magnets (SMMs) in emerging quantum information science initiatives, we report first-principles calculations of the magnetic exchange interactions in [$\mathrm{Mn}_{3}$]$_{2}$ dimers of $\mathrm{Mn}_3$ SMMs, connected by covalently-attached organic linkers, that have been synthesized and studied experimentally by magnetochemistry and EPR spectroscopy. Energy evaluations calibrated to experimental results give the sign and order of magnitude of the exchange coupling constant ($J_{12}$) between the two $\mathrm{Mn}_{3}$ units that match with fits of magnetic susceptibility data and EPR spectra. Downfolding into the $\mathrm{Mn}$ $d$-orbital basis, Wannier function analysis has shown that magnetic interactions can be channeled by ligand groups that are bonded by van der Waals interaction and/or by the linkers via covalent bonding of specific systems, and effective tight-binding Hamiltonians are obtained. We call this long-range coupling that involves a group of atoms a collective exchange. Orbital projected spin density of states and alternative Wannier transformations support this observation. To assess the sensitivity of $J_{12}$ to external pressure, stress-strain curves have been investigated for both hydrostatic and uniaxial pressure, which have revealed a switch of $J_{12}$ from ferromagnetic to antiferromagnetic with increasing pressure.

We develop a first-principles theory for Schottky barrier physics. The Poisson equation is solved completely self-consistently with the electrostatic charge density and outside the normal density functional theory (DFT) electronic structure iteration loop, allowing computation of a Schottky barrier entirely from DFT involving thousands of atomic layers in the semiconductor. The induced charge in the bulk consists of conduction and valence band charges from doping and band bending, as well as charge from the evanescent states in the gap of the semiconductor. The Schottky barrier height is determined when the induced charge density and the induced electrostatic potential reach self-consistency.

The giant $\{ \mathrm{Mn}_{70} \}$ and $\{ \mathrm{Mn}_{84} \}$ wheels are the largest nuclearity single-molecule magnets synthesized to date and understanding their magnetic properties poses a challenge to theory. Starting from first principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled $\{ \mathrm{Mn}_{7} \}$ subunits carrying an effective $S=2$ spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest energy excitations arising from Heisenberg-ring-like excitations of the $\{ \mathrm{Mn}_{7} \}$ subunits around the wheel, at energies consistent with the observed temperature dependence of the magnetic susceptibility. We further suggest an important role for weak longer-range couplings in selecting the precise spin ground-state of the $\mathrm{Mn}$ wheels out of the nearly degenerate ground-state band., Comment: 7 pages, 8 figures. HFS and DTC contributed equally

We use density functional theory to study the structural, magnetic and electronic structure of the organo-metallic quantum magnet $\mathrm{NiCl_2-4SC(NH_2)_2}$ (DTN). Recent work has demonstrated the quasi-1D nature of the molecular crystal and its quantum phase transitions at low temperatures. This includes a magneto-electric coupling and, when doped with Br, the presence of an exotic Bose-glass state. We systematically show that, by using the generalized gradient approximation (GGA) with inclusion of a van der Waals term to account for weak inter-molecular forces and by introducing a Hubbard $U$ term to the total energy, our calculations reproduce the magnetic anisotropy, the inter-molecular exchange coupling strength and the magneto-electric effect in DTN, which were observed in previous experiments. Further analysis into the electronic structure gives insight into the underlying magnetic interactions, including what mechanisms may be causing the ME effect. Using this computationally efficient model, we predict what effect applying an electric field might have on the magnetic properties of this quantum magnet.

Quantum states are described by wave functions whose phases cannot be directly measured, but which play a vital role in quantum effects such as interference and entanglement. The loss of the relative phase information, termed decoherence, arises from the interactions between a quantum system and its environment. Decoherence is perhaps the biggest obstacle on the path to reliable quantum computing. Here we show that decoherence occurs even in an isolated molecule although not all phase information is lost via a theoretical study of a central electron spin qubit interacting with nearby nuclear spins in prototypical magnetic molecules. The residual coherence, which is molecule-dependent, provides a microscopic rationalization for the nuclear spin diffusion barrier proposed to explain experiments. The contribution of nearby molecules to the decoherence has a non-trivial dependence on separation, peaking at intermediate distances. Molecules that are far away only affect the long-time behavior. Because the residual coherence is simple to calculate and correlates well with the coherence time, it can be used as a descriptor for coherence in magnetic molecules. This work will help establish design principles for enhancing coherence in molecular spin qubits and serve to motivate further theoretical work., Comment: one-column, 26 pages, 5 figures

Three high-spin phases recently discovered in the spin-crossover system Mn(taa) are identified through analysis by a combination of first-principles calculations and Monte Carlo simulation as a low-temperature Jahn-Teller ordered (solid) phase, an intermediate-temperature dynamically correlated (liquid) phase, and an uncorrelated (gas) phase. In particular, the Jahn-Teller liquid phase arises from competition between mixing with low-spin impurities, which drive the disorder, and inter-molecular strain interactions. The latter are a key factor in both the spin-crossover phase transition and the magnetoelectric coupling. Jahn-Teller liquids may exist in other spin-crossover materials and materials that have multiple equivalent Jahn-Teller axes.