We propose a Berry phase effect on the chiral degrees of freedom of a triangular magnetic molecule. The phase is induced by adiabatically varying an external electric field in the plane of the molecule via a spin-electric coupling mechanism present in these frustrated magnetic molecules. The Berry phase effect depends on spin-orbit interaction splitting and on the electric dipole moment. By varying the amplitude of the applied electric field, the Berry phase difference between the two spin states can take any arbitrary value between zero and Ï, which can be measured as a phase shift between the two chiral states by using spin-echo techniques. Our result can be used to realize an electric-field-induced geometric phase-shift gate acting on a chiral qubit encoded in the ground-state manifold of the triangular magnetic molecule.
We study time-dependent electronic and spin transport through an electronic level connected to two leads and coupled with a single-molecule magnet via exchange interaction. The molecular spin is treated as a classical variable and precesses around an external magnetic field. We derive expressions for charge and spin currents by means of the Keldysh nonequilibrium Green's functions technique in linear order with respect to the time-dependent magnetic field created by this precession. The coupling between the electronic spins and the magnetization dynamics of the molecule creates inelastic tunneling processes which contribute to the spin currents. The inelastic spin currents, in turn, generate a spin-transfer torque acting on the molecular spin. This back-action includes a contribution to the Gilbert damping and a modification of the precession frequency. The Gilbert damping coefficient can be controlled by the bias and gate voltages or via the external magnetic field and has a nonmonotonic dependence on the tunneling rates.
The high-spectral-resolution optical studies of the energy gap evolution, supplemented with electronic, magnetic, and structural characterization, show that the modification of the GaAs valence band caused by Mn incorporation occurs already for a very low Mn content, much lower than that required to support ferromagnetic spin-spin coupling in (Ga,Mn) As. Only for n-type (Ga,Mn) As with the Mn content below about 0.3% the Mn-related extended states are visible as a feature detached from the valence-band edge and partly occupied with electrons. The combined magnetic and low-temperature photoreflectance studies presented here indicate that the paramagnetic <-> ferromagnetic transformation in p-type (Ga,Mn) As takes place without imposing changes of the unitary character of the valence band with the Fermi level located therein. The whole process is rooted in the nanoscale fluctuations of the local (hole) density of states and the formation of a superparamagnetic-like state. The Fermi level in (Ga,Mn) As is coarsened by the carrier concentration of the itinerant valence band holes and further fine-tuned by the many-body interactions.
We describe a first-principles method to calculate scanning tunneling microscopy (STM) images, and compare the results to well-characterized experiments combining STM with atomic force microscopy (AFM). The theory is based on density functional theory with a localized basis set, where the wave functions in the vacuum gap are computed by propagating the localized-basis wave functions into the gap using a real-space grid. Constant-height STM images are computed using Bardeen's approximation method, including averaging over the reciprocal space. We consider copper adatoms and single CO molecules adsorbed on Cu(111), scanned with a single-atom copper tip with and without CO functionalization. The calculated images agree with state-of-the-art experiments, where the atomic structure of the tip apex is determined by AFM. The comparison further allows for detailed interpretation of the STM images.
We present a method capable of calculating elastic scanning tunneling microscopy (STM) currents from localized atomic orbital density functional theory (DFT). To overcome the poor accuracy of the localized orbital description of the wave functions far away from the atoms, we propagate the wave functions, using the total DFT potential. From the propagated wave functions, the Bardeen's perturbative approach provides the tunneling current. To illustrate the method we investigate carbon monoxide adsorbed on a Cu(111) surface and recover the depression/protrusion observed experimentally with normal/CO-functionalized STM tips. The theory furthermore allows us to discuss the significance of s- and p-wave tips.
The supercurrent through a quantum point contact coupled to a nanomagnet strongly depends on the dynamics of the nanomagnet's spin. We employ a fully microscopic model to calculate the transport properties of a junction coupled to a spin whose dynamics is modeled as Larmor precession brought about by an external magnetic field and find that the dynamics affects the charge and spin currents by inducing transitions between the continuum states outside the superconducting gap region and the Andreev levels. This redistribution of the quasiparticles leads to a nonequilibrium population of the Andreev levels and an enhancement of the supercurrent which is visible as a modified current-phase relation as well as a nonmonotonous critical current as function of temperature. The nonmonotonous behavior is accompanied by a corresponding change in spin-transfer torques acting on the precessing spin and leads to the possibility of using temperature as a means to tune the back-action on the spin.
We investigate the charge and spin transport of a voltage-biased superconducting point contact coupled toa nanomagnet. The magnetization of the nanomagnet is assumed to precess with the Larmor frequencyωLwhen exposed to ferromagnetic resonance conditions. The Larmor precession locally breaks the spin-rotationsymmetry of the quasiparticle scattering and generates spin-polarized Shapiro steps for commensurate Josephsonand Larmor frequencies that lead to magnetization reversal. This interplay between the ac Josephson current andthe magnetization dynamics occurs at voltages|V|=ωL/2enforn=1,2,..., and the subharmonic steps withn>1 are a consequence of multiple Andreev reflection (MAR). Moreover, the spin-precession-assisted MARgenerates quasiparticle scattering amplitudes that, due to interference, lead to current-voltage characteristics ofthe dc charge and spin currents with subharmonic gap structures displaying an even-odd effect.
We present a theoretical study of a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin. When an external magnetic field is applied, the classical spin will precess with the Larmor frequency. This magnetically active interface results in a time-dependent boundary condition with different tunneling amplitudes for spin-up and spin-down quasiparticles and where the precession produces spin-flip scattering processes. We show that as a result, the Andreev states develop sidebands and a nonequilibrium population which depend on the precession frequency and the angle between the classical spin and the external magnetic field. The Andreev states lead to a steady-state Josephson current whose current-phase relation could be used for characterizing the precessing spin. In addition to the charge transport, a magnetization current is also generated. This spin current is time dependent and its polarization axis rotates with the same precession frequency as the classical spin.
The quantum anomalous Hall effect (QAHE) has recently been reported to emerge in magnetically doped topological insulators. Although its general phenomenology is well established, the microscopic origin is far from being properly understood and controlled. Here, we report on a detailed and systematic investigation of transition metal (TM) doped Sb2Te3. By combining density functional theory calculations with complementary experimental techniques, i.e., scanning tunneling microscopy, resonant photoemission, and x-raymagnetic circular dichroism, we provide a complete spectroscopic characterization of both electronic and magnetic properties. Our results reveal that the TM dopants not only affect the magnetic state of the host material, but also significantly alter the electronic structure by generating impurity-derived energy bands. Our findings demonstrate the existence of a delicate interplay between electronic and magnetic properties in TM doped topological insulators. In particular, we find that the fate of the topological surface states critically depends on the specific character of the TM impurity: while V-and Fe-doped Sb2Te3 display resonant impurity states in the vicinity of the Dirac point, Cr and Mn impurities leave the energy gap unaffected. The single-ion magnetic anisotropy energy and easy axis, which control the magnetic gap opening and its stability, are also found to be strongly TM impurity dependent and can vary from in plane to out of plane depending on the impurity and its distance from the surface. Overall, our results provide general guidelines for the realization of a robust QAHE in TM doped Sb2Te3 in the ferromagnetic state.
The quantum anomalous Hall effect (QAHE), characterized by dissipationless quantized edge transport, relies crucially on a nontrivial topology of the electronic bulk band structure and a robust ferromagnetic order that breaks time-reversal symmetry. Magnetically doped topological insulators (TIs) satisfy both these criteria, and are the most promising quantum materials for realizing the QAHE. Because the spin of the surface electrons aligns along the direction of the magnetic-impurity exchange field, only magnetic TIs with an out-of-plane magnetization are thought to open a gap at the Dirac point (DP) of the surface states, resulting in the QAHE. Using a continuum model supported by atomistic tight-binding and first-principles calculations of transition-metal doped Bi2Se3, we show that a surface-impurity potential generates an additional effective magnetic field which spin polarizes the surface electrons along the direction perpendicular to the surface. The predicted gap-opening mechanism results from the interplay of this additional field and the in-plane magnetization that shifts the position of the DP away from the Γ point. This effect is similar to the one originating from the hexagonal warping correction of the band structure but is one order of magnitude stronger. Our calculations show that in a doped TI with in-plane magnetization the impurity-potential-induced gap at the DP is comparable to the one opened by an out-of-plane magnetization.
Fundamental upper bounds are given for the plasmonic multipole absorption and scattering of a rotationally invariant dielectric sphere embedded in a lossy surrounding medium. A specialized Mie theory is developed for this purpose and when combined with the corresponding generalized optical theorem, an optimization problem is obtained which is explicitly solved by straightforward analysis. In particular, the absorption cross section is a concave quadratic form in the related Mie (scattering) parameters and the convex scattering cross section can be maximized by using a Lagrange multiplier constraining the absorption to be non-negative. For the homogeneous sphere, the Weierstrass preparation theorem is used to establish the existence and the uniqueness of the plasmonic singularities and explicit asymptotic expressions are given for the dipole and the quadrupole. It is shown that the optimal passive material for multipole absorption and scattering of a small homogeneous dielectric sphere embedded in a dispersive medium is given approximately as the complex conjugate and the real part of the corresponding pole positions, respectively. Numerical examples are given to illustrate the theory, including a comparison with the plasmonic dipole and quadrupole resonances obtained in gold, silver, and aluminum nanospheres based on some specific Brendel-Bormann (BB) dielectric models for these metals. Based on these BB models, it is interesting to note that the metal spheres can be tuned to optimal absorption at a particular size at a particular frequency.
Achieving a high intensity in inelastic scanning tunneling spectroscopy (IETS) is important for precise measurements. The intensity of the IETS signal can vary by up to a factor of 3 for various tips without an apparent reason accessible by scanning tunneling microscopy (STM) alone. Here, we show that combining STM and IETS with atomic force microscopy enables carbon monoxide front-atom identification, revealing that high IETS intensities for CO/Cu(111) are obtained for single-atom tips, while the intensity drops sharply for multiatom tips. Adsorption of the CO molecule on a Cu adatom [CO/Cu/Cu(111)] such that the molecule is elevated over the substrate strongly diminishes the tip dependence of IETS intensity, showing that an elevated position channels most of the tunneling current through the CO molecule even for multiatom tips, while a large fraction of the tunneling current bypasses the CO molecule in the case of CO/Cu(111).
We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically doped Bi2Se3-family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is based on a simple continuum model of sidewall states whose parameters are extracted from detailed ribbon and film geometry tight-binding model calculations. In contrast to the familiar case of the quantum Hall effect in semiconductor quantum wells, the number of microscopic chiral channels depends simply and systematically on the ribbon thickness and on the position of the Fermi level within the surface state gap. We use our theory to interpret recent transport experiments that exhibit nonzero longitudinal resistance in samples with accurately quantized Hall conductances.
Historically, comprehensive studies of dilute ferromagnetic semiconductors, e.g., p-type (Cd,Mn) Te and (Ga,Mn) As, paved the way for a quantitative theoretical description of effects associated with spin-orbit interactions in solids, such as crystalline magnetic anisotropy. In particular, the theory was successful in explaining uniaxial magnetic anisotropies associated with biaxial strain and nonrandom formation of magnetic dimers in epitaxial (Ga,Mn) As layers. However, the situation appears much less settled in the case of the cubic term: the theory predicts switchings of the easy axis between in-plane < 100 > and < 110 > directions as a function of the hole concentration, whereas only the < 100 > orientation has been found experimentally. Here, we report on the observation of such switchings by magnetization and ferromagnetic resonance studies on a series of high-crystalline quality (Ga,Mn) As films. We describe our findings by themean-field p-d Zener model augmented with three new ingredients. The first one is a scattering broadening of the hole density of states, which reduces significantly the amplitude of the alternating carrier-induced contribution. This opens the way for the two other ingredients, namely the so-far disregarded single-ion magnetic anisotropy and disorder-driven nonuniformities of the carrier density, both favoring the < 100 > direction of the apparent easy axis. However, according to our results, when the disorder gets reduced, a switching to the < 110 > orientation is possible in a certain temperature and hole concentration range.
Josephson currents are carried by sharp Andreev states within the superconducting energy gap. We theoretically study the electronic transport of a magnetically tunable nanoscale junction consisting of a quantum dot connected to two superconducting leads and coupled to the spin of a molecular magnet. The exchange interaction between the molecular magnet and the quantum dot modifies the Andreev states due to a spin-dependent renormalization of the quantum dot's energy level and the induction of spin flips. A magnetic field applied to the central region of the quantum dot and the molecular magnet further tunes the Josephson current and starts a precession of the molecular magnet's spin. We use a nonequilibrium Green's function approach to evaluate the transport properties of the junction. Our calculations reveal that the energy level of the dot, the magnetic field, and the exchange interaction between the molecular magnet and the electrons occupying the energy level of the quantum dot can trigger transitions from a 0 to a π state of the Josephson junction. The redistribution of the occupied states induced by the magnetic field strongly modifies the current-phase relation. The critical current exhibits a sharp increase as a function of either the energy level of the dot, the magnetic field, or the exchange interaction.
We study dc-transport and magnetization dynamics in a junction of arbitrary transparency consisting of two spin-singlet superconducting leads connected via a single classical spin precessing at the frequency Ω. The presence of the spin in the junction provides different transmission amplitudes for spin-up and spin-down quasiparticles as well as a time-dependent spin-flip transmission term. For a phase-biased junction, we show that a steady-state superconducting charge current flows through the junction and that an out-of-equilibrium circularly polarized spin current, of frequency Ω, is emitted in the leads. Detailed understanding of the charge and spin currents is obtained in the entire parameter range. In the adiabatic regime, ℏΩ⪡2Δ, where Δ is the superconducting gap, and for high transparencies of the junction, a strong suppression of the current takes place around φ≈0 due to an abrupt change in the occupation of the Andreev bound states. At higher values of the phase and/or precession frequency, extended (quasiparticlelike) states compete with the bound states in order to carry the current. Well below the superconducting transition, these results are shown to be weakly affected by the backaction of the spin current on the dynamics of the precessing spin. Indeed, we show that the Gilbert damping due to the quasiparticle spin current is strongly suppressed at low temperatures, which goes along with a shift of the precession frequency due to the condensate. The results obtained may be of interest for ongoing experiments in the field of molecular spintronics.
Inelastic tunneling of electrons can generate the emission of photons with energies intuitively limited by the applied bias voltage. However, experiments indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission with overbias energies. We recently proposed a model of this observation in Phys. Rev. Lett. 113, 066801 (2014), in analogy to the dynamical Coulomb blockade, originally developed for treating the electromagnetic environment in mesoscopic circuits. This model describes the correlated tunneling of two electrons interacting with a local plasmon-polariton mode, represented by a resonant circuit, and shows that the overbias emission is due to the non-Gaussian fluctuations. Here we extend our model to study the overbias emission at finite temperature. We find that the thermal smearing strongly masks the overbias emission. Hence, the detection of the correlated tunneling processes requires temperatures k(B)T much lower than the bias energy eV and the plasmon energy h omega(0), a condition which is fortunately realized experimentally.