Leakage and dephasing in 28^{28}Si-based exchange-only spin qubits

Exchange-only spin qubits hosted in $^{28}$Si-based triple quantum dots do not suffer from decoherence caused by randomly fluctuating nuclear-spin ensembles and can be relatively robust against electrical noise when operated at a sweet spot. Remaining sources of decoherence are qubit relaxation, leakage out of the qubit subspace, and dephasing due to residual effects of charge noise, the latter two of which are the focus of this work. We investigate spin-orbit-mediated leakage rates to the three-spin ground state accompanied by virtual (i) tunneling, (ii) orbital excitation, and (iii) valley excitation of an electron. We find different power-law dependencies on the applied magnetic field $B$ for the three mechanisms as well as for the two leakage rates, ranging from $\propto B^5$ to $\propto B^{11}$, and identify the sweet spot as a point of minimal leakage. We also revisit the role of electrical noise at the sweet spot, and show that it causes a decay of coherent qubit oscillations that follows a power law $\propto 1/t$ (as opposed to the more common exponential decay) and introduces a $\pi/2$ phase shift.Comment: 10 pages, three figures. Minor changes with respect to the previous version. The supplemental material is now included as appendice

Multi-level interference resonances in strongly-driven three-level systems

We study multi-photon resonances in a strongly-driven three-level quantum system, where one level is periodically swept through a pair of levels with constant energy separation $E$. Near the multi-photon resonance condition $n\hbar\omega = E$, where $n$ is an integer, we find qualitatively different behavior for $n$ even or odd. We explain this phenomenon in terms of families of interfering trajectories of the multi-level system. Remarkably, the behavior is insensitive to fluctuations of the energy of the driven level, and survives deep into the strong dephasing regime. The setup can be relevant for a variety of solid state and atomic or molecular systems. In particular, it provides a clear mechanism to explain recent puzzling experimental observations in strongly-driven double quantum dots.Comment: 4 pages, 3 figure

Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.Comment: 9 pages, 3 figures; submitted as invited contribution to a special issue in Physica E in memory of Markus Buettike

Spin-wave-induced correction to the conductivity of ferromagnets

We calculate the correction to the conductivity of a disordered ferromagnetic metal due to spin-wave-mediated electron--electron interactions. This correction is the generalization of the Altshuler-Aronov correction to spin-wave-mediated interactions. We derive a general expression for the conductivity correction to lowest order in the spin-wave-mediated interaction and for the limit that the exchange splitting $\Delta$ is much smaller than the Fermi energy. For a "clean" ferromagnet with $\Delta\tau_{\rm el}/\hbar \gg 1$, with $\tau_{\rm el}$ the mean time for impurity scattering, we find a correction $\delta \sigma \propto -T^{5/2}$ at temperatures $T$ above the spin wave gap. In the opposite, "dirty" limit, $\Delta\tau_{\rm el}/\hbar \ll 1$, the correction is a non-monotonous function of temperature.Comment: 9 pages, 6 figure

Conductance spectroscopy on Majorana wires and the inverse proximity effect

Recent experimental searches for signatures of Majorana-like excitations in proximitized semiconducting nanowires involve conductance spectroscopy, where the evidence sought after is a robust zero-bias peak (in longer wires) and its characteristic field-dependent splitting (in shorter wires). Although experimental results partially confirm the theoretical predictions, commonly observed discrepancies still include (i) a zero-bias peak that is significantly lower than the predicted value of $2e^2/h$ and (ii) the absence of the expected "Majorana oscillations" of the lowest-energy modes at higher magnetic fields. Here, we investigate how the inevitable presence of a normal drain lead connected to the hybrid wire can affect the conductance spectrum of the hybrid wire. We present numerical results using a one-band model for the proximitized nanowire, where the superconductor is considered to be in the diffusive regime, described by semi-classical Green functions. We show how the presence of the normal drain could (at least partially) account for the observed discrepancies, and we complement this with analytic results providing more insights in the underlying physics.Comment: 10 pages, 7 figure

Phase-tunable Majorana bound states in a topological N-SNS junction

We theoretically study the differential conductance of a one-dimensional normal-superconductor-normal-superconductor (N-SNS) junction with a phase bias applied between the two superconductors. We consider specifically a junction formed by a spin-orbit coupled semiconducting nanowire with regions of the nanowire having superconducting pairing induced by a bulk $s$-wave superconductor. When the nanowire is tuned into a topologically non-trivial phase by a Zeeman field, it hosts zero-energy Majorana modes at its ends as well as at the interface between the two superconductors. The phase-dependent splitting of the Majorana modes gives rise to features in the differential conductance that offer a clear distinction between the topologically trivial and non-trivial phases. We calculate the transport properties of the junction numerically and also present a simple analytical model that captures the main properties of the predicted tunneling spectroscopy.Comment: 11 pages, 7 figure

Spin-wave-induced corrections to the electronic density of states in metallic ferromagnets

We calculate the correction to the electronic density of states in a disordered ferromagnetic metal induced by spin-wave mediated interaction between the electrons. Our calculation is valid for the case that the exchange splitting in the ferromagnet is much smaller than the Fermi energy, but we make no assumption on the relative magnitude of the exchange splitting and the elastic electronic scattering time. In the "clean limit", where the exchange splitting is much larger than the electronic scattering rate, we find a correction with a T^{d/2} temperature dependence, where d is the effective dimensionality of the ferromagnet. In the opposite "dirty limit" the density-of-states correction is a non-monotonous function of energy and temperature.Comment: 8 pages, 4 figure

Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires

We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusion-rule testing protocol proposed recently [arXiv:1511.05153]. We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures

Interaction effects on proximity-induced superconductivity in semiconducting nanowires

We investigate the effect of electron-electron interactions on proximity-induced $s$-wave superconductivity in one-dimensional nanowires. We treat the interactions on a self-consistent mean-field level, and find an analytic expression for the effective pairing potential in the presence of interactions, valid for a weakly tunnel coupled wire. We show that for a set of two nanowires placed in parallel on a superconducting substrate, the interaction-induced reduction of the pairing energy could result in the effective interwire pairing potential exceeding the intrawire potential, which is one of the requirements for creating a time-reversal symmetric topological superconducting state in such a two-wire system.Comment: 7 pages, 1 figur