General scheme for stable single and multiatom nanomagnets according to symmetry selection rules

At low temperature, information can be stored in the orientation of the localized magnetic moment of an adatom. However, scattering of electrons and phonons with the nanomagnet leads its state to have incoherent classical dynamics and might cause fast loss of the encoded information. Recently, it has been understood that such scattering obeys certain selection rules due to the symmetries of the system. By analyzing the point-group symmetry of the surface, the time-reversal symmetry and the magnitude of the adatom effective spin, we identify which nanomagnets configurations are to be avoided and which are promising to encode a stable bit. A new tool of investigation is introduced and exploited: the quasi-spin quantum number. By means of this tool, our results are easily generalized to a broad class of bipartite cluster configurations where adatoms are coupled through Heisenberg-like interactions. Finally, to make contact with the experiments, numerical simulations have been performed to show how such stable configurations respond to typical scanning tunneling microscopy measurements.Comment: 15 pages, 7 figures. Published versio

Effect of chiral symmetry on chaotic scattering from Majorana zero modes

In many of the experimental systems that may host Majorana zero modes, a so-called chiral symmetry exists that protects overlapping zero modes from splitting up. This symmetry is operative in a superconducting nanowire that is narrower than the spin-orbit scattering length, and at the Dirac point of a superconductor/topological insulator heterostructure. Here we show that chiral symmetry strongly modifies the dynamical and spectral properties of a chaotic scatterer, even if it binds only a single zero mode. These properties are quantified by the Wigner-Smith time-delay matrix $Q=-i\hbar S^\dagger dS/dE$, the Hermitian energy derivative of the scattering matrix, related to the density of states by $\rho=(2\pi\hbar)^{-1}\,{\rm Tr}\,Q$. We compute the probability distribution of $Q$ and $\rho$, dependent on the number $\nu$ of Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral symmetry is essential for a significant $\nu$-dependence.Comment: 5 pages, 3 figures + appendix (3 pages, 1 figure

Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard

We calculate the joint distribution $P(S,Q)$ of the scattering matrix $S$ and time-delay matrix $Q=-i\hbar S^\dagger dS/dE$ of a chaotic quantum dot coupled by point contacts to metal electrodes. While $S$ and $Q$ are statistically independent for ballistic coupling, they become correlated for tunnel coupling. We relate the ensemble averages of $Q$ and $S$ and thereby obtain the average density of states at the Fermi level. We apply this to a calculation of the effect of a tunnel barrier on the Majorana resonance in a topological superconductor. We find that the presence of a Majorana bound state is hidden in the density of states and in the thermal conductance if even a single scattering channel has unit tunnel probability. The electrical conductance remains sensitive to the appearance of a Majorana bound state, and we calculate the variation of the average conductance through a topological phase transition.Comment: Contribution for the special issue of Physica E in memory of Markus B\"{u}ttiker. 13 pages, 7 figure

Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard

We derive the statistics of the time-delay matrix (energy derivative of the scattering matrix) in an ensemble of superconducting quantum dots with chaotic scattering (Andreev billiards), coupled ballistically to $M$ conducting modes (electron-hole modes in a normal metal or Majorana edge modes in a superconductor). As a first application we calculate the density of states $\rho_0$ at the Fermi level. The ensemble average $\langle\rho_0\rangle=\delta_0^{-1}M[\max(0,M+2\alpha/\beta)]^{-1}$ deviates from the bulk value $1/\delta_0$ by an amount depending on the Altland-Zirnbauer symmetry indices $\alpha,\beta$. The divergent average for $M=1,2$ in symmetry class D ($\alpha=-1$, $\beta=1$) originates from the mid-gap spectral peak of a closed quantum dot, but now no longer depends on the presence or absence of a Majorana zero-mode. As a second application we calculate the probability distribution of the thermopower, contrasting the difference for paired and unpaired Majorana edge modes.Comment: 13 pages, 6 figure

X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot

The quasi-bound states of a superconducting quantum dot that is weakly coupled to a normal metal appear as resonances in the Andreev reflection probability, measured via the differential conductance. We study the evolution of these Andreev resonances when an external parameter (such as magnetic field or gate voltage) is varied, using a random-matrix model for the $N\times N$ scattering matrix. We contrast the two ensembles with broken time-reversal symmetry, in the presence or absence of spin-rotation symmetry (class C or D). The poles of the scattering matrix in the complex plane, encoding the center and width of the resonance, are repelled from the imaginary axis in class C. In class D, in contrast, a number $\propto\sqrt{N}$ of the poles has zero real part. The corresponding Andreev resonances are pinned to the middle of the gap and produce a zero-bias conductance peak that does not split over a range of parameter values (Y-shaped profile), unlike the usual conductance peaks that merge and then immediately split (X-shaped profile).Comment: Contribution for the JETP special issue in honor of A.F. Andreev's 75th birthday. 9 pages, 8 figure

General scheme for stable single and multiatom nanomagnets according to symmetry selection rules

Article / Letter to editorLeids Instituut Onderzoek Natuurkund

General scheme for stable single and multiatom nanomagnets according to symmetry selection rules

Article / Letter to editorLeids Instituut Onderzoek Natuurkund

On the random-matrix theory of Majorana fermions in topological superconductors

The thesis mainly contributes to the characterization of Majorana fermions as they appear in the Condensed Matter context. Large attention is devoted to discuss signatures in the density of states and transport observables of unpaired Majorana zero modes confined in chaotic and superconducting billiards. The final chapter concerns magnetic adatoms, promising small logic units future computer technologies. In particular, an analysis on the relation between the symmetries of isolated nanomagnets and their magnetic stability is performed.  Theoretical Physic

Increased cortical excitability after selective REM sleep deprivation in healthy humans: a transcranial magnetic stimulation study

REM sleep has antiepileptogenic properties whereas, its loss is known to have a proconvulsive role. However, the mechanisms underlying the proepileptogenic effects of REM sleep deprivation are yet not fully understood. The aim of our study was to evaluate the effects of selective REM sleep deprivation (SRD) on cortical excitability in healthy subjects by means of transcranial magnetic stimulation (TMS)

Dairy food structures influence the rates of nutrient digestion through different in vitro gastric behaviour

The purpose of this study was to investigate in vitro the extent to which specific food structures alter gastric behaviour and could therefore impact on nutrient delivery and digestion in the small intestine. Results obtained from a specifically developed gastric digestion model, were compared to results from a previous human study on the same foods. The semi-dynamic model could simulate the main gastric dynamics including gradual acidification, lipolysis, proteolysis and emptying. Two dairy-based foods with the same caloric content but different structure were studied. The semi-solid meal comprised a mixture of cheese and yogurt and the liquid meal was an oil in water emulsion stabilised by milk proteins. Our findings showed similar gastric behaviour to that seen previously in vivo. Gastric behaviour was affected by the initial structure with creaming and sedimentation observed in the case of liquid and semi-solid samples, respectively. Lipid and protein digestion profiles showed clear differences in the amount of nutrients reaching the simulated small intestine and, consequently, the likely bioaccessibility after digestion. The semi-solid sample generated higher nutrient released into the small intestine at an early stage of digestion whereas nutrient accessibility from liquid sample was delayed due to the formation of a cream layer in the gastric phase. This shows the strong effect of the matrix on gastric behaviour, proteolysis and lipolysis, which explains the differences in physiological responses seen previously with these systems in terms of fullness and satiety