Effective Low-energy Hamiltonian Research Articles

Testing lepton flavour universality with (semi)-leptonic varvec{D_{(s)}} decays

Data in B-meson decays indicate violations of lepton flavour universality, thereby raising the question about such phenomena in the charm sector. We perform a model-independent analysis of NP contributions in (semi)-leptonic decays of D_{(s)} mesons which originate from c rightarrow d bar{{ell }} nu _l and c rightarrow s bar{{ell }} nu _{ell } charged-current interactions. Starting from the most general low-energy effective Hamiltonian containing four-fermion operators and the corresponding short-distance coefficients, we explore the impact of new (pseudo)-scalar, vector and tensor operators and constrain their effects through the interplay with current data. We pay special attention to the elements |V_{cd}| and |V_{cs}| of the Cabibbo–Kobayashi–Maskawa matrix and extract them from the D_{(s)} decays in the presence of possible NP decay contributions, comparing them with determinations utilizing unitarity. We find a picture in agreement with the Standard Model within the current uncertainties. Using the results from our analysis, we make also predictions for leptonic D_{(s)}^+ rightarrow e^+ nu _e modes which could be hugely enhanced with respect to their tiny Standard Model branching ratios. It will be interesting to apply our strategy at the future high-precision frontier.

Exchange Interaction between the Excited States of Magnetic Ions

Within the framework of the LDA + GTB multielectron approach to the electron structure of Mott–Hubbard insulators a scheme is developed for constructing the effective low-energy Hamiltonian that includes not only the ground state of the magnetic cations, but also the excited terms. The mathematical apparatus of the theory are Hubbard operators built on the many-electron states of the cation in the dn configuration. The occupation of the excited term under optical pumping can change the sign of the exchange interaction of the excited cation with the neighboring cation in the ground state. Another variant of the occupation of the excited states is connected with a spin crossover when the excited and the ground terms change over, for example, at high pressure. Examples are given for such crystals as FeBO3, Nd0.5Gd0.5Fe3(BO3)4 and NiO.

Spin polaronics: Static and dynamic properties of spin polarons in La-doped CaMnO3

The static and dynamic properties of spin polarons in La-doped CaMnO3 are explored theoretically, by means of an effective low-energy Hamiltonian. All parameters of the effective Hamiltonian are ev ...

Topological properties in ABA trilayer graphene under the irradiation of light**Project supported by the National Natural Science Foundation of China (Grant No. 61604106) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2014FL025).

We study ABA trilayer graphene under irradiation of a circularly polarized light. In high-frequency regime, the effective low-energy Hamiltonian is obtained based on the Floquet theory. With increasing circularly polarized light intensity, the band structure shows a band gap closing and reopening, which happen twice. The process of the band gap closing and reopening is accompanied with a topological phase transition. We investigate the Chern numbers and the anomalous Hall conductivities to confirm the topological phase transition. The interplay between light-induced circularity-dependent effective potential and effective sublattice potential is discussed.

Magnetism in spin crossover systems: Short-range order and effects beyond the Heisenberg model

To study non-Heisenberg effects in the vicinity of spin crossover in strongly correlated electron systems we derive an effective low-energy Hamiltonian for the two-band Kanamori model. It contains Heisenberg high-spin term proportional to exchange constant as well as low-spin term proportional to spin gap parameter $\varepsilon_s$. Using cluster mean field theory we obtain several non-Heisenberg effects. Near critical value of spin gap $\varepsilon^c_s$ there is a magnetic phase transition of first order. In the vicinity of $\varepsilon^c_s$ in the paramagnetic phase we observe non trivial behavior of the Curie constant in the paramagnetic susceptibility in the wide range of temperature. Reentrant temperature behavior of nearest-neighbor spin-spin correlations is observed at $\varepsilon_s > \varepsilon^c_s$. Finally, pressure-temperature magnetic phase diagram for ferroperriclase is obtained using the effective Hamiltonian.

Global fit to b \u2192 c\u03c4\u03bd transitions

We perform a general model-independent analysis of bto ctau {overline{nu}}_{tau } transitions, including measurements of ℛD, ℛD∗, their q2 differential distributions, the recently measured longitudinal D* polarization {F}_L^{Dast } , and constraints from the {B}_cto tau {overline{nu}}_{tau } lifetime, each of which has significant impact on the fit. A global fit to a general set of Wilson coefficients of an effective low-energy Hamiltonian is presented, the solutions of which are interpreted in terms of hypothetical new-physics mediators. From the obtained results we predict selected bto ctau {overline{nu}}_{tau } observables, such as the baryonic transition {Lambda}_bto {Lambda}_ctau {overline{nu}}_{tau } , the ratio ℛJ/ψ, the forward-backward asymmetries {mathcal{A}}_{mathrm{FB}}^{Dleft(ast right)} , the τ polarization asymmetries {mathcal{P}}_{tau}^{Dleft(ast right)} , and the longitudinal D* polarization fraction {F}_L^{Dast } . The latter shows presently a slight tension with any new-physics model, such that an improved measurement could have an important impact. We also discuss the potential change due the very recently announced preliminary {mathrm{mathcal{R}}}_{mathcal{D}left(ast right)} measurement by the Belle collaboration.

Transport across junctions of pseudospin-one fermions

We study transport across ballistic junctions of materials which host pseudospin-one fermions as emergent low-energy quasiparticles. The effective low-energy Hamiltonians of such fermions are described by integer spin Weyl models. We show that current conservation in such integer spin-$s$ Weyl systems requires continuity across a boundary of only $2s$ (out of $2s+1$) components of the wave function. Using the current conservation conditions, we study the transport between normal metal-barrier-normal metal (NBN) and normal metal-barrier-superconductor (NBS) junctions of such systems in the presence of an applied voltage $eV$. We show that for a specific value of the barrier potential $U_0$, such NBN junctions act as perfect collimators; any quasiparticle which is incident on the barrier with a non-zero angle of incidence is reflected back with unit probability for any barrier width $d$. We discover an interesting symmetry of this system, namely, the conductance is invariant under $U_0 \to 2(\mu_L \pm eV)-U_0$, where $\mu_L$ is the chemical potential and the +(-) sign corresponds to particle (hole) mediated transport. For NBS junctions with a proximity-induced $s$-wave pairing potential, which also display such a collimation, we chart out the properties of the subgap tunneling conductance $G$ as a function of the barrier strength and applied voltage. We point out the effect of the collimation on the subgap tunneling conductance of these NBS junctions and discuss experiments which can test our theory.

Ab initio derivation of an effective Hamiltonian for the La2CuO4/La1.55Sr0.45CuO4 heterostructure

We formulate a method of deriving effective low-energy Hamiltonian for nonperiodic systems such as interfaces for strongly correlated electron systems by extending conventional multi-scale $\textit{ab initio}$ scheme for correlated electrons (MACE). We apply the formalism to copper-oxide high $T_{\rm c}$ superconductors in an example of the interface between overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ and Mott insulating La$_{2}$CuO$_{4}$ recently realized experimentally. We show that the parameters of the $E_g$ Hamiltonian derived for the La$_{2}$CuO$_{4}$/La$_{1.55}$Sr$_{0.45}$CuO$_{4}$ superlattice differ considerably from those for the bulk La$_{2}$CuO$_{4}$, particularly significant in the partially-screened Coulomb parameters and the level offset between the $d_{x^{2}-y^{2}}$ and $d_{z^{2}}$ orbitals, $\Delta E$. In addition, we investigate the effect of the lattice relaxation on the $E_g$ Hamiltonian by carefully comparing the parameters derived before and after the structure optimization. We find that the CuO$_{6}$ octahedra distort after the relaxation as a consequence of the Madelung potential difference between the insulator and metal sides, by which the layer dependence of the hopping and Coulomb parameters becomes more gradual than the unrelaxed case. Furthermore, the structure relaxation dramatically changes the $\Delta E$ value and the occupation number at the interface. This study not only evidences the importance of the ionic relaxation around interfaces but also provides a set of layer-dependent parameters of the $E_g$ Hamiltonian, which is expected to provide further insight into the interfacial superconductivity when solved with low-energy solvers.

Quantum Simulation of Resonant Transitions for Solving the Eigenproblem of an Effective Water Hamiltonian.

It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum algorithm which could solve this problem via simulated resonant transitions. Using a four-qubit quantum simulator in which two qubits are used as ancillas for control and measurement, we obtain the energy spectrum of a 2-qubit low-energy effective Hamiltonian of the water molecule. The simulated transitions allow the state of the quantum simulator to transform and access large regions of the Hilbert space, including states that have no overlap with the initial state. Furthermore, we make use of this algorithm to efficiently prepare specific eigenstates on the simulator according to the measured eigenenergies.

Tunable superconducting effective gap in graphene-TMDC heterostructures

Growth of graphene on monolayer transition-metal dichalcogenides presents opening on band gap and giant spin-orbit coupling which paves the way to achieve a useful hybrid structure for electronics and spintronics applications. Increase of the atomic number of transition-metal results in a large SOC, where eventually a band inversion appears in graphene-WSe2. We consider superconductor induction by proximity effect to the graphene-TMDC hybrid structure. As a necessity of formalism, we introduce a proper time-reversal and particle-hole symmetry operators, under which the 8 × 8 Dirac-Bogoliubov-de Gennes low-energy effective Hamiltonian is invariant. Resulting superconducting electron-hole excitations shows that, the essential dynamical parameters λIA,B and λR have significant effect on superconducting excitations and, specifically, subgap energy. Dependence of the superconducting energy excitation on chemical potential is explored. The signature of spin triplet p-wave pairing symmetry in the system is found to increase the subgap superconducting energy, in comparing to s-wave symmetry.

Type-II Dirac line node in strained Na3N

Dirac line node (DLN) semimetals are a class of topological semimetals that feature band-crossing lines in momentum space. We study the type-I and type-II classification of DLN semimetals by developing a criterion that determines the type using band velocities. Using first-principles calculations, we also predict that ${\mathrm{Na}}_{3}\mathrm{N}$ under an epitaxial tensile strain realizes a type-II DLN semimetal with vanishing spin-orbit coupling, characterized by the Berry phase, which is ${\mathbb{Z}}_{2}$ quantized in the presence of inversion and time-reversal symmetries. The surface energy spectrum is calculated to demonstrate the topological phase and the type-II nature is demonstrated by calculating the band velocities. We also develop a tight-binding model and a low-energy effective Hamiltonian that describe the low-energy electronic structure of strained ${\mathrm{Na}}_{3}\mathrm{N}$. The occurrence of a DLN in ${\mathrm{Na}}_{3}\mathrm{N}$ under strain is captured in the optical conductivity, which we propose as a means to experimentally confirm the type-II class of DLN semimetals.

Transport in topological insulators with bulk-surface coupling: Interference corrections and conductance fluctuations

Motivated by the experimental difficulty to produce topological insulators (TIs) of the Bi$_2$Se$_3$ family with pure surface-state conduction, we study the effect that the bulk can have on the low-temperature transport properties of gated thin TI films. In particular, we focus on interference corrections, namely weak localization (WL) or weak-antilocalization (WAL), and conductance fluctuations (CFs) based on an effective low-energy Hamiltonian. Utilizing diagrammatic perturbation theory we first analyze the bulk and the surface separately and subsequently discuss WL/WAL and CFs when a tunneling-coupling is introduced. We identify the relevant soft diffusion modes of the coupled system and use this insight to make simultaneous predictions for both interference corrections and conductance fluctuations in various parameter regimes. The results strongly suggest that the combined measurement of both quantities can provide an improved understanding of the physics underlying the low-temperature transport processes in thin TI films with bulk-surface coupling.

Ab initio effective Hamiltonians for cuprate superconductors

Ab initio low-energy effective Hamiltonians of two typical high-temperature copper-oxide superconductors, whose mother compounds are ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}$, are derived by utilizing the multiscale ab initio scheme for correlated electrons (MACE). The effective Hamiltonians obtained in the present study serve as platforms of future studies to accurately solve the low-energy effective Hamiltonians beyond the density functional theory. It allows further study on the superconducting mechanism from first principles and a quantitative basis without adjustable parameters not only for the available cuprates but also for future design of higher ${T}_{\mathrm{c}}$ in general. More concretely, we derive effective Hamiltonians for three variations: (1) a one-band Hamiltonian for the antibonding orbital generated from strongly hybridized Cu $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and O $2{p}_{\ensuremath{\sigma}}$ orbitals, (2) a two-band Hamiltonian constructed from the antibonding orbital and Cu $3{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital hybridized mainly with the apex oxygen ${p}_{z}$ orbital, and (3) a three-band Hamiltonian consisting mainly of Cu $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals and two O $2{p}_{\ensuremath{\sigma}}$ orbitals. Differences between the Hamiltonians for ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}$, which have relatively low and high critical temperatures ${T}_{\mathrm{c}}$, respectively, at optimally doped compounds, are elucidated. The main differences are summarized as follows: (i) the oxygen $2{p}_{\ensuremath{\sigma}}$ orbitals are farther ($\ensuremath{\sim}3.7$ eV) below from the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital in the case of the La compound than the Hg compound ($\ensuremath{\sim}2.4$ eV) in the three-band Hamiltonian. This causes a substantial difference in the character of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}\ensuremath{-}2{p}_{\ensuremath{\sigma}}$ antibonding band at the Fermi level and makes the effective onsite Coulomb interaction $U$ larger for the La compound than the Hg compound for the two- and one-band Hamiltonians. (ii) The ratio of the second-neighbor to the nearest transfer ${t}^{\ensuremath{'}}/t$ is also substantially different (0.26 for the Hg and 0.15 for the La compound) in the one-band Hamiltonian. Heavier entanglement of the two bands in the two-band Hamiltonian implies that the two-band rather than the one-band Hamiltonian is more appropriate for the La compound. The relevance of the three-band description is also discussed especially for the Hg compound.

Dirac nodal line in bilayer borophene: Tight-binding model and low-energy effective Hamiltonian

Bilayer hexagonal borophene, which is bound together through pillars, is a novel topological semimetal. Using density functional theory, we investigate its electronic band structure and show that it is a Dirac material which exhibits a nodal line. A tight-binding model was constructed based on the Slater-Koster approach, which accurately models the electronic spectrum. We constructed an effective four-band model Hamiltonian to describe the spectrum near the nodal line. This Hamiltonian can be used as a new platform to study the new properties of nodal line semimetals. We found that the nodal line is created by edge states and is very robust against perturbations and impurities. Breaking symmetries can split the nodal line, but cannot open a gap.

Electronic structure theory of strained two-dimensional materials with hexagonal symmetry

We derive electronic tight-binding Hamiltonians for strained graphene, hexagonal boron nitride and transition metal dichalcogenides based on Wannier transformation of {\it ab initio} density functional theory calculations. Our microscopic models include strain effects to leading order that respect the hexagonal crystal symmetry and local crystal configuration, and are beyond the central force approximation which assumes only pair-wise distance dependence. Based on these models, we also derive and analyze the effective low-energy Hamiltonians. Our {\it ab initio} approaches complement the symmetry group representation construction for such effective low-energy Hamiltonians and provide the values of the coefficients for each symmetry-allowed term. These models are relevant for the design of electronic device applications, since they provide the framework for describing the coupling of electrons to other degrees of freedom including phonons, spin and the electromagnetic field. The models can also serve as the basis for exploring the physics of many-body systems of interesting quantum phases.

Dopant Introduced Valley Polarization, Spin, and Valley Hall Conductivity in Doped Monolayer MoS2

We study valley polarization, spin, and valley Hall conductivity in doped monolayer MoS2 considering dopant introduced magnetic exchange field using low energy effective Hamiltonian. We found that dopant introduced magnetic exchange field breaks the time inversion symmetry and decouples the energetically degenerated valleys into nondegenerate. Moreover, the calculated result reveals that, at low temperature, in insulating regime, anomalous Hall conductivity in a single valley and the total valley Hall conductivity are quantized, whereas the total spin Hall conductivity vanishes identically. We also found that the strength of the spin-orbit coupling together with the exchange field determines the valley polarization, which in turn controls valley and spin Hall conductivity in doped monolayer MoS2 system. The spin Hall and valley Hall conductivity is dissipationless in the absence of any external magnetic field. Therefore, our results are crucial to generate low power electronics devices.

Bond-ordered states and f -wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the van-Hove filling, the free Fermi surface is hole-like and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the van-Hove filling the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling the free Fermi surface becomes electron-like and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unitcell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.

A topological phase transition in topological insulator thin films exposed to an off-resonant light and its associated topological configuration

Surface-related properties of the three-dimensional topological insulators with/without considerable thickness are thought as the furthermost demandable in the field of condensed matter physics because of its rich technological applications. Motivated by these properties, we consider low energy effective Hamiltonian of three-dimensional topological insulators having a negligible thickness in the presence of irradiated off-resonant circularly polarized light to assess it's topological features. By evaluating the surface pseudo-spin Chern number analytically, we find that three dimensional topological insulator thin films pass through a phase transition from quantum pseudo spin Hall (QPSH) state to a photo-induced quantum Hall (P-QH) state when the effective energy induced by the circularly polarized light becomes greater in magnitude than the effective energy induced by the coupling between the top and bottom surfaces. We find that both the QPSH and P-QH states present a pronounced step-wise character. The phase-transition between these two topological states can be controlled by the degree of hybridization and off-resonant circularly polarized light. Additionally, we analyze the topological structure of QPSH and P-QH states by mapping the three-dimensional unit vector on a unit sphere and reveal that they display merons-like or anti-merons-like configurations in the real spin space.

Classification of symmetry derived pairing at the M point in FeSe

Using the constraints imposed by the crystalline symmetry of FeSe and the experimentally observed phenomenology, we analyze the possible pairing symmetry of the superconducting order parameter focusing on intercalated and monolayer FeSe compounds. Such analysis leads to three possible pairing symmetry states -- s-wave, d-wave, and helical p-wave. Despite the differences in the pairing symmetry, each of these states is fully gapped with gap minimum centered above the normal state Fermi surface, in agreement with photoemission data of Y. Zhang et al. The analysis provides additional insights into the possible pairing mechanism for each of these states, highlighting the detrimental role of the renormalized repulsive intra-orbital Hubbard $U$ and inter-orbital $U'$ , and the beneficial role of the pair hopping $J'$ and the Hunds $J$ terms, as well as the spin-orbit coupling in the effective low-energy Hamiltonian.

Charge-Kondo effect mediated by repulsive interactions

We investigate the Kondo effect in a double-quantum-dot which is capacitively coupled to a charge-Qubit. It is shown that due to this capacitive coupling, the bare inter-dot repulsive interaction in the double-quantum-dot is effectively reduced and eventually changed to an attractive interaction for strong couplings between the double-quantum-dot and the Qubit. By deriving the low-energy effective Hamiltonian of the system, we find that the low energy dynamics of the system corresponding to these two positive or negative effective interaction regimes can be described, respectively, by an isotropic orbital-Kondo or an anisotropic charge-Kondo Hamiltonian. Moreover, we study various thermodynamic and electronic transport properties of the system by using the numerical renormalization group method.