Recent experiments have demonstrated the efficacy of chiral helically shaped molecules in polarizing the scattered electron spin, an effect termed as chiral-induced spin selectivity (CISS). Here we solve a simple tight-binding model for electron transport through a single helical molecule, with spin-orbit interactions on the bonds along the helix. Quantum interference is introduced via additional electron hopping between neighboring sites in the direction of the helix axis. When the helix is connected to two one-dimensional single-mode leads, time-reversal symmetry prevents spin polarization of the outgoing electrons. One possible way to retrieve such a polarization is to allow leakage of electrons from the helix to the environment, via additional outgoing leads. Technically, the leakage generates complex site self-energies, which break unitarity. As a result, the electron waves in the helix become evanescent, with different decay lengths for different spin polarizations, yielding a net spin polarization of the outgoing electrons, which increases with the length of the helix (as observed experimentally). A maximal polarization can be measured at a finite angle away from the helix axis.

Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.

The analytical solution for the low-temperature 1/f noise in the microwave dielectric constant of amorphous films at frequency ν 0 ∼ 5 GHz due to tunneling two-level systems (TLSs) is derived within the standard tunneling model including the weak dipolar or elastic TLS-TLS interactions. The 1/f frequency dependence is caused by TLS spectral diffusion characterized by the width growing logarithmically with time. Temperature and field dependencies are predicted for the noise spectral density in typical glasses with universal TLSs. The satisfactory interpretation of the recent experiment by Burnett et al. [J. Burnett et al., Nat. Commun. 5, 4119 (2014)] in Pt capped Nb superconducting resonator is attained by assuming a smaller density of TLSs compared to ordinary glasses, which is consistent with the very high internal quality factor in those samples.

Unlike the two-terminal device, in which the time-reversal invariant spin-orbit interaction alone cannot polarize the spins, such a polarization can be generated when electrons from one source reservoir flow into two (or more) separate drain reservoirs. We present analytical solutions for two examples. First, we demonstrate that the electrons transmitted through a "diamond" interferometer into two drains can be simultaneously fully spin-polarized along different tunable directions, even when the two arms of the interferometer are not identical. Second, we show that a single helical molecule attached to more than one drain can induce a significant spin polarization in electrons passing through it. The average polarization remains non-zero even when the electrons outgoing into separate leads are eventually mixed incoherently into one absorbing reservoir. This may explain recent experiments on spin selectivity of certain helical-chiral molecules.

In an earlier paper [Phys. Rev. B 84, 035323 (2011)], we proposed a spin filter which was based on a diamond-like interferometer, subject to both an Aharonov-Bohm flux and (Rashba and Dresselhaus) spin-orbit interactions. Here we show that the full polarization of the outgoing electron spins remains the same even when one allows leakage of electrons from the branches of the interferometer. Once the gate voltage on one of the branches is tuned to achieve an effective symmetry between them, this polarization can be controlled by the electric and/or magnetic fields which determine the spin-orbit interaction strength and the Aharonov-Bohm flux.

We study the dephasing of an individual high-frequency tunneling two-level system (TLS) due to its interaction with an ensemble of low-frequency thermal TLSs which are described by the standard tunneling model (STM). We show that the dephasing by the bath of TLSs explains both the dependence of the Ramsey dephasing rate on an externally applied strain as well as its order of magnitude, as observed in a recent experiment [J. Lisenfeld et al.]. However, the theory based on the STM predicts the Hahn-echo protocol to be much more efficient, yielding too low echo dephasing rates, as compared to the experiment. Also the strain dependence of the echo dephasing rate predicted by the STM does not agree with the measured quadratic dependence, which would fit to a high-frequency white noise environment. We suggest that few fast TLSs which are coupled much more strongly to the strain fields than the usual TLSs of the STM give rise to such a white noise. This explains the magnitude and strong fluctuations of the echo dephasing rate observed in the experiment.

We study the spin-dependent transport of spin-1/2 electrons through an interferometer made of two elongated quantum dots or quantum nanowires, which are subject to both an Aharonov-Bohm flux and (Rashba and Dresselhaus) spin-orbit interactions. Similar to the diamond interferometer proposed in our previous papers (Aharony et al 2011 Phys. Rev. B 84 035323; Matityahu et al 2013 Phys . Rev. B 87 205438), we show that the double-dot interferometer can serve as a perfect spin filter due to a spin interference effect. By appropriately tuning the external electric and magnetic fields which determine the Aharonov-Casher and Aharonov-Bohm phases, and with some relations between the various hopping amplitudes and site energies, the interferometer blocks electrons with a specific spin polarization, independent of their energy. The blocked polarization and the polarization of the outgoing electrons is 6

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