Linear Response Regime Research Articles

Time-Dependent Second-Order Green’s Function Theory for Neutral Excitations

We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

Unique extension of the maximum entropy principle to phase coexistence in heat conduction

The maximum entropy principle determines the values of thermodynamic variables in thermally isolated equilibrium systems. This paper extends the principle to a variational principle that applies to liquid--gas coexistence in heat conduction. We show the uniqueness of the extension under the assumption that the variational principle and the fundamental thermodynamic relation are simultaneously extended in the linear response regime with the total energy fixed. Using the extended variational principle, we calculate the thermodynamic quantities in this steady state and find that the temperature of the liquid--gas interface deviates from the equilibrium transition temperature, which should be verified in experiments.

TurboMagnon – A code for the simulation of spin-wave spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory

We introduce turboMagnon, an implementation of the Liouville-Lanczos approach to linearized time-dependent density-functional theory, designed to simulate spin-wave spectra in solid-state materials. The code is based on the noncollinear spin-polarized framework and the self-consistent inclusion of spin-orbit coupling that allow to model complex magnetic excitations. The spin susceptibility matrix is computed using the Lanczos recursion algorithm that is implemented in two flavors - the non-Hermitian and the pseudo-Hermitian one. turboMagnon is open-source software distributed under the terms of the GPL as a component of Quantum ESPRESSO. As with other components, turboMagnon is optimized to run on massively parallel architectures using native mathematical libraries (LAPACK and FFTW) and a hierarchy of custom parallelization layers built on top of MPI. The effectiveness of the code is showcased by computing magnon dispersions for the CrI3 monolayer, and the importance of the spin-orbit coupling is discussed. Program summaryProgram title:turboMagnonCPC Library link to program files:https://doi.org/10.17632/6zxwzv5dt4.1Licensing provisions: GNU General Public License V 2.0Programming language: Fortran 95External routines:turboMagnon is a tightly integrated component of the Quantum ESPRESSO distribution and requires the standard libraries linked by it: BLAS, LAPACK, FFTW, MPI.Nature of problem: Calculation of the spin-wave spectra for solid-state materials.Solution method: The spin susceptibility matrix of a periodic system is expressed in terms of the resolvent of its Liouvillian superoperator within time-dependent density-functional perturbation theory. It is calculated using non-Hermitian or pseudo-Hermitian variants of the Lanczos recursion scheme, whose implementation does not require the calculation of empty electronic states. Norm-conserving pseudopotentials are used in conjunction with plane-wave basis sets and periodic boundary conditions. Relativistic effects (spin-orbit coupling) can be included in calculations.Additional comments including restrictions and unusual features: Linear-response regime only. Collinear spin-polarized formalism is not supported, only noncollinear spin-polarized case can be used. Adiabatic LSDA exchange-correlation functionals only (no GGA, no meta-GGA, no hybrid functionals, no Hubbard U, etc.). No ultrasoft and projector-augmented-wave pseudopotentials. No symmetry.Empty states are not used, nor even calculated. Three Lanczos recursions give access to the whole spectrum of magnetic excitations at fixed transferred momentum; one Lanczos recursion is enough for a specific orientation of the magnetic field and the ground-state magnetization of the system.The distribution file of this program can be downloaded from the Quantum ESPRESSO website: http://www.quantum-espresso.org/, and the development version of this program can be downloaded via Git from the GitLab website: https://gitlab.com/QEF/q-e. Interactions with end users of the turboMagnon code happen via a mailing-list forum of Quantum ESPRESSO: https://www.quantum-espresso.org/forum. Documentation of the turboMagnon code is tightly coupled with the code and is done via standard code comments.

High-frequency limit of spectroscopy.

We consider an arbitrary quantum mechanical system, initially in its ground-state, exposed to a time-dependent electromagnetic pulse with a carrier frequency ω0 and a slowly varying envelope of finite duration. By working out a solution to the time-dependent Schrödinger equation in the high-ω0 limit, we find that, to the leading order in ω0 -1, a perfect self-cancellation of the system's linear response occurs as the pulse switches off. Surprisingly, the system's observables are, nonetheless, describable in terms of a combination of its linear density response function and nonlinear functions of the electric field. An analysis of a jellium slab and jellium sphere models reveals a very high surface sensitivity of the considered setup, producing a richer excitation spectrum than accessible within the conventional linear response regime. On this basis, we propose a new spectroscopic technique, which we provisionally name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the traditional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS has a potential to evolve into a powerful characterization method for nanoscience and nanotechnology.

General solutions of linear poro-viscoelastic materials in spherical coordinates

The cell cytoskeleton is a dynamic assembly of semi-flexible filaments and motor proteins. The cytoskeleton mechanics is a determining factor in many cellular processes, including cell division, cell motility and migration, mechanotransduction and intracellular transport. Mechanical properties of the cell, which are determined partly by its cytoskeleton, are also used as biomarkers for disease diagnosis and cell sorting. Experimental studies suggest that in whole cell scale, the cell cytoskeleton and its permeating cytosol may be modelled as a two-phase poro-viscoelastic (PVE) material composed of a viscoelastic (VE) network permeated by a viscous cytosol. We present the first general solution to this two-phase system in spherical coordinates, where we assume that both the fluid and network phases are in their linear response regime. Specifically, we use generalized linear incompressible and compressible VE constitutive equations to describe the stress in the fluid and network phases, respectively. We assume a constant permeability that couples the fluid and network displacements. We use these general solutions to study the motion of a rigid sphere moving under a constant force inside a two-phase system, composed of a linear elastic network and a Newtonian fluid. It is shown that the network compressibility introduces a slow relaxation of the sphere and non-monotonic network displacements with time along the direction of the applied force. Our results can be applied to particle-tracking microrheology to differentiate between PVE and VE materials, and to measure the fluid permeability as well as VE properties of the fluid and the network phases.

Linear and nonlinear thermoelectric transport in a quantum spin Hall insulators coupled with a nanomagnet

Thermoelectric effects in quantum systems have been focused in recent years. Thermoelectric energy conversion study of systems with edge states, such as quantum Hall insulators and quantum spin Hall insulators, is one of the most important frontier topics in material science and condensed-matter physics. Based on the previous paper (Gresta in Phys Rev Lett 123:186801, 2019), we further investigated the linear and nonlinear thermoelectric transport properties of helical edge states of the quantum spin Hall insulators coupled with double nanomagnet, calculated the Seebeck coefficients S_c and the thermoelectrical figure of merit ZT, discussed the influence of the length of the nanomagnet and the relative tilt angle of component of the magnetization perpendicular on the thermoelectric coefficients (S_c and ZT), and summarized some meaningful conclusions in the linear response regime. In the nonlinear regime, we calculated the equivalent figure of merit ZT_M and the power-generation efficiency eta in different length of the nanomagnet, obtain the temperature difference of achieving optimal thermoelectricity. The results of this paper further confirm that the setup can indeed be used as a device for achieving high performance thermoelectric.

Fano effect in a thermally induced transport through a triple quantum dot within the Coulomb blockade regime

In the present work we theoretically study thermoelectric transport and heat transfer in a junction including a T-shaped double quantum dot coupled to nonmagnetic electrodes and supplemented with a third dot in a parallel configuration. We focus on the combined effect of Coulomb interactions and quantum interference occurring in the T-shaped portion of the considered triple quantum dot on the thermoelectric electron transport. The transport through the system is studied within the Coulomb blockade regime in the limit of strong intra-dot interactions between electrons beyond the linear response regime. It is shown that under these conditions both charge and heat transfer through the considered system may be significantly affected by the quantum interference and inter-dot Coulomb interactions.

Irreversible efficiency and Carnot theorem for heat engines operating with multiple heat baths in linear response regime

The Carnot theorem, one expression of the second law of thermodynamics, places a fundamental upper bound on the efficiency of heat engines operating between two heat baths. The Carnot theorem can be stated in a more generalized form for heat engines operating with multiple heat baths, where the maximum efficiency is achieved for reversible heat engines operating quasistatically between two heat baths. In this study, we determine the irreversible efficiency of heat engines operating with multiple heat baths in a linear response regime, i.e., under small temperature differences and a slow variation of the control parameters, by quantifying the impact of the dissipation by irreversible operations. The Carnot theorem is derived as a natural consequence of it. Because the result obtained is based on the linear response relation and fluctuation-dissipation theorem in the universal framework of linear response theory, it has wide applicability to irreversible heat engines operating in the linear response regime.

Quantum transport in quasiperiodic lattice systems in the presence of Büttiker probes

Quasi-periodic lattice systems offer diverse transport properties. In this work, we investigate the environment induced effects on transport properties for quasi-periodic systems, namely the one-dimensional Aubry-Andr\'e-Harper (AAH) lattice chain and its generalized version (GAAH) by considering the B\"uttiker probe approach. We first consider voltage probe situation and study the electrical conductance properties in the linear response regime. At zero temperature, we observe enhancement in conductance at all the no-transport regimes, located both inside and outside of the band of the original system, for small probe coupling strength $\gamma$ with a power-law scaling $\gamma^4$. Whereas, for large probe coupling strengths, the conductance at all Fermi energies is the same and decays as a power-law with scaling $1/\gamma^4$. This particular scaling survives even in the finite-temperature limit. Interestingly, this scaling result is different from the one recently predicted following the local Lindblad master equation approach. The transport eventually becomes diffusive for all energy ranges and in all regimes of the original model for a sufficiently strong coupling with the probes. We further extend our study and consider voltage-temperature probes to analyze the thermoelectric performance of the chain in terms of the figure of merit. We also demonstrate the validity of two recently obtained bounds on thermoelectric efficiency that are tighter than the seminal Carnot bound and express the same in terms of the Onsager's transport coefficients.

Nonlinear magnetoconductivity in Weyl and multi-Weyl semimetals in quantizing magnetic field

Magnetotransport and magneto-optics experiments offer a very powerful probe for studying the physical properties of materials. Here, we investigate the second-order nonlinear magnetoconductivity of the tilted type-I Weyl and multi-Weyl semimetals. In contrast to the existence of chiral charge pumping in the linear response regime, we reproduce the absence of chiral charge pumping in the nonlinear transport regime, using the Boltzmann transport framework with the Landau levels. We predict that an inversion symmetry broken and tilted Weyl semimetal can support finite longitudinal nonlinear magnetoconductivity, which is otherwise absent in untilted Weyl semimetals. The nonlinear magnetoconductivity vanishes in the ultraquantum limit, oscillates in the intermediate magnetic field regime, and saturates in the semiclassical limit. The nonlinear magnetoconductivity depends intricately on the tilt orientation, and it can be used to determine the tilt orientation in Weyl and multi-Weyl semimetals, via nonlinear magnetoresistivity or second harmonic generation experiments.

The Charge and Spin Thermoelectric Properties across Double Quantum Dots Serially Coupled to Ferromagnetic Leads: The Case of Parallel Magnetic Configuration

In this article, the charge and spin thermoelectric properties of double quantum dots system connected to ferromagnetic leads with collinear magnetic configurations will be studied in the linear response regime. Our results are calculated in a strong interdot coupling regime by taking into consideration all parameters affecting the system such as interaction between dots and their coupling to the leads, intradot Coulomb correlation energy and spin-polarization on the leads. It is found that in the parallel magnetic configuration, the thermoelectric efficiency can reach a large value around the spin-down resonance levels when the tunneling coupling between the quantum dots and the leads for the spin-down electrons are small, which leads to the pure spin Seebeck contribution. As a result, this system can generate a spin-polarized current. The value of the spin figure of merit is enhanced by increasing the spin-polarization and decreasing the correlation energy.

Spectral density reconstruction with Chebyshev polynomials

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and semiexclusive scattering cross sectionsin atomic nuclei and transport properties of nuclear and neutron star matter. Integral transform techniques play an important role in accessing the spectral density in a variety of nuclear systems. However, their accuracy is in practice limited by the need to perform a numerical inversion which is often ill-conditioned. In the present work we extend a recently proposed quantum algorithm which circumvents this problem. We show how to perform controllable reconstructions of the spectral density over a finite energy resolution with rigorous error estimates. An appropriate expansion in Chebyshev polynomials allows for efficient simulations also on classical computers. We apply our idea to obtain the local density of states for graphene in a magnetic field as a proof of principle. This paves the way for future applications in nuclear and condensed matter physics.

Second-order magnetic responses in quantum magnets: Magnetization under ac magnetic fields

We investigate second-order magnetic responses of quantum magnets against ac magnetic fields. We focus on the case where the $z$ component of the spin is conserved in the unperturbed Hamiltonian and the driving field is applied in the $xy$ plane. We find that linearly polarized driving fields induce a second-harmonic response, while circularly polarized fields generate only a zero-frequency response, leading to a magnetization with a direction determined by the helicity. Employing an unbiased numerical method, we demonstrate the nonlinear magnetic effect driven by the circularly polarized field in the XXZ model and show that the magnitude of the magnetization can be predicted by the dynamical spin structure factor in the linear response regime.

Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach

Using an effective Dirac model, we study the orbital Hall effect (OHE) in bilayers of transition metal dichalcogenides with 2H stacking (2H-TMD). We use first-order perturbation theory in the interlayer coupling of the bilayer system to obtain analytical expressions for the orbital Hall conductivity in the linear response regime. We use two distinct descriptions of the orbital angular momentum (OAM) operator. The first one is the intra-atomic approximation that considers only the intrasite contribution to the OAM [Cysne et al., Phys. Rev. Lett. 126, 056601 (2021)]. The second one uses the Berry phase formula of the orbital (valley) magnetic moment to describe the OAM operator [Bhowal and Vignale, Phys. Rev. B 103, 195309 (2021)]. This approach includes both intersite and intrasite contributions to the OAM. Our results suggest that the two approaches agree qualitatively in describing the OHE in bilayers of 2H-TMDs, although they present some quantitative differences. We also show that interlayer coupling plays an essential role in understanding the OHE in the unbiased bilayer of 2H-TMD. This coupling causes the Bloch states to become bonding (antibonding) combinations of states of individual layers, demanding the consideration of the non-Abelian structure of the orbital magnetic moment to the occurrence of OHE. As we discuss throughout the work, the emerging picture of transport of OAM in the unbiased bilayer of 2H-TMDs based on OHE is very different from the usual picture based on the valley Hall effect, shedding new light on previous experimental results. We also discuss the effect of the inclusion of a gate-voltage bias in the bilayer system. Our work gives support to recent theoretical predictions on OHE in two-dimensional materials.

Large Seebeck coefficient resulting from chiral interactions in triangular triple quantum dots

We theoretically study thermoelectric transport properties through a triangular triple-quantum-dot (TTQD) structure in the linear response regime using the hierarchical equations of motion approach. It is demonstrated that large Seebeck coefficient can be obtained when properly matching the interdot tunneling strength and magnetic flux at the electron–hole symmetry point, as a result of spin chiral interactions in the TTQD system. We present a systematic investigation of the thermopower (the Seebeck coefficient) dependence on the tunneling strength, magnetic flux, and on-site energy. The Seebeck coefficient shows a clear breakdown of electron–hole symmetry in the vicinity of the Kondo regime, accompanied by the deviation from the semiclassical Mott relation in the Kondo and mixed-valence regimes, which result from the many-body effects of the Kondo correlated induced resonance together with spin chiral interactions.

Chaotic dynamics of Bose–Einstein condensate induced by density-dependent gauge field

In this work we study the effect of density-dependent gauge field on the collective dynamics of a harmonically trapped Bose–Einstein condensate (BEC), beyond the linear response regime. The density-dependent gauge field, as a backaction of the condensate, can in turn affect the condensate dynamics, resulting in highly nonlinear equations of motion. The dipole and breathing oscillations of the condensate along the direction of gauge field are coupled by this field. We find that, in the presence of this coupling, the collective motion of a quasi-one-dimensional condensate is still regular, i.e., periodic or quasiperiodic. In contrast, for a quasi-two-dimensional condensate, the collective dynamics of the condensate can become chaotic, when the density-dependent gauge field is strong. The mechanism is that the gauge field can also induce a Hall effect, manifested as an additional coupling between dipole and breathing oscillations in perpendicular direction, and chaotic motion is resulted from the interplay between these oscillations. Our findings reveal an important effect of dynamical gauge field on the nonlinear dynamics of a BEC.

Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice

We present numerical tests of the fluctuation-dissipation theorem (FDT) in the dumbbell model of spin ice with parameters suitable for dysprosium titanate. The tests are made for local spin variables, magnetic monopole density, and energy. We are able to achieve local equilibrium in which the FDT is satisfied down to $T=0.4$ K below which the system completely freezes. Non-equilibrium dynamics, together with violation of the FDT, are nonetheless observed following a thermal quench into the non-contractable monopole pair regime. Despite FDT violation, an approximate linear response regime allows for the identification of effective non-equilibrium temperatures which are different for each variable. The spin variable appears hotter than the heat reservoir, the monopole concentration responds with a lower effective temperature while the energy has a negative effective temperature. Results are discussed in the context of the monopole picture of spin ice and compared to the structure of FDT violations in other glassy materials. Prospectives for future experiments are reviewed.

Suppression of magneto-optical transport in tilted Weyl semimetals by orbital magnetic moment

By incorporating the orbital magnetic moment, we investigate the magneto-optical transport of Weyl semimetals within a semiclassical approximation. In the linear or nonlinear response regime, an analytic expression for the magnetoconductivity is obtained, where a new term due to the orbital magnetic moment is added, and leads to a partial cancellation for the total magnetoconductivities. This suppressed feature is further manifested by analyzing the linear and quadratic contribution in the magnetic field to magnetoconductivities. This result may be used to explain the deviation between the recent theory and experiment.

Energy transport in Sachdev-Ye-Kitaev networks coupled to thermal baths

We develop a general framework for studying the equilibrium and non-equilibrium properties of arbitrary networks of Sachdev-Ye-Kitaev clusters coupled to thermal baths. We proceed to apply this technique to the problem of energy transport, which is known to be diffusive due to the strange metal behavior of these models. We use the external baths to impose a temperature gradient in the system and study the emerging non-equilibrium steady state using the Schwinger-Keldysh formalism. We consider two different configurations for the baths, implementing either a boundary or bulk driving, and show that the latter leads to a significantly faster convergence to the steady state. This setup allows us to compute both the temperature and frequency dependence of the diffusion constant. At low temperatures, our results agree perfectly with the previously known values for diffusivity in the conformal limit. We also establish a relationship between energy transport and quantum chaos by showing that the diffusion constant is upper bounded by the chaos propagation rate at all temperatures. Moreover, we find a simple analytical form for the non-equilibrium Green's functions in the linear response regime and use it to derive exact closed-form expressions for the diffusion constant in various limits. We mostly focus on uniform one-dimensional chains, but we also discuss higher-dimensional generalizations.

Phase and frequency linear response theory for hyperbolic chaotic oscillators.

We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory using co-variant Lyapunov vectors. It can also be used to identify the limits of the regime of linear response.