Quantum computation in solid-state systems

In the last few years, as superconducting devices reached tens and later hundred qubits on a single chip, quantum computing has become a reality, tackling problems that would be prohibitively time-consuming even with the most powerful classical supercomputers. These early quantum computers (QC) are called noisy intermediate-scale quantum computers, since environmental noise cannot be efficiently counteracted in such small qubit arrays. While certain algorithms can indeed leverage the potential of hundreds of imperfect qubits, the great promises of quantum computing require perfect qubits that can be realized only in qubit arrays of much larger scales, using quantum error correction (QEC). Spin qubits in semiconductors are the only platform to date that has the potential of reaching such scales, paving way for fault-tolerant quantum computing. Qubits hosted in quantum dots (QDs) have dimensions of few tens of nanometers, facilitating the integration of potentially millions of qubit on a single chip. Especially compelling candidates are spin qubits in silicon nanostructures. With decades of experience coming from the semiconductor industry, silicon is one of the most studied elements with the prosperity of uniquely advanced manufacturing techniques. Electron spin qubits in silicon have immensely matured in the last few years reaching single- and two-qubit gate fidelities matching the error thresholds of QEC algorithms. However, the weak intrinsic spin-orbit interaction (SOI) in the conduction band necessitates the use of micromagnets to aid the all-electical qubit control. This additional complication presents new challenges in device design and fabrication. Hole spin qubits in silicon and germanium QDs, on the other hand, benefit from strong direct Rashba SOI accelerating qubit control speeds to several hundreds of megahertz, without the need to integrate additional elements in the device. In this thesis, we start with an introduction and a brief overview of the field, in Chapter 1, where we discuss the fundamental physics of hole quantum dots and how they satisfy the stringent prerequisites of quantum computing. Furthermore, we take a glimpse at the various components of scalable architectures and the requirements on the qubit architecture posed by QEC codes. In the subsequent chapters we address the question how the enhanced anisotropy and SOI affect two-qubit gates in hole QDs. In particular, we discuss exchange anisotropy due to orbital effects of the magnetic field and crystalline anisotropy in Chapter 2. We also confirm the emergence of the zero-field splitting of triplet states in hole QDs numerically, and develop an analytical model linking the effect to the cubic Rashba SOI in Chapter 3. This work presents the first theoretical model to explain this recently observed effect in hole QDs. Afterwards, in collaboration with the Zumbühllab, we decipher the strong spin-orbit effects in an experiment on Ge/Si nanowire QDs, where we also identify the strong g factor renormalization caused by enhanced SOI (Chapter 4). Furthermore, we study the tunability of SOI in silicon FinFET devices in Chapter 5, identifying sweet spots where the qubit lifetime is greatly prolonged. Finally, we study the prospects of coupling distant spin qubits by a chiral magnon mode localized at the edge of a two-dimensional ferromagnet in Chapter 6

Tunable High-Field/ High-Frequency ESR and High-Field Magnetization on Single-Molecule Clusters

In this work, low dimensional iron group clusters have been studied by application of high magnetic fields. The magnetization has been probed with an MPMS as function of temperature and field. The combination with pulse field measurements up to 52\,T allowed determination of the magnetic exchange coupling parameters, and to probing the effective spin of the ground state. The main focus was on tunable high-field/high-frequency (tHF) ESR in static fields < 17 T and pulse field ESR up to 36 T. This magnetic resonance method has been used for the characterization of the local magnetic properties: The detailed analysis of the field dependence of dedicated spin states allowed to determine the magnetic anisotropy and g-factors. The results were analyzed in the framework of the appropriate effective spin Hamiltonians in terms of magnetization fits and ESR spectrum simulations

Tunable High-Field/ High-Frequency ESR and High-Field Magnetization on Single-Molecule Clusters

In this work, low dimensional iron group clusters have been studied by application of high magnetic fields. The magnetization has been probed with an MPMS as function of temperature and field. The combination with pulse field measurements up to 52\,T allowed determination of the magnetic exchange coupling parameters, and to probing the effective spin of the ground state. The main focus was on tunable high-field/high-frequency (tHF) ESR in static fields < 17 T and pulse field ESR up to 36 T. This magnetic resonance method has been used for the characterization of the local magnetic properties: The detailed analysis of the field dependence of dedicated spin states allowed to determine the magnetic anisotropy and g-factors. The results were analyzed in the framework of the appropriate effective spin Hamiltonians in terms of magnetization fits and ESR spectrum simulations

High-field Electron Spin Resonance study on Correlated Transition Metal Compounds and Metal-Organic Compounds

High-frequency as well as X-band electron spin resonance (ESR) spectroscopy, and static magnetization measurements of correlated electron systems and metal-organic spins systems are presented. ESR data of the honeycomb-lattice spin systems Na3Ni2SbO6 and Li3Ni2SbO6 reveal uniaxial and orthorhombic antiferromagnetic resonances (AFMR), respectively, in the ordered state. In both materials, AFMR gaps of 358 GHz and 200 GHz, respectively, are found. The bilayer Kagome lattice Ca10Cr7O28, which is a frustrated spin system, demonstrates g anisotropy (gb = 1.94, gc = 2.01) depending on the crystallographic axes on high-frequency ESR data. X-band ESR data show a similar temperature dependence of the linewidths for the different axes. The two Ni dimer compounds [Ni2L(dppba)]ClO4 and [Ni2L(dppba)AuPh]BPh4 (1) have a similar ligand except an Au atom attached to the phosphorus atom of (1). In both materials, ferromagnetic coupling and uniaxial anisotropy of about -12 GHz is found. The Au ligand however does not significantly affect the magnetic properties. Results presented for the mixed valence complex [Ni(III)Ni(II)(LDA)](BPh4)2 demonstrate a total spin S = 3/2 which implies ferromagnetic coupling between the Ni2+ ion (S = 1) and the low spin Ni3+ ion (S = 1/2). Again, there is an uniaxial anisotropy which amounts to -49 GHz. ESR measurements of (HNEt3)2Cu(II)[12-MCCu(II)N(Shi)-4] with Cu5-clusters organized in a metal-organic framework show typical powder spectra which are described by a S = 1/2 spin-Hamiltonian and gx = 2.03, gy = 2.04 and gz = 2.23. [Gd(III)2L(OAc)4]PF6 has a magnetic anisotropy which can be ascribed to dipolar coupling between the Gd ions

Solid-state NMR study of nitric oxide adsorption in carboxylate based MOFs

Solid-state NMR study of nitric oxide adsorption in MOFs. Amine functionalized Cu3btc2 MOFs shows chemisorption of NO as NONOates. NO also adsorbed in Cu open metal site(OMS). All of these information is characterized by 1H, 13C and 15N NMR studies. NO adsoprtion in Al based MOFs MIL-100(Al) is investigated to get details about direct detection of OMS site by 27Al NMR. First time detection of 15NO as dimer is acheived by 15N NMR studies.:Contents.............................................................................. v List of Figures...................................................................... vii Abbreviations............................................................................. ix 1 Motivation .............................................................................1 2 Introduction .............................................................................3 2.1 Nitric oxide (NO): A Potent Gasotransmitter . . . . . . . . . . . . . . . . . . 3 2.1.1 Biological action in human biology: . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Structure and chemistry of NO . . . . . . . . . . . . . . . . . . . . . . 4 2.2 NO storage in porous materials . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Physisorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Chemisorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Current NO storage materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Metal-organic frameworks (MOFs) . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.1 Cu3btc2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.2 MIL-100(Al) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Experimental techniques .............................................................................15 3.1 Nuclear spin interactions in solid-state NMR . . . . . . . . . . . . . . . . . . . 15 3.2 NMR Techniques and Pulse Sequences . . . . . . . . . . . . . . . . . . . . . . 19 3.3 NMR sample tube preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 Gas adsorption procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Overview and enclosed papers 29 References .............................................................................121 5 Contribution .............................................................................137Gas storage in solids is becoming more important as a technology, with applications ranging in fields such as energy, the environment, and more importantly in biology and medicine. Porous solid storage materials are also increasingly important to advancements in science, as seen through their use in emergent gas-delivery technologies that include storage of the signaling molecule, nitric oxide (NO). The deficiencies of NO biosynthesis have been interconnected to a number of diseases, such as cardiovascular dysfunction, thrombosis and cancer. To date, one of the promising NO delivery materials are the metal-organic frameworks (MOFs), a new class of porous materials, which can store significant quantities of NO and then deliver it to specific sites in the body. MOFs contain open metal sites (OMS) that can physisorbed NO. Furthermore, amine functionalized MOFs can store NO covalently as N,N -diazeniumdiolates (NONOate). The thesis at hand is a collection of the publications written and co-authored by the author. The following thesis will investigate NO adsorption of one of the most highly studied carboxylate-based MOFs, Cu3btc2, and its amine derivatives, and MIL-100(Al) [Materials Institute Lavoisier] by magic angle spinning (MAS) NMR. However, NMR observation of Cu3btc2 is quite difficult, because it behaves as a paramagnet at room temperature. This paramagnetic behavior originates from the presence of antiferromagnetically coupled Cu-Cu ions, which result in an S=1 electronic state at higher temperatures (above 90 K). In that case, a significant insight into the understanding of NO interaction and the changing of electronic properties of NO loaded Cu3btc2 and the formation of NONOate in Cu3(NH2btc)2, which is known as University of Hamburg materials (UHM-30), has been obtained by MAS NMR. In paper (A) the effect of NO adsorption on the Cu3btc2 and UHM-30 has been followed by adsorbing different amounts of NO/Cu via the gas phase. The relevant NMR parameters, e.g., chemical shift, hyperfine coupling and 1H T1 of NO loaded MOFs displayed the change of electron density at the Cu site because of NO adsorption as well as indirect suggestion of NONOate formation. Further studies are carried out on the secondary amine functionalized MOFs, Cu3(NHRbtc)2, as they opened up the greater potential for NONOate formation in the MOFs. The structural characterization of four different Cu3(NHRbtc)2 is carried out by MAS NMR in (B) which revealed better incorporation of the btc ligand compared to NHRbtc in MOFs. In (C) NO loaded UHM-37 is extensively investigated by MAS NMR in order to understand the sorption priority, e.g., chemisorption or physiosorption. The multinuclear approach together with the fact that the MOFs contain antiferromagnetically coupled Cu-Cu pairs and NO being paramagnetic shows significant effects on spectra that allow for the deduction of adsorption effects in these MOFs. In the amine-functionalized UHM-37, first chemisorption of NO takes place to form NONOates. When this reaction is completed, additional adsorption at the OMS takes place. This observation is also in accordance with observed 13C shift changes upon NO adsorption. With 15N-labeled NO, we were able to directly determine signals of NONOate formation in UHM-37. To the best of our knowledge, this is the first report on 15N NMR data of NONOates in porous systems. In (D), NO interaction of another type of carboxylate MOF, MIL-100(Al) is investigated by 1H, 13C and 27Al MAS NMR. 27Al NMR data show that half of all Al sites are free for gas adsorption and that additional Al(OH)3 is present inside the pores, which is well-documented by 27Al 1H HETCOR spectra. 1H T1 of NO loaded MIL-100(Al) decreases with NO loading representing uniform distribution of NO in the MOF. In addition, the MIL-100(Al) five-coordinated Al site intensity is decreasing with increasing NO loading, while six-coordinated site intensity is increasing and a maximum of 1 NO per Al trimer can be adsorbed. This indicates rather weak NO adsorption. The magnetic properties of NO make it quite interesting for NMR measurements. Therefore, isotopically leveled bulk 15NO is studied for the first time by NMR in (E). The manuscript is accepted for publication and is included in this thesis. 15N NMR spectra have been obtained in the liquid and the solid state. The dynamic equilibrium ranges between (NO)2 and NO is characterized in gas - liquid transition temperature of NO. The variation of 15N chemical shift, line width and 15N T1 of NO with temperature represents the fast dynamic equilibrium. SQUID measurements are carried out on the same sample for further confirmation of the NMR results.:Contents.............................................................................. v List of Figures...................................................................... vii Abbreviations............................................................................. ix 1 Motivation .............................................................................1 2 Introduction .............................................................................3 2.1 Nitric oxide (NO): A Potent Gasotransmitter . . . . . . . . . . . . . . . . . . 3 2.1.1 Biological action in human biology: . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Structure and chemistry of NO . . . . . . . . . . . . . . . . . . . . . . 4 2.2 NO storage in porous materials . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Physisorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Chemisorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Current NO storage materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Metal-organic frameworks (MOFs) . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.1 Cu3btc2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.2 MIL-100(Al) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Experimental techniques .............................................................................15 3.1 Nuclear spin interactions in solid-state NMR . . . . . . . . . . . . . . . . . . . 15 3.2 NMR Techniques and Pulse Sequences . . . . . . . . . . . . . . . . . . . . . . 19 3.3 NMR sample tube preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 Gas adsorption procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Overview and enclosed papers 29 References .............................................................................121 5 Contribution .............................................................................13

Optical control of molecular high spin states via spin-forbidden transitions

We show TDESR to measure the high frequency electron spin resonance spectra of the molecular nanomagnet Fe3CrSMe. We demonstrate the use of a mechanically-detected EPR setup with optical excitations and tunable frequency sources to induce magnetic resonance transitions which are detected using cantilever torque magnetometry. Furthermore we show how we combined TDESR with Photon excited Torque Magnetometry (PheToM) to excite and detect a spin forbidden transition (S=6 to S=7) in Fe3CrSMe. The results are compared to simulations and AC-SQUID results. The use of spin-forbidden transitions is particularly tempting, as it allows connecting otherwise separated Hilbert spaces. This enables to operate qubits in an excited state, without disrupting their ground state coherences. Such spin-forbidden manipulation scheme had been proposed nearly thirty years ago by the pioneer of molecular magnetism O. Kahn, but has remained unobserved due to the considerable experimental diffculties involved

Magnetostructural characterization of compounds based on the highly anisotropic Mn(III) and Re(IV) metal ions

El trabajo desarrollado en el marco de esta Tesis confeccionada como compendio de artículos se encuentra comprendido en el campo del Magnetismo Molecular y la Química de Coordinación. La investigación desarrollada se ha centrado en la caracterización estructural y estudio de propiedades magnéticas de sistemas basados en los iones metálicos Mn(III) y Re(IV). El primero es un ion 3d mientras que el último es un ion metálico 5d. Estos iones metálicos han sido seleccionados a cuenta de que, dados los altos valores de anisotropía y espín que presentan, pueden brindar resultados destacables desde el punto de vista del Magnetismo Molecular. Centrándonos en los complejos basados en Mn (III), se ha buscado ampliar el conocimiento, mejorar las propiedades y funcionalizar sistemas pertenecientes a la familia de los [Mn6]s. En este sentido, seis nuevos miembros de la familia de complejos [Mn6], basados en oximas como ligando principal, han sido sintetizados y caracterizados magnetoestructuralmente. Estos compuestos han sido reportados en tres publicaciones y muestran un comportamiento magnético consistente con el fenómeno de imán molecular (SMM por sus siglas en inglés). Además, dos de ellos han sido funcionalizados empleando para ello ligandos conteniendo el grupo funcional tioéster. Dicha funcionalización permitirá, en trabajos futuros, estudiar la integración de estos compuestos a dispositivos a escala nanométrica. En lo que respecta al trabajo realizado sobre compuestos basados en Re(IV), se han obtenido y reportado cuatro nuevas estructuras de sales de hexahalogenorenato(IV), para lo cual se han empleado cationes de diferente naturaleza. En dos de ellos se ha empleado un catión orgánico de interés bilógico y en los otros dos un catión paramagnético conteniendo Fe(II). Así, se han estudiado y llevado a cabo un estudio comparativo de las propiedades magnetoestructurales de dichos compuestos. Seguidamente, se ha explorado una nueva estrategia para la obtención isométricamente selectiva de nuevas especies mononucleares basadas en Re(IV). Como resultado de este trabajo se han reportado el estudio estructural y magnético de dos nuevas especies. Finalmente se ha reportado la estructura y el estudio de las propiedades magnéticas de dos nuevos complejos heteropolinucleares basados en Re(IV)-Zn(II) y Re(IV)-Cu(II), el primero presentando un comportamiento del tipo SMM y el segundo siendo una cadena ferrimagnética