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arXiv:2303.09944 · Physical review. B./Physical review. B

Many-body nonequilibrium effects in all-electric electron spin resonance

José Reina Gálvez, Christoph Wolf, Nicolás Lorente

Published Jun 7, 2023• 21 citations
arXivHTMLPDF

Abstract

Motivated by recent developments in measurements of electron spin resonances of individual atoms and molecules with a scanning tunneling microscope (ESR-STM), we study electron transport through an impurity under periodic driving as a function of the transport parameters in a model junction. The model consists of a single-orbital quantum impurity connected to two electrodes via time-dependent hopping terms. The hopping terms are treated at the lowest order in perturbation theory to recover a Lindblad-like quantum master equation with electron transport. As in the experiment, the ESR-STM signal is given by the variation of the long-time DC current with the driving frequency. The density-matrix coherences play an important role in the evaluation of the ESR-STM signal. Electron correlation is included in our impurity mode. The charging energy $U$ has significant influence on the spin dynamics depending on the sign and magnitude of the applied DC bias. Our model allows direct insight into the origin of the ESR signal from the many-body dynamics of the impurity.

DOI
10.1103/physrevb.107.235404

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Motivated by recent developments in measurements of electron spin resonances of individual atoms and molecules with a scanning tunneling microscope (ESR-STM), we study electron transport through an impurity under periodic driving as a function of the transport parameters in a model junction. The model consists of a single-orbital quantum impurity connected to two electrodes via time-dependent hopping terms. The hopping terms are treated at the lowest order in perturbation theory to recover a Lindblad-like quantum master equation with electron transport. As in the experiment, the ESR-STM signal is given by the variation of the long-time DC current with the driving frequency. The density-matrix coherences play an important role in the evaluation of the ESR-STM signal. Electron correlation is included in our impurity mode. The charging energy UUU has significant influence on the spin dynamics depending on the sign and magnitude of the applied DC bias. Our model allows direct insight into the origin of the ESR signal from the many-body dynamics of the impurity.
Electron spin resonance in scanning tunneling microscopy enabled the study of electronic transitions of magnetic impurities on surfaces at the atomic scale. This ESR-STM technique allows to spectroscopically probe and coherently manipulate spins using an all-electrical method without oscillating external magnetic driving fields. Here, we aim to review recent advancements in ESR-STM. We will discuss possible fundamental mechanisms by which the electric field drives spin resonance based on Heisenberg exchange, Kondo scattering, and Anderson impurity models. We validate theoretical predictions against experimental observations, to understand how electronic correlations, spin exchange, and many-body effects manifest in ESR-STM signals. After reviewing coherent spin control in the STM junction, we discuss potential applications of the ESR-STM method for coherent multi-spin control which enables multiple-qubit operations. Finally, we address recent developments in coupled electron-nuclear spin systems, including hyperfine-resolved ESR spectroscopy, and the driving and polarization of nuclear spins in ESR-STM.
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Electron spin resonance scanning tunneling microscopy (ESR-STM) has become a powerful tool for probing spin dynamics and coherence of individual atoms and molecules on surfaces. In this work, we perform Rabi oscillation and Hahn echo pulse protocols on individual iron phthalocyanine (FePc) molecules on MgO/Ag(001) using ESR-STM. While Hahn echo protocols are widely used to extract spin coherence times, we show that in ESR-STM they are particularly susceptible to misinterpretation due to tunneling electrons generated by the applied radio-frequency (RF) voltage. The RF voltage not only drives the spin, but simultaneously probes and relaxes it, which consequently leads to an exponential decay that reflects spin relaxation rather than intrinsic phase coherence. We moreover show that varying both delay times in the refocusing pulse sequence is a reliable way to ensure a coherent nature of the echo signal. The extracted decay for the latter protocol suggests that T2 is approximately 30 ns and is thus closer to the decoherence time observed in Rabi oscillation measurements. This is significantly shorter than values reported in previous echo measurements. Our findings underscore the need for caution in interpreting T2 times from Hahn echo and Carr-Purcell protocols in ESR-STM and provide practical criteria for distinguishing true spin echoes from tunneling-induced relaxometry signals.
The eigenstates of an isolated nanostructure may get mixed by the coupling to external leads. This effect is the stronger, the smaller the level splitting on the dot and the larger the broadening induced by the coupling to the leads. We describe how to calculate the nondiagonal density matrix of the nanostructure efficiently in the cotunneling regime. As an example, we consider a system of two quantum dots in the Kondo regime, the two spins coupled by an antiferromagnetic exchange interaction and each dot tunnel coupled to two leads. Calculating the nonequilibrium density matrix and the corresponding current, we demonstrate the importance of the off-diagonal terms in the presence of an applied magnetic field and a finite bias voltage.
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electron spin resonance combined with scanning tunneling microscopy (ESR-STM). Using two titanium atoms on a MgO/Ag(100) substrate as a model, we construct a two-qubit system whose dynamics are coherently manipulated through tailored microwave pulse sequences. We generate Bell states by implementing a Hadamard gate followed by a controlled-NOT gate, and evaluate its fidelity and concurrence using the quantum-master equation-based code TimeESR. Our results demonstrate that ESR-STM can create entangled states with significant fidelity. This study paves the way for the realization of atom-based quantum circuits and highlights ESR-STM as a powerful tool for probing and engineering entangled states on surfaces.