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arXiv:1903.10381 · Physical review. B./Physical review. B

Quench dynamics of spin in quantum dots coupled to spin-polarized leads

Kacper Wrześniewski, Ireneusz Weymann

Published Jul 3, 2019• 13 citations
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Abstract

We investigate the quench dynamics of a quantum dot strongly coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework. We examine the system's response to a quench in the spin-dependent coupling strength to ferromagnetic leads as well as in the position of the dot's orbital level. The spin dynamics is analyzed by calculating the time-dependent expectation values of the quantum dot's magnetization and occupation. Based on these, we determine the time dependence of a ferromagnetic-contact-induced exchange field and predict its nonmonotonic buildup. In particular, two timescales are identified, describing the development of the exchange field and the dot's magnetization sign change. Finally, we study the effects of finite temperature on the dynamical behavior of the system.

DOI
10.1103/physrevb.100.035404

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We investigate the quench dynamics of a quantum dot strongly coupled to spin-polarized ferromagnetic leads. The real-time evolution is calculated by means of the time-dependent density-matrix numerical renormalization group method implemented within the matrix product states framework. We examine the system's response to a quench in the spin-dependent coupling strength to ferromagnetic leads as well as in the position of the dot's orbital level. The spin dynamics is analyzed by calculating the time-dependent expectation values of the quantum dot's magnetization and occupation. Based on these, we determine the time dependence of a ferromagnetic-contact-induced exchange field and predict its nonmonotonic buildup. In particular, two timescales are identified, describing the development of the exchange field and the dot's magnetization sign change. Finally, we study the effects of finite temperature on the dynamical behavior of the system.
Dynamical buildup of spin-singlet correlations between the two quantum dots is investigated by means of the time-dependent numerical renormalization group method. By calculating the time evolution of the spin-spin expectation value upon a quench in the hopping between the quantum dots, we examine the timescales associated with the development of an entangled spin-singlet state in the system. Interestingly, we predict a nonmonotonic buildup of entanglement between the two dots. In particular, we find that in short timescales the effective exchange interaction between the quantum dots is of ferromagnetic type, favoring spin-triplet correlations, as opposed to the long-time limit, when strong antiferromagnetic correlations develop and eventually an entangled spin-singlet state is formed between the dots. We also numerically determine the relevant timescales and show that the physics is generally governed by the interplay between the Kondo correlations on each dot and exchange interaction between the spins of both quantum dots.
We theoretically explore the non-equilibrium dynamics of a single quantum dot system coupled to both ferromagnetic and superconducting electrodes. To investigate its time evolution, we utilize the time-dependent numerical renormalization group technique, which captures the system's response to abrupt parameter changes in a fully non-perturbative manner. Our analysis focuses on dynamics following a sudden modification in the couplings to the leads or a shift of the orbital level. In particular, we calculate the time evolution of the induced local superconducting pairing correlations and magnetization. In this context, the relevant energy spectra are examined. Moreover, we study the behavior of the Loschmidt echo and the return function to shed light on the signatures of dynamical quantum phase transitions. The determined dependencies reveal non-trivial competition between relevant correlations, involving superconducting pairing and ferromagnetic-contacted induced exchange field, and deepen our understanding of nanoscale hybrid systems' dynamical behavior.
Motivated by recent experiments on molecular quantum dots we investigate the relaxation of pure spin states when coupled to metallic leads. Under suitable conditions these systems are well described by a ferromagnetic Kondo model. Using two recently developed theoretical approaches, the time-dependent numerical renormalization group and an extended flow equation method, we calculate the real-time evolution of a Kondo spin into its partially screened steady state. We obtain exact analytical results which agree well with numerical implementations of both methods. Analytical expressions for the steady state magnetization and the dependence of the long-time relaxation on microscopic parameters are established. We find the long-time relaxation process to be much faster in the regime of anisotropic Kondo couplings. The steady state magnetization is found to deviate significantly from its thermal equilibrium value.
We develop a general approach to the nonequilibrium dynamics of quantum-impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of the time evolution. We benchmark our method with the exact analytical solution for the resonant-level model. As a first application, we investigate the equilibration of an ultrasmall quantum dot subject to a sudden change of gate voltage and external magnetic field. Two distinct relaxation times are identified for the spin and charge dynamics.
Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group(TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the 1-D nearest-neighbor tight-binding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot $$ as a function of bias voltage.
Using a real-time renormalization group method we study the minimal model of a quantum dot dominated by charge fluctuations, the two-lead interacting resonant level model, at finite bias voltage. We develop a set of RG equations to treat the case of weak and strong charge fluctuations, together with the determination of power-law exponents up to second order in the Coulomb interaction. We derive analytic expressions for the charge susceptibility, the steady-state current, and the conductance in the situation of arbitrary system parameters, in particular away from the particle-hole symmetric point and for asymmetric Coulomb interactions. In the asymmetric situation we find that power laws can be observed for the current only as a function of the level position (gate voltage) but in general not as a function of the voltage except for extremely large voltages. Furthermore, we study the quench dynamics after sudden switch-on of the level-lead couplings. The time evolution of the dot occupation and current is governed by exponential relaxation accompanied by voltage-dependent oscillations and characteristic algebraic decay.