16,165 research outputs found
Fractional periodicity of persistent current in coupled quantum rings
We study the transmission properties of a few-site Hubbard rings with up to
second-nearest neighbor coupling embedded to a ring-shaped lead using exact
diagonalization. The approach captures all the correlation effects and enables
us to include interactions both in the ring and in the ring-shaped lead, and
study on an equal footing weak and strong coupling between the ring and the
lead as well as asymmetry. In the weakly coupled case, we find fractional
periodicity at all electron fillings at sufficiently high Hubbard U, similar to
isolated rings. For strongly coupled rings, on the contrary, fractional
periodicity is only observed at sufficiently large negative gate voltages and
high interaction strengths. This is explained by the formation of a bound
correlated state in the ring that is effectively weakly coupled to the lead
Signatures of topological phase transitions in mesoscopic superconducting rings
We investigate Josephson currents in mesoscopic rings with a weak link which
are in or near a topological superconducting phase. As a paradigmatic example,
we consider the Kitaev model of a spinless p-wave superconductor in one
dimension, emphasizing how this model emerges from more realistic settings
based on semiconductor nanowires. We show that the flux periodicity of the
Josephson current provides signatures of the topological phase transition and
the emergence of Majorana fermions situated on both sides of the weak link even
when fermion parity is not a good quantum number. In large rings, the Majorana
fermions hybridize only across the weak link. In this case, the Josephson
current is h/e periodic in the flux threading the loop when fermion parity is a
good quantum number but reverts to the more conventional h/2e periodicity in
the presence of fermion-parity changing relaxation processes. In mesoscopic
rings, the Majorana fermions also hybridize through their overlap in the
interior of the superconducting ring. We find that in the topological
superconducting phase, this gives rise to an h/e-periodic contribution even
when fermion parity is not conserved and that this contribution exhibits a peak
near the topological phase transition. This signature of the topological phase
transition is robust to the effects of disorder. As a byproduct, we find that
close to the topological phase transition, disorder drives the system deeper
into the topological phase. This is in stark contrast to the known behavior far
from the phase transition, where disorder tends to suppress the topological
phase.Comment: 14 pages, 9 figures, minor changes in the text, published versio
Temperature enhanced persistent currents and " periodicity"
We predict a non-monotonous temperature dependence of the persistent currents
in a ballistic ring coupled strongly to a stub in the grand canonical as well
as in the canonical case. We also show that such a non-monotonous temperature
dependence can naturally lead to a periodicity of the persistent
currents, where =h/e. There is a crossover temperature , below
which persistent currents increase in amplitude with temperature while they
decrease above this temperature. This is in contrast to persistent currents in
rings being monotonously affected by temperature. is parameter-dependent
but of the order of , where is the level spacing
of the isolated ring. For the grand-canonical case is half of that for
the canonical case.Comment: some typos correcte
Topological Hochschild homology and the Hasse-Weil zeta function
We consider the Tate cohomology of the circle group acting on the topological
Hochschild homology of schemes. We show that in the case of a scheme smooth and
proper over a finite field, this cohomology theory naturally gives rise to the
cohomological interpretation of the Hasse-Weil zeta function by regularized
determinants envisioned by Deninger. In this case, the periodicity of the zeta
function is reflected by the periodicity of said cohomology theory, whereas
neither is periodic in general
Crossover from hc/e to hc/2e current oscillations in rings of s-wave superconductors
We analyze the crossover from an hc/e-periodicity of the persistent current
in flux threaded clean metallic rings towards an hc/2e-flux periodicity of the
supercurrent upon entering the superconducting state. On the basis of a model
calculation for a one-dimensional ring we identify the underlying mechanism,
which balances the hc/e versus the hc/2e periodic components of the current
density. When the ring circumference exceeds the coherence length of the
superconductor, the flux dependence is strictly hc/2e periodic. Further, we
develop a multi-channel model which reduces the Bogoliubov - de Gennes
equations to a one-dimensional differential equation for the radial component
of the wave function. The discretization of this differential equation
introduces transverse channels, whose number scales with the thickness of the
ring. The periodicity crossover is analyzed close the critical temperature
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