arXiv subjects

Frithjof B. Anders

Publications and source records attributed to Frithjof B. Anders.

At least 37 records · Page 2Linked to original sources

arXiv2019

Fourth-order spin correlation function in the extended central spin model

Spin noise spectroscopy has developed into a very powerful tool to access the electron spin dynamics. While the spin-noise power spectrum in an ensemble of quantum dots in a magnetic field is essentially understood, we argue that the investigation of the higher order cumulants promises to provide additional information not accessible by the conventional power noise spectrum. We present a quantum mechanical approach to the correlation function of the spin-noise power operators at two different frequencies for small spin bath sizes and compare the results with a simulation obtained from the classical spin dynamics for large number of nuclear spins. This bispectrum is defined as a two-dimensional frequency cut in the parameter space of the fourth-order spin correlation function. It reveals information on the influence of the nuclear-electric quadrupolar interactions on the long-time electron spin dynamics dominated by a magnetic field. For large bath sizes and spin lengths the quantum mechanical spectra converge to those of the classical simulations. The broadening of the bispectrum across the diagonal in the frequency space is a direct measure of the quadrupolar interaction strength. A narrowing is found with increasing magnetic field indicating a suppression of the influence of quadrupolar interactions in favor of the nuclear Zeeman effect.

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arXiv2018

Magnetic field dependence of the electron spin revival amplitude in periodically pulsed quantum dots

Periodic laser pulsing of singly charged semiconductor quantum dots in an external magnetic field leads to a synchronization of the spin dynamics with the optical excitation. The pumped electron spins partially rephase prior to each laser pulse, causing a revival of electron spin polarization with its maximum at the incidence time of a laser pulse. The amplitude of this revival is amplified by the frequency focusing of the surrounding nuclear spins. Two complementary theoretical approaches for simulating up to 20 million laser pulses are developed and employed that are able to bridge between 11 orders of magnitude in time: a fully quantum mechanical description limited to small nuclear bath sizes and a technique based on the classical equations of motion applicable for a large number of nuclear spins. We present experimental data of the nonmonotonic revival amplitude as function of the magnetic field applied perpendicular to the optical axis. The dependence of the revival amplitude on the external field with a profound minimum at $4\;$T is reproduced by both of our theoretical approaches and is ascribed to the nuclear Zeeman effect. Since the nuclear Larmor precession determines the electronic resonance condition, it also defines the number of electron spin revolutions between pump pulses, the orientation of the electron spin at the incidence time of a pump pulse, and the resulting revival amplitude. The magnetic field of $4\;$T, for example, corresponds to half a revolution of nuclear spins between two laser pulses.

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arXiv2018

Realistic quantum critical point in one-dimensional two-impurity models

We show that the two-impurity Anderson model exhibits an additional quantum critical point at infinitely many specific distances between both impurities for an inversion symmetric one-dimensional dispersion. Unlike the quantum critical point previously established, it is robust against particle-hole or parity symmetry breaking. The quantum critical point separates a spin doublet from a spin singlet ground state and is, therefore, protected. A finite single-particle tunneling $t$ or an applied uniform gate voltage will drive the system across the quantum critical point. The discriminative magnetic properties of the different phases cause a jump in the spectral functions at low temperature, which might be useful for future spintronics devices. A local parity conservation will prevent the spin-spin correlation function from decaying to its equilibrium value after spin manipulations.

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arXiv2018

Equilibrium and real-time properties of the spin correlation function in the two-impurity Kondo model

We investigate the equilibrium and real-time properties of the spin correlation function $\langle \vec{S}_1\vec{S}_2 \rangle$ in the two-impurity Kondo model for different distances $R$ between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\langle \vec{S}_1\vec{S}_2 \rangle$. For distances $R$ exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings $J$ between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long time behavior which reflects that for small $J$ the system is driven by the RKKY interaction while for large $J$ the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying $ε(k)=ε(-k)$ may lead to a local parity conservation of the impurities such that $\langle \vec{S}_1\vec{S}_2 \rangle$ becomes a conserved quantity for long times and does not decay to its equilibrium value.

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arXiv2018

Nuclear Spin Noise in the Central Spin Model

We study theoretically the spin fluctuations of nuclei in quantum dots. We employ the central spin model which accounts for the hyperfine interaction of the nuclei with the electron spin. We present an analytical solution in the frame of the box model approximation where all hyperfine coupling constants are assumed to be equal. These results are in good agreement with numerical simulations. We demonstrate that in rather high magnetic field the nuclear spin noise spectra has a two-peak structure centered at the nuclear Zeeman frequency with the shape of the spectrum controlled by the distribution of the hyperfine constants.

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arXiv2018

Signatures of long-range spin-spin interactions in an (In,Ga)As quantum dot ensemble

We present an investigation of the electron spin dynamics in an ensemble of singly-charged quantum dots subject to an external magnetic field and laser pumping with circularly polarized light. The spectral laser width is tailored such that different groups of quantum dots are coherently pumped. Surprisingly, the dephasing time $T^*$ of the electron spin polarization depends only weakly on the laser spectral width. These findings can be consistently explained by a cluster theory of coupled quantum dots with a long range electronic spin-spin interaction. We present a numerical simulation of the spin dynamics based on the central spin model that includes a quantum mechanical description of the laser pulses as well as a time-independent Heisenberg interaction between each pair of electron spins. We discuss the individual dephasing contributions stemming from the Overhauser field, the distribution of the electron $g$-factors and the electronic spin-spin interaction as well as the spectral width of the laser pulse. This analysis reveals the counterbalancing effect of the total dephasing time when increasing the spectral laser width. On one hand, the deviations of the electron $g$-factors increase. On the other hand, an increasing number of coherently pumped electron spins synchronize due to the spin-spin interaction. We find an excellent agreement between the experimental data and the dephasing time in the simulation using an exponential distribution of Heisenberg couplings with a mean value $\overline{J}\approx 0.26\,\mathrm{μeV}$.

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arXiv2018

Effective low-energy description of the two impurity Anderson model: RKKY interaction and quantum criticality

We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.

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arXiv2018

Electron Spin Noise under the Conditions of Nuclei Induced Frequency Focusing

We study theoretically the electron spin noise in quantum dots under non-equilibrium conditions caused by the pumping by a train of circularly polarized optical pulses. In such a situation, the nuclear spins are known to adjust in such a way, that the electron spin precession frequencies become multiples of the pump pulse repetition frequency. This so called phase synchronization effect was uncovered in [Science {\bf 317}, 1896 (2007)] and termed nuclei-induced frequency focusing of electron spin coherence. Using the classical approach to the central spin model we evaluate the nuclear spin distribution function and the electron spin noise spectrum. We show that the electron spin noise spectrum consists of sharp peaks corresponding to the phase synchronization conditions and directly reveal the distribution of the nuclear spins. We discuss the effects of nuclear spin relaxation after the pumping is over and analyze the corresponding evolution of nuclear spin distributions and electron spin noise spectra.

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arXiv2018

Modeling of gate controlled Kondo effect at carbon point-defects in graphene

We study the magnetic properties in the vicinity of a single carbon defect in a monolayer of graphene. We include the unbound $σ$ orbital and the vacancy induced bound $π$ state in an effective two-orbital single impurity model. The local magnetic moments are stabilized by the Coulomb interaction as well as a significant ferromagnetic Hund's rule coupling between the orbitals predicted by a density functional theory calculation. A hybridization between the orbitals and the Dirac fermions is generated by the curvature of the graphene sheet in the vicinity of the vacancy. We present results for the local spectral function calculated using Wilson's numerical renormalization group approach for a realistic graphene band structure and find three different regimes depending on the filling, the controlling chemical potential, and the hybridization strength. These different regions are characterized by different magnetic properties. The calculated spectral functions qualitatively agree with recent scanning tunneling spectra on graphene vacancies.

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arXiv2018

Quantum Critical Transition and Kondo Screening of Magnetic Moments in Graphene

In normal metals, the magnetic moment of impurity spins disappears below a characteristic Kondo temperature, TK, where coupling with the conduction-band electrons produces an entangled state that screens the local moment. In contrast, moments embedded in insulators remain unscreened at all temperatures. This raises the question about the fate of magnetic moments in intermediate, pseudogap systems, such as graphene. In these systems theory predicts a quantum phase-transition at a critical coupling strength which separates a local magnetic-moment phase from a Kondo screened phase. However, attempts to experimentally confirm these predictions and their intriguing consequences such as the ability to electrostatically control magnetic moments, have thus far been elusive. Here we report the observation of Kondo screening and the quantum phase-transition between screened and unscreened phases of vacancy magnetic-moments in graphene. Using scanning tunneling microscopy (STM), spectroscopy (STS) and numerical renormalization group (NRG) calculations, we identified Kondo screening by its spectroscopic signature and mapped the phase-transition as a function of coupling strength and chemical potential. We show that this transition makes it possible to turn the magnetic-moment on and off electrostatically through a gate voltage or mechanically through variations in local curvature.

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arXiv2017

Quantum model for mode locking in pulsed semiconductor quantum dots

Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is dramatically increased if the system is subjected to a magnetic field and to repeated optical pulsing. This enhancement is due to mode locking: Oscillation frequencies resonant with the pulsing frequencies are enhanced, while off-resonant oscillations eventually die out. Because the resonant frequencies are determined by the pulsing frequency only, the system becomes immune to frequency shifts caused by the nuclear coupling and by slight variations between individual quantum dots. The effects remain even after the optical pulsing is terminated. In this work, we explore the phenomenon of mode locking from a quantum mechanical perspective. We treat the dynamics using the central spin model, which includes coupling to 10-20 nuclei and incoherent decay of the excited electronic state, in a perturbative framework. Using scaling arguments, we extrapolate our results to realistic system parameters. We find that the synchronization to the pulsing frequency needs time scales in the order of 1 s.

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arXiv2017

Long-time coherence in fourth-order spin correlation functions

We study the long-time decay of fourth-order electron spin correlation functions for an isolated singly charged semi-conductor quantum dot. The electron spin dynamics is governed by the applied external magnetic field as well as the hyperfine interaction. While the long-time coherent oscillations in the correlation functions can be understood within an semi-classical approach treating the Overhauser field as frozen, the field dependent decay of its amplitude reported in different experiments cannot be explained by the central-spin model indicating the insufficiency of such a description. By incorporating the nuclear Zeeman splitting and the strain induced nuclear-electric quadrupolar interaction, we find the correct crossover from a fast decay in small magnetic fields to a slow exponential asymptotic in large magnetic fields. It originates from a competition between the quadrupolar interaction inducing an enhanced spin decay and the nuclear Zeeman term that suppressed the spin-flip processes. We are able to explain the magnetic field dependency of the characteristic long-time decay time $T_2$ depending on the experimental setups. The calculated asymptotic values of $T_2 = 3 -4\,μ$s agree qualitatively well with the experimental data.

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arXiv2017

Influence of the nuclear Zeeman effect on mode locking in pulsed semiconductor quantum dots

The coherence of the electron spin in a semiconductor quantum dot is strongly enhanced by mode locking through nuclear focusing, where the synchronization of the electron spin to periodic pulsing is slowly transferred to the nuclear spins of the semiconductor material, mediated by the hyperfine interaction between these. The external magnetic field that drives the Larmor oscillations of the electron spin also subjects the nuclear spins to a Zeeman-like coupling, albeit a much weaker one. For typical magnetic fields used in experiments, the energy scale of the nuclear Zeeman effect is comparable to that of the hyperfine interaction, so that it is not negligible. In this work, we analyze the influence of the nuclear Zeeman effect on mode locking quantitatively. Within a perturbative framework, we calculate the Overhauser-field distribution after a prolonged period of pulsing. We find that the nuclear Zeeman effect can exchange resonant and non-resonant frequencies. We distinguish between models with a single type and with multiple types of nuclei. For the latter case, the positions of the resonances depend on the individual $g$ factors, rather than on the average value.

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arXiv2017

Non-equilibrium nuclear spin distribution function in quantum dots subject to periodic pulses

Electron spin dephasing in a singly charged semiconductor quantum dot can partially be suppressed by periodic laser pulsing. We propose a semi-classical approach describing the decoherence of the electron spin polarization governed by the hyperfine interaction with the nuclear spins as well as the probabilistic nature of the photon absorption. We use the steady-state Floquet condition to analytically derive two subclasses of resonance conditions excellently predicting the peak locations in the part of the Overhauser field distribution which is projected in the direction of the external magnetic field. As a consequence of the periodic pulsing, a non-equilibrium distribution develops as a function of time. The numerical simulation of the coupled dynamics reveals the influence of the hyperfine coupling constant distribution onto the evolution of the electron spin polarisation before the next laser pulse. Experimental indications are provided for both subclasses of resonance conditions.

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arXiv2017

Open Wilson chains for quantum impurity models: Keeping track of all bath modes

When constructing a Wilson chain to represent a quantum impurity model, the effects of truncated bath modes are neglected. We show that their influence can be kept track of systematically by constructing an "open Wilson chain" in which each site is coupled to a separate effective bath of its own. As a first application, we use the method to cure the so-called mass-flow problem that can arise when using standard Wilson chains to treat impurity models with asymmetric bath spectral functions at finite temperature. We demonstrate this for the strongly sub-Ohmic spin-boson model at quantum criticality where we directly observe the flow towards a Gaussian critical fixed point.

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arXiv2016

Interplay of Coulomb interaction and spin-orbit coupling

We employ the Gutzwiller variational approach to investigate the interplay of Coulomb interaction and spin-orbit coupling in a three-orbital Hubbard model. Already in the paramagnetic phase we find a substantial renormalization of the spin-orbit coupling that enters the effective single-particle Hamiltonian for the quasi-particles. Only close to half band-filling and for sizable Coulomb interaction we observe clear signatures of Hund's atomic rules for spin, orbital, and total angular momentum. For a finite local Hund's-rule exchange interaction we find a ferromagnetically ordered state. The spin-orbit coupling considerably reduces the size of the ordered moment, it generates a small ordered orbital moment, and it induces a magnetic anisotropy. To investigate the magnetic anisotropy energy, we use an external magnetic field that tilts the magnetic moment away from the easy axis $(1,1,1)$.

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arXiv2016

Decoherence of a single spin coupled to an interacting spin bath

Decoherence of a central spin coupled to an interacting spin bath via inhomogeneous Heisenberg coupling is studied by two different approaches, namely an exact equations of motion (EOMs) method and a Chebyshev expansion technique (CET). By assuming a wheel topology of the bath spins with uniform nearest-neighbor $XX$-type intrabath coupling, we examine the central spin dynamics with the bath prepared in two different types of bath initial conditions. For fully polarized baths in strong magnetic fields, the polarization dynamics of the central spin exhibits a collapse-revival behavior in the intermediate-time regime. Under an antiferromagnetic bath initial condition, the two methods give excellently consistent central spin decoherence dynamics for finite-size baths of $N\leq14$ bath spins. The decoherence factor is found to drop off abruptly on a short time scale and approach a finite plateau value which depends on the intrabath coupling strength non-monotonically. In the ultrastrong intrabath coupling regime, the plateau values show an oscillatory behavior depending on whether $N/2$ is even or odd. The observed results are interpreted qualitatively within the framework of the EOM and perturbation analysis. The effects of anisotropic spin-bath coupling and inhomogeneous intrabath bath couplings are briefly discussed. Possible experimental realization of the model in a modified quantum corral setup is suggested.

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arXiv2015

Influence of a bosonic environment onto the non-equilibrium dynamics of local electronic states in a quantum impurity system close to a quantum phase transition

We investigate the influence of an additional bosonic bath onto the real-time dynamics of a localized orbital coupled to conduction band with an energy-dependent coupling function $Γ(\varepsilon) \propto |\varepsilon|^r$. Recently, a rich phase diagram has been found in this Bose-Fermi Anderson model, where the transitions between competing ground states are governed by quantum critical points. In addition to a transition between a Kondo singlet and a local moment, a localized phase has been established once the coupling to a sub-ohmic bosonic bath exceeds a critical value. Using the time-dependent numerical renormalization group approach, we show that the non-equilibrium dynamics with F-type of bath exponents can be fully understand within an effective single-impurity Anderson model using a renormalized local Coulomb interaction $U_{\rm ren}$. For regimes with B-type of bath exponents, the nature of the bosonic bath and the coupling strength has a profound impact on the electron dynamics which can only partially be understood using an appropriate $U_{\rm ren}$. The local expectation values always reach a steady state at very long times. By a scaling analysis for $Λ\to 1^+$, we find thermalization of the system only in the strong coupling regime. In the local moment and in the localized phase significant deviations between the steady-state value and the thermal equilibrium value are found that are related to the distance to the quantum critical point.

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