在Manchon和Pezo近期的研究[Phys. Rev. B 109, 184409(2024)]中，他们建立了一种关于磁化强度的线性理论，用以研究高次谐波产生（HHG）。在此，我们指出，这种线性理论无法描述HHG，因为HHG从定义上就是一个非线性过程。
英文摘要：
In their recent work [Phys. Rev. B 109, 184409(2024)], Manchon and Pezo develop a linear (in magnetization) theory, in order to investigate high-order harmonic generation (HHG). Here, we show that such linear theory cannot describe HHG, which, by definition is a nonlinear process.
We propose a realization of higher-order topological phases in a spring-mass model with a breathing kagome structure. To demonstrate the existence of the higher-order topological phases, we characterize the topological properties and show that the corner states appear under the fixed boundary condition. To characterize the topological properties, we introduce a formula for the $\mathbb{Z}_3$ Berry phases in the Brillouin zone. From the numerical result of this $\mathbb{Z}_3$ Berry phase, we have elucidated that coupling between the longitudinal and transverse modes yields a state characterized…
We have investigated pumping in quantum dots from the perspective of non-Abelian (matrix) Berry phases by solving the time dependent Schr{ö}dinger equation exactly for adiabatic changes. Our results demonstrate that a pumped charge is related to the presence of a finite matrix Berry phase. When consecutive adiabatic cycles are performed the pumped charge of each cycle is different from the previous ones.
We analytically investigate the non-equilibrium pumping for a double quantum dots system on the basis of the quantum master equation (QME), where the double quantum dots are connected to two external leads by the spin coupling. Each of leads has two tunable parameters, temperature and chemical potential. Using QME formalism, we obtain an analytical expression of the Berry-like phase for eigenstate of the QME in the parameter space. We show that the Berry-like curvature is non zero in the whole region in the parameter space. We also show that the Berry-like curvature vanishes in the case of sin…
Finding new phase is a fundamental task in physics. Landau's theory explained the deep connection between symmetry breaking and phase transition commonly occurring in magnetic, superconducting and super uid systems. The discovery of the quantum Hall effect led to Z topological phases which could be different for same symmetry and are characterized by the discrete values of the Berry phases. By studying 1D trimer lattices we report new phases characterized by Berry phases which are piecewise continuous rather than discrete numbers. The phase transition occurs at the discontinuity point. With ti…
We present the first measurements of the Berry phase in a superconducting Cooper pair pump. A fixed amount of Berry phase is accumulated to the quantum-mechanical ground state in each adiabatic pumping cycle, which is determined by measuring the charge passing through the device. The dynamic and geometric phases are identified and measured quantitatively from their different response when pumping in opposite directions. Our observations, in particular, the dependencies of the dynamic and geometric effects on the superconducting phase bias across the pump, agree with the basic theoretical model…
Several works investigated the connection between Cooper pair pumping and the geometric and topological properties of the pumping cycle in the parameters space. Recently the predicted connection between Berry's phase and pumped charge was observed experimentally. In the present work we analyze the effects of noise on Cooper pair pumping. We show that dissipation induces a new geometric contribution in the transferred charge and we propose an experiment where the theory can be probed.
The topological pumping [1-3] is revisited from a view point of the bulk-edge correspondence. Shift of the center of mass (CM) as a pumped charge is explicitly given by the Berry connection in time direction. We show that observed pumping is due to the bulk, but its quantization is guaranteed by singular motion of the CM caused by edge states. This is the bulk-edge correspondence in the topological pumping. A gauge invariant form of the pumped charge is proposed by the temporal gauge and is used to establish this bulk-edge correspondence.
Applying adiabatic, cyclic two parameter modulations we investigate quantum heat transfer across an anharmonic molecular junction contacted with two heat baths. We demonstrate that the pumped heat typically exhibits a Berry phase effect in providing an additional geometric contribution to heat flux. Remarkably, a robust fractional quantized geometric phonon response is identified as well. The presence of this geometric phase contribution in turn causes a breakdown of the fluctuation theorem of the Gallavotti-Cohen type for quantum heat transfer. This can be restored only if (i) the geometric p…
We formulate adiabatic charge pumping via a single-level quantum dot (QD) induced by reser- voir parameter driving, i.e., temperature and electrochemical potential driving. Our formulation describes arbitrary strength of dot-reservoir coupling and Coulomb interaction in the QD, and is applicable to the low-temperature regime, where the Kondo effect becomes important. The adia- batic charge pumping is expressed by the Berry connection and is related to delayed response of the QD. We calculate the pumped charge by the renormalized perturbation theory, and discuss how the Coulomb interaction affe…
We present a study of adiabatic Cooper pair pumping in one dimensional array of Cooper pair boxes. We do a detailed theoretical analysis of an experimentally realizable stabilized charge pumping scheme in a linear array of Cooper pair boxes. Our system is subjected to synchronized flux and voltage fields and travel along a loop which encloses their critical ground state of the system in the flux-voltage plane. The locking potential in the sine-Gordon model slides and changes its minimum which yields the Cooper pair pumping. Our analytical methods are the Berry phase analysis and Abelian bosoni…
Generally the adiabatic quantum pumping phenomenon can be interpreted by the surface integral of the Berry curvature inside the cyclic loop. Spin angular momentum flow without charge current can be pumped out by magnetization precession in ferromagnet-based structures. When an electron is scattered by a helimagnet, spin-dependent diffraction occurs due to the spatial modulation of the spiral. In this work, we consider the charge and spin flow driven by magnetization precession in normal-metal/multiferroic-helimagnet/ferromagnet heterostructures. The pumping behavior is governed by the diffract…
Spin pumping is a widely recognized method to generate the spin current in the spintronics, which is acknowledged as a fundamentally dynamic process equivalent to the spin-transfer torque. In this work, we theoretically verify that the oscillating spin current can be pumped from the microwave-motivated breathing skyrmion. The skyrmion spin pumping can be excited by a relatively low frequency compared with the ferromagnetic resonance (FMR) and the current density is larger than the ordinary FMR spin pumping. Based on the skyrmion spin pumping, we build a high reading-speed racetrack memory mode…
The one-dimensional Rice-Mele lattice consisting of two-site unit cells enables topological charge pumping at low enough temperatures. We show here that energy pumping is feasible in this system. We analyze energy polarization using the second-quantization formalism and connect it to intercell energy current by the relevant continuity equation. Following this formulation, we numerically evaluate the energy current pumped in an adiabatic cycle when the system parameters vary periodically and slowly with time. Unlike the pumped charge, the pumped energy is entirely temperature-independent at hal…
In this work, pumped currents of the adiabatically-driven double-barrier structure based on the pseudospin-1 Dirac-Weyl fermions are studied. As a result of the three-band dispersion and hence the unique properties of pseudospin-1 Dirac-Weyl quasiparticles, sharp current-direction reversal is found at certain parameter settings especially at the Dirac point of the band structure, where apexes of the two cones touches at the flat band. Such a behavior can be interpreted consistently by the Berry phase of the scattering matrix and the classical turnstile mechanism.
We study the adiabatic pumping of the Chern-Simons axion (CSA) coupling along a parametric loop characterized by a non-zero second Chern number $C^{(2)}$ from the viewpoint of the hybrid Wannier representation, in which the Wannier charge centers (WCCs) are visualized as sheets defined over a projected 2D Brillouin zone. We derive a new formula for the CSA coupling, expressing it as an integral involving Berry curvatures and potentials defined on the WCC sheets. We show that a loop characterized by a non-zero $C^{(2)}$ requires a series of sheet-touching events at which $2π$ quanta of Berry cu…
We comment on the relation between Berry phase and quantized Hall conductivities for charge and spin currents in some Bloch states, such as Bloch electrons in the presence of electromagnetic fields and quasiparticles in the vortex states of superfluid $^3$He. One can find out that the arguments presented here are closely related to the spontaneous polarization in crystalline dielectrics and the adiabatic pumping.
We give a gauge description of the adiabatic charge pumping in closed systems, both in Abelian and non-Abelian processes, and by means of asymptotic Wilson loops in a suitable parameter manifold. Our geometric formulation provides new insights into this issue, and a very simple algorithm for numerical computations. Indeed, as we show first, discretized Berry--Wilczeck--Zee holonomies are easy to implement. Finally, we study non-Abelian pumping in a solvable four-state model, already used in several contexts, to demonstrate the relevance of our approach.
We show that the spin quantum Hall effect in the vortex state of two-dimensional rotating superfluid He3 can be described as an adiabatic spin transport of Bloch quasiparticles. We show that the spin Hall conductivity is written by the Berry phase as well as the Chern number. The results have similarity to the adiabatic pumping of Bloch electrons and the spontaneous polarization in crystalline dielectrics.
We use exact techniques to demonstrate theoretically the pumping of fractional charges in a single-level non-interacting quantum dot, when the dot-reservoir coupling is adiabatically driven from weak to strong coupling. The pumped charge averaged over many cycles is quantized at a fraction of an electron per cycle, determined by the ratio of Lamb shift to level-broadening; this ratio is imposed by the reservoir band-structure. For uniform density of states, half an electron is pumped per cycle. We call this "adiabatic almost-topological pumping", because the pumping's Berry curvature is sharpl…
We present a formalism to study adiabatic pumping through a superconductor - normal - superconductor weak link. At zero temperature, the pumped charge is related to the Berry phase accumulated, in a pumping cycle, by the Andreev bound states. We analyze in detail the case when the normal region is short compared to the superconducting coherence length. The pumped charge turns out to be an even function of the superconducting phase difference. Hence, it can be distinguished from the charge transferred due to the standard Josephson effect.
Antiferromagnets (AFMs), in contrast to ferromagnets, show a nontrivial magnetic structure with zero net magnetization. However, they share a number of spintronic effects with ferromagnets, including spin-pumping and spin transfer torques. Both phenomena stem from the coupled dynamics of free carriers and localized magnetic moments. In the present paper I study the adiabatic dynamics of a spin-polarized electrons in a metallic AFM exhibiting a noncollinear 120$^\circ$ magnetic structure. I show that the slowly varying AFM spin texture produces a non-Abelian gauge potential related to the time/…
We look at the time dependent fluctuations of the electrical charge in an open 1D quantum system represented by a quantum dot experiencing random lateral motion. In essentially non-adiabatic settings we study both diffusive and ballistic (Levy) regimes of the barrier motion where the electric current as well as the net pumped electric charge experience random fluctuations over the static background. We show that in the large-time limit, $t \to \infty$, the wavefunction is naturally separated into the Berry-phase component (resulting from the singular part of the wave amplitude in the co-moving…
We study the topological phase in dipolar-coupled two-dimensional breathing square lattice of magnetic vortices. By evaluating the quantized Chern number and $\mathbb{Z}_{4}$ Berry phase, we obtain the phase diagram and identify that the second-order topological corner states appear only when the ratio of alternating bond lengths goes beyond a critical value. Interestingly, we uncover three corner states at different frequencies ranging from sub GHz to tens of GHz by solving the generalized Thiele's equation, which has no counterpart in condensed matter system. We show that the emerging corner…
We study the electromagnetic response and surface electromagnetic modes in a generic gapped Dirac material under pumping with circularly polarized light. The valley imbalance due to pumping leads to a net Berry curvature, giving rise to a finite transverse conductivity. We discuss the appearance of nonreciprocal chiral edge modes, their hybridization and waveguiding in a nanoribbon geometry, and giant polarization rotation in nanoribbon arrays.
We optimize the operation of single-electron charge pumps using full counting statistics techniques. To this end, we evaluate the statistics of pumped charge on a wide range of driving frequencies using Floquet theory, focusing here on the current and the noise. For charge pumps controlled by one or two gate voltages, we demonstrate that our theoretical framework may lead to enhanced device performance. Specifically, by optimizing the driving parameters, we predict a significant increase in the frequencies for which a quantized current can be produced. For adiabatic two-parameter pumps, we exp…
We consider the process of pumping charge through an open quantum system, motivated by the example of a quantum dot with strong repulsive or attractive electron-electron interaction. Using the geometric formulation of adiabatic nonunitary evolution put forward by Sarandy and Lidar, we derive an encompassing approach to ideal charge measurements of time-dependently driven transport, that stays near the familiar approach to closed systems. Following Schaller, Kießlich and Brandes we explicitly account for a meter that registers the transported charge outside the system. The gauge freedom underly…
The Berry curvature involving time and momentum derivatives, which we term emergent electric field, induces a nondisspative current known as the adiabatic charge pumping or Thouless pumping in periodically driven systems. We study dissipative currents originated from the interplay between emergent electric fields and electric/magnetic fields in two and three dimensions on the basis of the Boltzmann transport theory. As an example of two-dimensional models, we study the Rashba Hamiltonian with time-dependent and anisotropic spin-orbit coupling. We show that the interplay between emergent electr…
We investigate the dispersion topology of elastic lattices characterized by spatial stiffness modulation. The modulation is defined by the sampling of a two-dimensional surface, which provides the lattices with topological properties that are usually attributed to two-dimensional crystals. We show that the cyclic variation of the phase of the stiffness modulation leads to a Berry phase accumulation for the Bloch eigenmodes, which is characterized by integer valued Chern numbers for the bands and associated gap labels. The resulting non-trivial gaps are spanned by edge modes localized at one of…
The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U(n). As the result, one can create a theory of particle evolution that is gauge invariant with regards to the group U^n(1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U(1…
We propose a two-dimensional (2D) version of Thouless pumping that can be realized by using ultracold atoms in optical lattices. To be specific, we consider a 2D square lattice tight-binding model with an obliquely introduced superlattice. It is demonstrated that quantized particle transport occurs in this system, and that the transport is expressed as a solution of a Diophantine equation. This topological nature can be understood by mapping the Hamiltonian to a three-dimensional (3D) cubic lattice model with a homogeneous magnetic field. We also propose a continuum model with obliquely introd…
We set up a general density-operator approach to geometric steady-state pumping through slowly driven open quantum systems. This approach applies to strongly interacting systems that are weakly coupled to multiple reservoirs at high temperature, illustrated by an Anderson quantum dot, but shows potential for generalization. Pumping gives rise to a nonadiabatic geometric phase that can be described by a framework originally developed for classical dissipative systems by Landsberg. This geometric phase is accumulated by the transported observable (charge, spin, energy) and not by the quantum sta…
In the course of searching for promising topological materials for applications in future topological electronics, we evaluated spin-orbit torques (SOTs) in high-quality sputtered $δ-$TaN/Co20Fe60B20 devices through spin-torque ferromagnetic resonance ST-FMR and spin pumping measurements. From the ST-FMR characterization we observed a significant linewidth modulation in the magnetic Co20Fe60B20 layer attributed to the charge-to-spin conversion generated from the $δ-$TaN layer. Remarkably, the spin-torque efficiency determined from ST-FMR and spin pumping measurements is as large as $Θ =$ 0.034…
The phenomenon of charge pumping and the modern theory of electric polarization are reconsidered by analytically taking into account emergent non-Hermitian contributions. These are accounted for through the use of an extended definition of the velocity operator and are determined by means of a dynamic Hellmann-Feynman theorem (DHFT) that we derive here for the first time. The DHFT introduces generalized Berry curvatures and it is valid for calculating observables nonperturbatively, hence with results valid to all orders of the external fields. By using the extended velocity operator we rigorou…
We investigate the quantization of adiabatic charge transport in the insulating ground state of finite systems. Topological charge pumps are used in experiments as an indicator of topological order. In the thermodynamic limit the transport can be related to a topological Berry phase and is thus strictly quantized. This is no longer true for finite systems. We derive finite-size corrections to the transport both for non-interacting and interacting systems and relate them to analytic properties of the single- and many-body Berry curvature. We find that they depend on the details of experimental …
The recent discovery of higher-order topological insulators (HOTIs) has significantly extended our understanding of topological phases of matter. Here, we predict that second-order corner states can emerge in the dipolar-coupled dynamics of topological spin textures in two-dimensional artificial crystals. Taking a breathing honeycomb lattice of magnetic vortices as an example, we derive the full phase diagram of collective vortex gyrations and identify three types of corner states that have not been discovered before. We show that the topological "zero-energy" corner modes are protected by a g…
The newly discovered topological Dirac semimetals host the possibilities of various topological phase transitions through the control of spin-orbit coupling as well as symmetries and dimensionalities. Here, we report a magnetotransport study of high-mobility (Cd1-xZnx)3As2 films, where the topological Dirac semimetal phase can be turned into a trivial insulator via chemical substitution. By high-field measurements with a Hall-bar geometry, magnetoresistance components ascribed to the chiral charge pumping have been distinguished from other extrinsic effects. The negative magnetoresistance exhi…
We investigate the pumped charge and spin at zero-bias by adiabatic modulation of two control parameters using the full counting statistics with quantum master equation approach. First we study higher order effects of the pumping frequency in general Markov systems and show the equivalence between our approach and the real-time diagrammatic approach. An adiabatic modulation of the control parameters induces the Berry-Sinitsyn-Nemenman (BSN) phase. We show that the origin of the BSN phase is a non-adiabatic effect. The adiabatically pumped charge (spin) is given by a summation of (i) a time int…
