Effective Low-energy Model Research Articles

Controllable nonreciprocal optical response and handedness-switching in magnetized spin-orbit coupled graphene

Starting from a low-energy effective Hamiltonian model, we theoretically calculate the dynamical optical conductivity and permittivity tensor of a magnetized graphene layer with Rashba spin orbit coupling (SOC). Our results reveal a transverse Hall conductivity correlated with the usual nonreciprocal longitudinal conductivity. Further analysis illustrates that for intermediate magnetization strengths, the relative magnitudes of the magnetization and SOC can be identified experimentally by two well-separated peaks in the dynamical optical response (both the longitudinal and transverse components) as a function of photon frequency. Moreover, the frequency dependent permittivity tensor is obtained for a wide range of chemical potentials and magnetization strengths. Employing experimentally realistic parameter values, we calculate the circular dichroism of a representative device consisting of magnetized spin orbit coupled graphene and a dielectric insulator layer, backed by a metallic plate. The results reveal that this device has different relative absorptivities for right-handed and left-handed circularly polarized electromagnetic waves. It is found that the magnetized spin orbit coupled graphene supports strong handedness-switchings, effectively controlled by varying the chemical potential and magnetization strength with respect to the SOC strength.

Spontaneously stabilised dark matter from a fermiophobic U(1)\u2032 gauge symmetry

We consider the possibility that dark matter is stabilised by a discrete Z2 symmetry which arises from a subgroup of a U(1)′ gauge symmetry, spontaneously broken by integer charged scalars, and under which the chiral quarks and leptons do not carry any charges. A chiral fermion χ with half-integer charge is odd under the preserved Z2, and hence becomes a stable dark matter candidate, being produced through couplings to right-handed neutrinos with vector-like U(1)′ charges, as in the type Ib seesaw mechanism. We calculate the relic abundance in such a low energy effective seesaw model containing few parameters, then consider a high energy renormalisable model with a complete fourth family of vector-like fermions, where the chiral quark and lepton masses arise from a seesaw-like mechanism. With the inclusion of the fourth family, the lightest vector-like quark can contribute to the dark matter production, enlarging the allowed parameter space that we explore.

Band structures and topological properties of twisted bilayer MoTe2 and WSe2

We calculate the electronic band structures and topological properties of twisted homobilayer transition metal dichalcogenides(t-TMDs), in particular, bilayer MoTe2 and WSe2 based on a low-energy effective continuum model. We systematically show how the twist angle, vertical electric field and pressure modify the band structures of t-TMDs, often accompanied by topological transitions.We find the variation of topological transitions mainly take place in a limited range of parameters. The electric field can efficiently tune the energy of the topmost second valence band to motify the Chern numbers of the topmost three valance bands. The topological property of the topmost first valance band can be modified by electric field and pressure, but doesn’t depend on twist angle. We show the band gap between the topmost second and third valance bands that both change from non-trivial to trivial closes at -point of the moiré Brillouin zone.

Chiral Phonons in Moiré Superlattices.

We discover chiral phonons at the lowest energy bands in moiré superlattices. The moiré chiral phonons we uncover are the collective excitations of the stacking domains. Their origin is uniquely attributed to the stacking configurations whose interlayer binding energy breaks the C2z symmetry on the moiré length scale. Within elastic theory, we use a general symmetry analysis to provide a complete classification of van der Waals heterostructures in respect to hosting moiré chiral phonons and show the calculation for twisted MoS2 as an example. We present a low-energy effective model to qualitatively understand the moiré chiral phonons and show that it captures the essential physics remarkably well. Our result potentially opens up new possibilities in phononic twistronics as the moiré chiral phonons have high tunability, moiré scale wavelengths, excitation energies in only a few meV and can possibly be mechanically excited.

Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. VI. Theγmodel and its phase diagram at2<γ<3

In this paper, the sixth in series, we continue our analysis of the interplay between non-Fermi liquid and pairing in the effective low-energy model of fermions with singular dynamical interaction $V(\Omega_m) = {\bar g}^\gamma/|\Omega_m|^\gamma$ (the $\gamma$ model). The model describes low-energy physics of various quantum-critical metallic systems at the verge of an instability towards density or spin order, pairing of fermions at the half-filled Landau level, color superconductivity, and pairing in SYK-type models. In previous Papers I-V we analyzed the $\gamma$ model for $\gamma \leq 2$ and argued that the ground state is an ordinary superconductor for $\gamma <1$, a peculiar one for $1<\gamma <2$, when the phase of the gap function winds up along real frequency axis due to emerging dynamical vortices in the upper half-plane of frequency, and that there is a quantum phase transition at $\gamma =2$, when the number of dynamical vortices becomes infinite. In this paper we consider larger $2< \gamma <3$ and address the issue what happens on the other side of this quantum transition. We argue that the system moves away from criticality in that the number of dynamical vortices becomes finite and decreases with increasing $\gamma$. The ground state is again a superconductor, however a highly unconventional one with a non-integrable singularity in the density of states at the lower edge of the continuum. This implies that the spectrum of excited states now contains a level with a macroscopic degeneracy, proportional to the total number of states in the system. We argue that the phase diagram in variables $(T,\gamma)$ contains two distinct superconducting phases for $\gamma <2$ and $\gamma >2$, and an intermediate pseudogap state of preformed pairs.

Intrinsic glue and Wilson lines within dressed quarks

We construct a quark target model (QTM) to incorporate intrinsic glue into effective low-energy models of QCD, which often contain only quark degrees of freedom. This method guarantees the gauge invariance of observables order by order in the strong coupling. The quark and gluon PDFs for the dressed quarks are obtained in the QTM at leading order. We demonstrate gauge invariance of the results by comparing both covariant and light cone gauges, with the former including an explicit Wilson line contribution. A key finding is that in covariant gauges the Wilson line can carry a significant amount of the light cone momentum. With coupling strength ${\ensuremath{\alpha}}_{s}=0.5$ and dressed quark mass ${M}_{q}=0.4\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$, we find quark and gluon momentum fractions of ${\ensuremath{\langle}x\ensuremath{\rangle}}_{q}=0.81$ and ${\ensuremath{\langle}x\ensuremath{\rangle}}_{g}=0.19$, where the Wilson line contribution to the quark momentum fraction is $\ensuremath{-}0.18$. We use the on-shell renormalization scheme and find that at one loop this Wilson line contribution does not depend on the covariant gauge but does vanish in light cone gauge as expected. This result demonstrates that it is crucial to account for Wilson line contributions when calculating quantum correlation functions in covariant gauges. We also consider the impact of a gluon mass using the gauge invariant formalism proposed by Cornwall, and combine these QTM results with two quark-level models to obtain quark and gluon PDFs for the pion.

Dynamical preparation of stripe states in spin-orbit-coupled gases

In spinor Bose-Einstein condensates, spin-changing collisions are a remarkable proxy to coherently realize macroscopic many-body quantum states. These processes have been, e.g., exploited to generate entanglement, to study dynamical quantum phase transitions, and proposed for realizing nematic phases in atomic condensates. In the same systems dressed by Raman beams, the coupling between spin and momentum induces a spin dependence in the scattering processes taking place in the gas. Here we show that, at weak couplings, such modulation of the collisions leads to an effective Hamiltonian which is equivalent to the one of an artificial spinor gas with spin-changing collisions that are tunable with the Raman intensity. By exploiting this dressed-basis description, we propose a robust protocol to coherently drive the spin-orbit coupled condensate into the ferromagnetic stripe phase via crossing a quantum phase transition of the effective low-energy model in an excited-state.

Comparison of optical response from DFT random phase approximation and a low-energy effective model: Strained phosphorene

The engineering of the optical response of materials is a paradigm that demands microscopic-level accuracy and reliable predictive theoretical tools. Here we compare and contrast the dispersive permittivity tensor, using both a low-energy effective model and density functional theory (DFT). As a representative material, phosphorene subject to strain is considered. Employing a low-energy model Hamiltonian with a Green's function current-current correlation function, we compute the dynamical optical conductivity and its associated permittivity tensor. For the DFT approach, first-principles calculations make use of the first-order random phase approximation. Our results reveal that although the two models are generally in agreement within the low-strain and low-frequency regime, the intricate features associated with the fundamental physical properties of the system and optoelectronics devices implementation such as band gap, Drude absorption response, vanishing real part, absorptivity, and sign of permittivity over the frequency range show significant discrepancies. Our results suggest that the random phase approximation employed in widely used DFT packages should be revisited and improved to be able to predict these fundamental electronic characteristics of a given material with confidence. Furthermore, employing the permittivity results from both models, we uncover the pivotal role that phosphorene can play in optoelectronics devices to facilitate highly programable perfect absorption of electromagnetic waves by manipulating the chemical potential and exerting strain and illustrate how reliable predictions for the dielectric response of a given material are crucial to precise device design.

Odd-frequency pairing inherent in a Bogoliubov Fermi liquid

The disorder and interaction effects on Bogoliubov-Fermi surfaces with preserved inversion symmetry are studied for a low-energy effective model coupled to bosonic degrees of freedom. It is shown that the non-ideal Bogoliubov quasiparticles (bogolons) generically induce the odd-frequency pair amplitude which reflects a Cooper pairing at different time. The self-energy of bogolons is mainly contributed by the disorder effects in the low frequency limit as in the usual electron liquid. Depending on the choice of the parameters, there are two kinds of solutions: one is frequency-independent (but with sign function of frequency) and the other is proportional to the inverse of the frequency, which exist in both the normal and anomalous parts of the self-energy. These characteristic self-energy structures are clearly reflected in the single-particle spectrum. Since the bogolons are originally composed of electrons, the connection between the two is also sought using the concrete $j=3/2$ fermion model, which reveals that the odd-frequency pairing of bogolons is mainly made of the electrons' odd-frequency pairing.

Ultrafast excitation and topological soliton formation in incommensurate charge density wave states

Topological soliton is a nonperturbative excitation in commensurate density wave states and connects degenerate ground states. In incommensurate density wave states, ground states are continuously degenerate and topological soliton is reckoned to be smoothly connected to the perturbative phason excitation. We study the ultrafast nonequilibrium dynamics due to photoexcited electron-hole pair in a one-dimensional chain with an incommensurate charge density wave ground state. Time-resolved evolution reveals both perturbative excitation of collective modes and nonperturbative topological phase transition due to creating novel topological solitons, where the continuous complex order parameter with amplitude and phase is essential. We identify the nontrivial phase-winding solitons in the complex plane unique to this nonequilibrium state and capture it by a low-energy effective model. The perturbative temporal gap oscillation and the solitonic in-gap states enter the optical conductivity absorption edge and the spectral density related to spectroscopic measurement, providing concrete connections to real experiments.

Strain-induced topological charge control in multifold fermion systems

Multifold fermion systems feature free fermionic excitations, which have no counterparts in high-energy physics, and exhibit several unconventional properties. Using first-principles calculations, we predict that strain engineering can be used to control the distribution of topological charges in transition metal silicide candidate CoSi, hosting multifold fermions. We demonstrate that breaking the rotational symmetry of the system, by choosing a suitable strain, destroys the multifold fermions, and at the same time results in the creation of Weyl points. We introduce a low energy effective model to complement the results obtained from density functional calculations. Our findings suggest that strain-engineering is a useful approach to tune topological properties of multifold fermions.

Dirac node engineering and flat bands in doped Dirac materials

We suggest the tried approach of impurity band engineering to produce flat bands and additional nodes in Dirac materials. We show that surface impurities give rise to nearly flat impurity bands close to the Dirac point. The hybridization of the Dirac nodal state induces the splitting of the surface Dirac nodes and the appearance of new nodes at high-symmetry points of the Brillouin zone. The results are robust and not model dependent: our tight-binding calculations are supported by a low-energy effective model of a topological insulator surface state hybridized with an impurity band. Finally, we address the effects of electron-electron interactions between localized electrons on the impurity site. We confirm that the correlation effects, while producing band hybridization and the Kondo effect, keep the hybridized band flat. Our findings open up prospects for impurity band engineering of nodal structures and flat-band correlated phases in doped Dirac materials.

Type-II Dirac point in RbAg5Se3

Using first-principles calculations and low-energy effective model analysis, we propose that silver selenide-based ${\mathrm{RbAg}}_{5}{\mathrm{Se}}_{3}$ compound is an ideal type-II Dirac semimetal. There is a pair of Dirac points appearing at about 25.68 meV below the Fermi energy. The Dirac points existing on the ${k}_{z}$ axis are protected by ${C}_{4z}$ rotation symmetry in addition to $\mathcal{PT}$ symmetry. Meanwhile, the system is also characterized by a nontrivial ${\mathbb{Z}}_{2}$ topological invariant. The long clean Fermi arcs exist on the (010) surface, connecting the projections of the Dirac points. In addition, the Landau levels of the type-II Dirac points under magnetic field are also calculated. Our discovery not only adds one promising candidate into the type-II Dirac semimetals family but also provides an ideal platform for the study of topological phase transitions.

Nematicity Liquid in a Trimerized-Kagome Antiferromagnet

We theoretically study low-temperature properties of the antiferromagnetic Heisenberg model with half-integer spin $S$ on the Kagome lattice with large trimerization. We have derived a low-energy effective model for general $S$ in terms of spin and nematicity operators in triangular units, and studied their low-temperature correlations for S=3/2 by classical Monte Carlo simulations. The previous study for the S=1/2 case [M. Ferrero et al., Phys. Rev. B 68, 214431 (2003)] reported a spin liquid state at low temperatures driven by a glassy behavior of isolated dimers and trimers of nematicities. The results for S=3/2 show that nematicity dimers and trimers are connected by weak links to form a defective planar network. At very low temperatures, nematicities show glassy slow dynamics, and cluster spins continue to fluctuate in a nonperiodically frozen background of nematicities. The characteristic time of glassy dynamics scales with temperature following a power law.

Current distribution and group velocities for electronic states on lattice ribbons in a magnetic field

We study the group velocities of electronic states and distributions of currents in lattice ribbons under a uniform perpendicular magnetic field. Using the effective low-energy model we analyze all possible simple configurations of lattice termination with zigzag and armchair boundaries. We show that the edge current depends on the type of zigzag termination, and can be zero or finite near the edge. Also similar dependence is observed in the case of armchair termination and is related to the size of the ribbon. The nonzero current flowing along the edge can be used a signature of formation of propagating edge states. In addition, we show the qualitative difference in the distribution of the edge current between the case of α = 1 (dice model) and other values of model parameter α ≠ 1 for armchair-terminated ribbons.

Downfolding approaches to electron-ion coupling: Constrained density-functional perturbation theory for molecules

Constrained electronic-structure theories enable the construction of effective low-energy models consisting of partially dressed particles. However, the interpretation and physical content of these theories is not straightforward. Here, we carefully explore the properties of downfolding theories for electron-ion problems, in particular constrained density-functional perturbation theory (cDFPT). We show that the dipole selection rules determine whether the partially dressed phonons satisfy Goldstone's theorem, and we prove that electronic screening always lowers the phonon frequencies. We illustrate the theory with cDFPT calculations for minimal example systems: the nitrogen and benzene molecule as well as graphene.

Orbital susceptibility of T-graphene: Interplay of high-order van Hove singularities and Dirac cones

Square-octagon lattice underlies the description of a family of two-dimensional materials such as tetragraphene. In the present paper we show that the tight-binding model of square-octagon lattice contains both conventional and high-order van Hove points. In particular, the spectrum of the model contains flat lines along some directions composed of high-order saddle points. Their role is analyzed by calculating orbital susceptibility of electrons. We find that the presence of van Hove singularities of different kinds in the density of states leads to strong responses: paramagnetic for ordinary singularities and more complicated for high-order singularities. It is shown that the orbital susceptibility as a function of hoppings ratio $\alpha$ reveals the dia- to paramagnetic phase transition at $\alpha\approx 0.94$. This is due to the competition of paramagnetic contribution of high-order VHS and diamagnetic contribution of Dirac cones. The results for the tight-binding model are compared with low-energy effective pseudospin-1 model near the three band touching point.

Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths

Quantum light-matter systems at strong coupling are notoriously challenging to analyze due to the need to include states with many excitations in every coupled mode. We propose a nonperturbative approach to analyze light-matter correlations at all interaction strengths. The key element of our approach is a unitary transformation that achieves asymptotic decoupling of light and matter degrees of freedom in the limit where light-matter interaction becomes the dominant energy scale. In the transformed frame, truncation of the matter or photon Hilbert space is increasingly well justified at larger coupling, enabling one to systematically derive low-energy effective models, such as tight-binding Hamiltonians. We demonstrate the versatility of our approach by applying it to concrete models relevant to electrons in crystal potential and electric dipoles interacting with a cavity mode. A generalization to the case of spatially varying electromagnetic modes is also discussed.

Low scale leptogenesis in a model with promising CP structure

We consider a simple extension of the standard model, which could give a solution to its CP issues through both the Peccei–Quinn mechanism and the Nelson–Barr mechanism. Its low energy effective model coincides with the scotogenic model in the leptonic sector. Although leptogenesis is known not to work well at lower reheating temperature than 10^9 GeV in simple seesaw and scotogenic frameworks, such low reheating temperature could be consistent with both neutrino mass generation and thermal leptogenesis via newly introduced fields without referring to the resonance effect. An alternative dark matter candidate to axion is prepared as an indispensable ingredient of the model.

Tunable double Weyl phonons driven by chiral point group symmetry

Different from spin-$\frac{1}{2}$ Weyl points which are robust due to the protection of topology, the unconventional chiral quasiparticles usually require extra crystalline symmetries for their existence, indicating that such quasiparticles are sensitive to perturbation. Herein, we present that the spin-1 Weyl can transform into quadratic Weyl phonons depending on symmetry variation. Specifically, the spin-1 Weyl nodes arisen from three-dimensional (3D) irreducible representations (IRs) of chiral point groups, $O$(432) or $T$(23), are verified to split into quadratic Weyl points if symmetry breaking decomposes 3D IRs into two-dimensional IRs. Symmetry analysis and low-energy effective models are performed to identify the splitting mechanisms. The evolution of Berry curvature and surface states driven by symmetry breaking is obtained in real materials. Our work not only builds the connection between double Weyl phonons but also offers guidance for exploring the transition among unconventional quasiparticles.