Nuclear magnetism and electron order in interacting one-dimensional conductors
Bernd Braunecker, Pascal Simon, Daniel Loss
备注：
30 pages, 10 figures; Sec. II contains a 2+ pages summary giving a complete overview to the main conditions and results; v3: updated references, typos corrected
The interaction between localized magnetic moments and the electrons of a one-dimensional conductor can lead to an ordered phase in which the magnetic moments and the electrons are tightly bound to each other. We show here that this occurs when a lattice of nuclear spins is embedded in a Luttinger liquid. Experimentally available examples of such a system are single wall carbon nanotubes grown entirely from 13C and GaAs-based quantum wires. In these systems the hyperfine interaction between the nuclear spin and the conduction electron spin is very weak, yet it triggers a strong feedback reaction that results in an ordered phase consisting of a nuclear helimagnet that is inseparably bound to an electronic density wave combining charge and spin degrees of freedom. This effect can be interpreted as a strong renormalization of the nuclear Overhauser field and is a unique signature of Luttinger liquid physics. Through the feedback the order persists up into the millikelvin range. A particular signature is the reduction of the electric conductance by the universal factor 2.
We discuss the orbital magnetism and the Hall effect in the weak magnetic field in two dimensional Dirac fermion systems with energy gap. This model is related to the graphene sheet, organic conductors, and $d$-density wave superconductors. We found the strong diamagnetism and finite Hall conductivity even in gapped systems. We also discuss the relation between the weak-magnetic field formalism and the Landau quantization with the Euler-Maclaurin expansion.
Single wall carbon nanotubes grown entirely from 13-C form an ideal system to study the effect of electron interaction on nuclear magnetism in one dimension. If the electrons are in the metallic, Luttinger liquid regime, we show that even a very weak hyperfine coupling to the 13-C nuclear spins has a striking effect: The system is driven into an ordered phase, which combines electron and nuclear degrees of freedom, and which persists up into the millikelvin range. In this phase the conductance is reduced by a universal factor of 2, allowing for detection by standard transport experiments.
We show how the orbital magnetization of an interacting disordered diffusive electron gas can be simply related to the magnetization of the non-interacting system having the same geometry. This result is applied to the persistent current of a mesoscopic ring and to the relation between Landau diamagnetism and the interaction correction to the magnetization of diffusive systems. The field dependence of this interaction contribution can be deduced directly from the de Haas-van Alphen oscillations of the free electron gas. Known results for the free orbital magnetism of finite systems can be used…
Electrostatic control of the magnetization of a normal mesoscopic conductor is analyzed in a hybrid superconductor-normal-superconductor system. This effect stems from the interplay between the non-equilibrium condition in the normal region and the Zeeman splitting of the quasiparticle density of states of the superconductor subjected to a static in-plane magnetic field. Unexpected spin-dependent effects such as magnetization suppression, diamagnetic-like response of the susceptibility as well as spin-polarized current generation are the most remarkable features presented. The impact of scatte…
We re-examine the wave function of two-dimensional massless Dirac electron in alpha-(BEDT-TTF)2I3 consisting of four molecules A, A', B and C in a unit cell, using a tight-binding model. We find zerolines in the Brillouin zone, on which the component of the wave function becomes zero for B or C sites. The zerolines, which are bounded by two Dirac points at k0 and pass through the M- or Y-points, result in a fact that the density of states of the B site exhibits no the Van Hove singularity near the energy of the Dirac points. By taking account of the on-site Coulomb interaction within the rando…
We study a one-dimensional (1D) interacting electronic liquid coupled to a 1D array of classical magnetic moments and to a superconductor. We show that at low energy and temperature the magnetic moments and the electrons become strongly entangled and that a magnetic spiral structure emerges without any adjustable parameters. For strong enough coupling between the two, the 1D electronic liquid is driven into a topological superconducting phase supporting Majorana fermions without any fine-tuning of external parameters. Our analysis applies at low enough temperature to a quantum wire in proximit…
The control of the magnetism of ultra-thin ferromagnetic layers using an electric field rather than a current, if large enough, would lead to many technologically important applications. To date, while it is usually assumed the changes in the magnetic anisotropy, leading to such a control, arises from surface charge doping of the magnetic layer, a number of key experiments cannot be understood within such a scenario. Much studied is the fact that, for non-magnetic metals or semi-conductors, a large surface electric field gives rise to a Rashba spin-orbit coupling which leads to a spin-splittin…
In this thesis we study electron transport through magnetic nanocontacts and nanowires with ab initio quantum transport calculations. The aim is to gain a thorough understanding of the interplay between electrical conduction and magnetism in atomic-size conductors and how it is affected by different aspects as e.g. the atomic structure and the chemical composition of the conductor. To this end our ab initio quantum transport program ALACANT which combines the non-equilibrium Green's function formalism (NEGF) with density functional theory (DFT) calculations has been extended to describe spin-p…
The hyperfine interaction between the electron spin and the nuclear spins is one of the main sources of decoherence for spin qubits when the nuclear spins are disordered. An ordering of the latter largely suppresses this source of decoherence. Here we show that such an ordering can occur through a thermodynamic phase transition in two-dimensional (2D) Kondo-lattice type systems. We specifically focus on nuclear spins embedded in a 2D electron gas. The nuclear spins interact with each other through the RKKY interaction, which is carried by the electron gas. We show that a nuclear magnetic order…
We demonstrate a new method for electrical manipulation of nuclear spins utilizing dynamic nuclear polarization induced by quantum Hall effect breakdown. Nuclear spins are polarized and detected through the hyperfine interaction between a nuclear spin system and a two-dimensional electron system located at an interface of GaAs/AlGaAs single heterostructure. Coherent oscillations between the nuclear-spin quantum states are observed by measuring the longitudinal voltage of the conductor.
We have developed a method for electrical polarization of nuclear spins in quantum Hall systems. In a breakdown regime of odd-integer quantum Hall effect (QHE), excitation of electrons to the upper Landau subband with opposite spin polarity dynamically polarizes nuclear spins through the hyperfine interaction. The polarized nuclear spins in turn accelerate the QHE breakdown, leading to hysteretic voltage-current characteristics of the quantum Hall conductor.
We investigate the magnetic behavior of nuclear spins embedded in a 2D interacting electron gas using a Kondo lattice model description. We derive an effective magnetic Hamiltonian for the nuclear spins which is of the RKKY type and where the interactions between the nuclear spins are strongly modified by the electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the (anomalous) behavior of the 2D static electron spin susceptibility, and thus provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D elect…
Using a conventional Hall-bar geometry with a micro-metal strip on top of the surface, we demonstrate an electrical coherent control of nuclear spins in an AlGaAs/GaAs semiconductor heterostructure. A breakdown of integer quantum Hall (QH) effect is utilized to dynamically polarize nuclear spins. By applying a pulse rf magnetic field with the metal strip, the quantum state of the nuclear spins shows Rabi oscillations, which is detected by measuring longitudinal voltage of the QH conductor.
The spin degree of freedom in solids offers opportunities beyond charge-based electronics and is actively investigated for both spintronics and quantum computation. However, the interplay of these spins with their native environment can give rise to detrimental effects such as spin relaxation and decoherence. Here, we use an all-electrical, lateral GaAs spin valve to manipulate and investigate the inherent nuclear spin system. Hanle satellites are used to determine the nuclear spin relaxation rates for the previously unexplored temperature range down to 100 mK, giving T1 times as long as 3 hou…
We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp$^3$ covalent functionalizations. We describe graphene with the single orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. In order to circumvent artefacts related to periodic unit cells, we use either huge simulation cells of up to $8\times10^5$ sites, or an embedding scheme that allows the modelling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the a…
Single molecule magnets distinguish themselves in the field of quantum magnetism through the ability to combine fundamental research with promising applications, the evolution of quantum spintronics in the last decade exemplifying the potential held by molecular based quantum devices. Notably, the read-out and manipulation of the embedded nuclear spin states was used in proof of principle studies of quantum computation at the single molecule level. In this paper we study the relaxation dynamics of the $^{159}$Tb nuclear spins in a diluted molecular crystal by using recently acquired understand…
Nuclear magnetism in n-doped semiconductors with positive hyperfine constant is revisited. Two kinds of nuclear magnetic ordering can be induced by resident electrons in a deeply cooled nuclear spin system. At positive nuclear spin temperature below a critical value, randomly oriented nuclear spin polarons similar to that predicted by I. Merkulov [I. Merkulov, Physics of the Solid State 40, 930 (1998)] should emerge. These polarons are oriented randomly and within each polaron nuclear and electron spins are aligned antiferromagnetically. At negative nuclear spin temperature below a critical va…
We study the electron dynamics in magnetic conductors with frustrated interactions dominated by isotropic exchange. We present a transport theory for itinerant carriers built upon the (single-band) doped Hubbard model and the slave-boson formalism, which incorporates the spin-exchange with the magnetically frustrated background into the representation of electron operators in a clear and controllable way. We also formulate hydrodynamic equations for the itinerant charge and spin degrees of freedom, whose currents contain new contributions that depend on the spatiotemporal variations of the ord…
We present transport measurements of cleaved edge overgrowth GaAs quantum wires. The conductance of the first mode reaches 2 e^2/h at high temperatures T > 10 K, as expected. As T is lowered, the conductance is gradually reduced to 1 e^2/h, becoming T-independent at T < 0.1 K, while the device cools far below 0.1 K. This behavior is seen in several wires, is independent of density, and not altered by moderate magnetic fields B. The conductance reduction by a factor of two suggests lifting of the electron spin degeneracy in absence of B. Our results are consistent with theoretical predictions f…
We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid ground state exists such an interaction could leave a fingerprint by ordering underlying localized moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. As a working example we investigate the two-dimensional spin-1/2 kagome antiferromagnet (KAFM), although the treatment remains gen…
Dynamical multiferroicity features entangled dynamic orders: fluctuating electric dipoles induce magnetization. Hence, the material with paraelectric fluctuations can develop magnetic signatures if dynamically driven. We identify the paraelectric KTaO$_3$ (KTO) as a prime candidate for the observation of the dynamical multiferroicity. We show that when a KTO sample is exposed to a circularly polarized laser pulse, the dynamically induced ionic magnetic moments are of the order of 5\% of the nuclear magneton per unit cell. We determine the phonon spectrum using ab initio methods and identify T$…
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 in…
Nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy of bulk quantum materials have provided insight into phenomena such as quantum phase criticality, magnetism, and superconductivity. With the emergence of nanoscale 2-D materials with magnetic phenomena, inductively-detected NMR and NQR spectroscopy are not sensitive enough to detect the smaller number of spins in nanomaterials. The nitrogen-vacancy (NV) center in diamond has shown promise in bringing the analytic power of NMR and NQR spectroscopy to the nanoscale. However, due to depth-dependent formation effi…
