Hanle Effect in Transport through Quantum Dots Coupled to Ferromagnetic Leads

We suggest a series of transport experiments on spin precession in quantum dots coupled to one or two ferromagnetic leads. Dot spin states are created by spin injection and analyzed via the linear conductance through the dot, while an applied magnetic field gives rise to the Hanle effect. Such a Hanle experiment can be used to determine the spin lifetime in the quantum dot, to measure the spin injection efficiency into the dot, as well as proving the existence of intrinsic spin precession which is driven by the Coulomb interaction.Comment: 7 pages, 4 figures, minor changes, added reference

Zero-bias anomaly in cotunneling transport through quantum-dot spin valves

We predict a new zero-bias anomaly in the differential conductance through a quantum dot coupled to two ferromagnetic leads with antiparallel magnetization. The anomaly differs in origin and properties from other anomalies in transport through quantum dots, such as the Kondo effect. It occurs in Coulomb-blockade valleys with an unpaired dot electron. It is a consequence of the interplay of single- and double-barrier cotunneling processes and their effect on the spin accumulation in the dot. The anomaly becomes significantly modified when a magnetic field is applied.Comment: 4 pages, 3 figure

Context and Compliance: A Comparison of State Supreme Courts and the Circuits

A host of scholars have argued that decision making in lower courts is at least partially determined by decision making in the U.S. Supreme Court. In other words, Supreme Court jurisprudence in a given area influences the way that the lower courts decide similar cases. This may seem like an unremarkable assertion given the principle of stare decisis and the expectation that lower courts are bound by decisions made by higher courts. Nonetheless, there are intriguing evidentiary omissions with regard to what we know about compliance with Supreme Court precedent. In particular, despite the voluminous expenditures of scholarly time and attention, we do not know how the High Court’s influence on the federal circuit courts compares with its influence on the state courts of last resort. We might well assume that the Supreme Court has far greater impact on the U.S. Courts of Appeals since those courts are more closely constrained to follow Supreme Court precedent by virtue of their position in the federal judicial system. In contrast, state courts of last resort are not direct members of the federal judicial system and are therefore more divorced from Supreme Court influence. Further, while we know that the Supreme Court hears very few cases from the federal courts of appeals, it hears an even smaller percentage of cases most recently decided by the state supreme courts. It seems, therefore, that the motivation to abide by Supreme Court rulings is dramatically reduced in the state courts and, accordingly, that a reasonable expectation is that Supreme Court precedent will fare worse in structuring decision making on state courts in comparison to decisions on the federal circuit courts. Contrary to these expectations, however, Martinek found that state court decisions actually do comport closely with Supreme Court policy in the area of search and seizure. In fact, Martinek found that the state supreme courts decide their cases in greater accord with High Court prescriptions than do the federal circuit courts. Benesh and Martinek’s findings are also suggestive in the area of confession, the area of law we consider in this Article. They found that state high courts are influenced by Supreme Court policy, even after controlling for the influence state elites (who are instrumental in staffing the bench) have on these courts. They characterize this influence as a legal one, rather than one driven by a fear of reversal, because only those facts the Court deemed relevant to the decision whether to admit a given confession were significant, while the ideological predisposition of the Supreme Court, which a lower court looking to avoid reversal would consider, was not. Motivated by these somewhat counterintuitive findings, we suggest an additional comparative analysis of Supreme Court impact on state and lower federal courts. Here, we undertake a systematic comparison of decision making in state supreme courts and the U.S. courts of appeals in the area of criminal confessions. Prior work has demonstrated that the Supreme Court does indeed influence the federal courts of appeals in this area of law.11 We provide additional evidence that all lower courts are constrained and that the influence of the Supreme Court is seen throughout the lower courts, be they state or federal courts, and without regard to the fact that the High Court appears to do little to induce that compliance. Further, an increasing number of decisions emanating from both state and federal lower courts are final. If one type of court—state high court or federal intermediate appellate court—more closely adheres to Supreme Court precedent than another, there are important ramifications for due process. Certainly, it is unremarkable to note that there are regional differences across the country—the federal nature of American government is both a product of and a reflection of this fact. And it is also unremarkable to observe that these differences most likely manifest themselves in the policy making of various branches and levels of government. But the Supreme Court is charged with interpreting the Constitution for the entire nation, and its interpretation of the rights afforded to the accused in terms of representation and self-incrimination, which the Court has confirmed are constitutionally based, must be effectuated in all criminal systems, not just in the one for which it is naturally the apex (i.e., the federal system). If Supreme Court decisions did not matter to the state supreme courts, there would be myriad cases decided in the legal systems of this country every day that may be inconsistent with (or perhaps downright abhorrent to) Supreme Court policy. Because the High Court is the final arbiter of the Constitution, surely we expect some attention to be paid to it by the state courts. Just how much attention, and how that attention compares with the attention paid by the U.S. courts of appeals, is the question of interest in this Article

The Two-impurity Anderson Model Revisited: Competition between Kondo Effect and Reservoir-mediated Superexchange in Double Quantum Dots

We study a series-coupled double quantum dot in the Kondo regime modeled by the two-impurity Anderson model and find a new conduction-band mediated superexchange interaction that competes with Kondo physics in the strong Coulomb interaction limit. Our numerical renormalization group results, complemented with the higher-order Rayleigh-Schr\"odinger perturbation theory, show that the novel exchange mechanism leads to clear experimental consequences that can be checked in transport measurements through double quantum dots

Frequency-Dependent Current Noise through Quantum-Dot Spin Valves

We study frequency-dependent current noise through a single-level quantum dot connected to ferromagnetic leads with non-collinear magnetization. We propose to use the frequency-dependent Fano factor as a tool to detect single-spin dynamics in the quantum dot. Spin precession due to an external magnetic and/or a many-body exchange field affects the Fano factor of the system in two ways. First, the tendency towards spin-selective bunching of the transmitted electrons is suppressed, which gives rise to a reduction of the low-frequency noise. Second, the noise spectrum displays a resonance at the Larmor frequency, whose lineshape depends on the relative angle of the leads' magnetizations.Comment: 12 pages, 15 figure

Kondo quantum dot coupled to ferromagnetic leads: Numerical renormalization group study

We systematically study the influence of ferromagnetic leads on the Kondo resonance in a quantum dot tuned to the local moment regime. We employ Wilson's numerical renormalization group method, extended to handle leads with a spin asymmetric density of states, to identify the effects of (i) a finite spin polarization in the leads (at the Fermi-surface), (ii) a Stoner splitting in the bands (governed by the band edges) and (iii) an arbitrary shape of the leads density of states. For a generic lead density of states the quantum dot favors being occupied by a particular spin-species due to exchange interaction with ferromagnetic leads leading to a suppression and splitting of the Kondo resonance. The application of a magnetic field can compensate this asymmetry restoring the Kondo effect. We study both the gate-voltage dependence (for a fixed band structure in the leads) and the spin polarization dependence (for fixed gate voltage) of this compensation field for various types of bands. Interestingly, we find that the full recovery of the Kondo resonance of a quantum dot in presence of leads with an energy dependent density of states is not only possible by an appropriately tuned external magnetic field but also via an appropriately tuned gate voltage. For flat bands simple formulas for the splitting of the local level as a function of the spin polarization and gate voltage are given.Comment: 18 pages, 18 figures, accepted for publication in PR

Electric-field controlled spin reversal in a quantum dot with ferromagnetic contacts

Manipulation of the spin-states of a quantum dot by purely electrical means is a highly desirable property of fundamental importance for the development of spintronic devices such as spin-filters, spin-transistors and single-spin memory as well as for solid-state qubits. An electrically gated quantum dot in the Coulomb blockade regime can be tuned to hold a single unpaired spin-1/2, which is routinely spin-polarized by an applied magnetic field. Using ferromagnetic electrodes, however, the properties of the quantum dot become directly spin-dependent and it has been demonstrated that the ferromagnetic electrodes induce a local exchange-field which polarizes the localized spin in the absence of any external fields. Here we report on the experimental realization of this tunneling-induced spin-splitting in a carbon nanotube quantum dot coupled to ferromagnetic nickel-electrodes. We study the intermediate coupling regime in which single-electron states remain well defined, but with sufficiently good tunnel-contacts to give rise to a sizable exchange-field. Since charge transport in this regime is dominated by the Kondo-effect, we can utilize this sharp many-body resonance to read off the local spin-polarization from the measured bias-spectroscopy. We show that the exchange-field can be compensated by an external magnetic field, thus restoring a zero-bias Kondo-resonance, and we demonstrate that the exchange-field itself, and hence the local spin-polarization, can be tuned and reversed merely by tuning the gate-voltage. This demonstrates a very direct electrical control over the spin-state of a quantum dot which, in contrast to an applied magnetic field, allows for rapid spin-reversal with a very localized addressing.Comment: 19 pages, 11 figure