We study the recently discovered even-odd effects in the normal state of single-electron devices manufactured at strontium titanium oxide/lanthanum aluminum oxide interfaces (STO/LAO). Within the framework of the number parity-projected formalism and a phenomenological fermion-boson model we find that, in sharp contrast to conventional superconductors, the crossover temperature $T^*$ for the onset of number parity effect is considerably larger than the superconducting transition temperature $T_c$ due to the existence of a pairing gap above $T_c$. Furthermore, the finite lifetime of the preformed pairs reduces by several orders of magnitude the effective number of states $N_{\rm eff}$ available for the unpaired quasiparticle in the odd parity state of the Coulomb blockaded STO/LAO island. Our findings are in qualitative agreement with the experimental results reported by Levy and coworkers for STO/LAO based single electron devices.
We show that odd-parity superconductivity occurs in multilayer Rashba systems without requiring spin-triplet Cooper pairs. A pairing interaction in the spin-singlet channel stabilizes the odd-parity pair-density-wave (PDW) state in the magnetic field parallel to the two-dimensional conducting plane. It is shown that the layer-dependent Rashba spin-orbit coupling and the orbital effect play essential roles for the PDW state in binary and tricolor heterostructures. We demonstrate that the odd-parity PDW state is a symmetry-protected topological superconducting state characterized by the one-dime…
We describe the transport properties of mesoscopic devices based on the two dimensional electron gas (2DEG) present at the LaAlO$_3$/SrTiO$_3$ interface. Bridges with lateral dimensions down to 500~nm were realized using electron beam lithography. Their detailed characterization shows that processing and confinement do not alter the transport parameters of the 2DEG. The devices exhibit superconducting behavior tunable by electric field effect. In the normal state, we measured universal conductance fluctuations, signature of phase-coherent transport in small structures. The achievement of relia…
Two dimensional electron gases based on SrTiO$_3$ are an intriguing platform for exploring mesoscopic superconductivity combined with spin-orbit coupling, offering electrostatic tunability from insulator to metal to superconductor within a single material. So far, however, quantum effects in SrTiO$_3$ nanostructures have been complicated by disorder. Here we introduce a facile approach to achieving high mobility and patterning gate-tunable structures in SrTiO$_3$, and use it to demonstrate ballistic constrictions with clean normal state conductance quantization. Conductance plateaus show two-f…
Using field effect devices with side gates, we modulate the 2 dimensional electron gas hosted at the LaAlO$_3$/SrTiO$_3$ interface to study the temperature and doping evolution of the magnetotransport. The analysis of the data reveals different transport regimes depending on the interplay between the different (elastic, inelastic, and spin-orbit) scattering times and their temperature dependencies. We find that the spin-orbit interaction strongly affects the low temperature transport in the normal state in a very large region of the phase diagram, extending beyond the superconducting dome.
The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4π$ (rather than a $2π$) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short- and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and f…
In this paper, we study the conductance and shot noise in transport through a multi-site system in a two terminal configuration. The dependence of the transport on the number of atoms in the atomic wire is investigated using a tight-binding Hamiltonian and the nonequilibrium Green's function method. In addition to reproducing the even-odd behavior in the transmission probability at the Fermi energy or the linear response conductance in the normal-atomic wire-normal metallic(NAN) junctions, we find the following: (i) The shot noise is larger in the even-numbered atomic wire than in the odd-numb…
We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. According to the parity formula proposed by Fu, Berg, and Sato, odd-parity pairing leads to conventional first-order topological superconductivity when a normal metal has an odd number of Fermi surfaces. Here, we derive generalized parity formulae for the topological invariants characterizing higher-order topology of centrosymmetric superconductors. Based on the form…
We study the superconductivity in small grains in the regime when the quantum level spacing $δ\varepsilon$ is comparable to the gap $Δ$. As $δ\varepsilon$ is increased, the system crosses over from superconducting to normal state. This crossover is studied by calculating the dependence of the ground state energy of a grain on the parity of the number of electrons. The states with odd numbers of particles carry an additional energy $Δ_P$, which shows non-monotonic dependence on $δ\varepsilon$. Our predictions can be tested experimentally by studying the parity-induced alternation of Coulomb blo…
We present a superconducting device showing a clear parity effect in the number of electrons, even when there is, on average, a single nonequilibrium quasiparticle present and the parity of the island switches due to quasiparticles tunneling in and out of the device at rates on the order of 100 Hz. We detect the switching by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kHz. We demonstrate that the pair breaking is caused by the backacti…
We investigate the transport properties through a finite dimer chain connected to two normal leads or one normal and one superconductor (SC) leads. The dimer chain is described by the Su-Schrieffer-Hegger model and can be tuned into a topologically nontrivial phase with a pair of zero-energy edge states (ZEESs). We find that if the dimer chain is of nontrivial topology, (1) it will show apparent but opposite odd-even parity of the number of sites, in comparison with the topologically trivial and plain chains, in the (Andreev) transmission probability at the Fermi energy (i.e. the conductance a…
We theoretically study the magnetism induced by the proximity effect in the normal metal of ferromagnetic Josephson junction composed of two $s$-wave superconductors separated by ferromagnetic metal/normal metal/ferromagnetic metal junction (${S}/{F}/{N}/{F}/{S}$ junction). We calculate the magnetization in the $N$ by solving the Eilenberger equation. We show that the magnetization arises in the ${N}$ when the product of anomalous Green's functions of the spin-triplet even-frequency odd-parity Cooper pair and spin-singlet odd-frequency odd-parity Cooper pair in the ${N}$ has a finite value. Th…
New physical effects emerge from an interplay between the electron parity number and persistent currents in superconducting nanorings. An odd electron, being added to the ring, produces a countercurrent which may substantially modify the ground state properties of the system. In superconducting nanorings with an embedded normal metal layer a novel ``$π/N$-junction'' state can occur for the odd number of electrons. Changing this number from even to odd yields spontaneous supercurrent in the ground state of such rings without any externally applied magnetic flux. Further peculiar features of the…
We study a general Majorana junction, where N helical nanowires are connected to a common s-wave superconductor proximity-inducing Majorana bound states in the wires. The normal part of each wire (j=1,...,N) acts as connected lead, where electrons can tunnel into the respective Majorana state γ_{A,j}. The Majorana states at the other end, γ_{B,j}, are coupled to each other by an arbitrary tunnel matrix. We examine the conditions for even-odd parity effects in the tunnel conductance for various junction topologies.
We study normal transport and the sub-gap spectrum of superconductor-normal-superconductor (SNS) junctions made of semiconducting nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on the role of confinement effects in long ballistic junctions. In the normal regime, scattering at the two contacts gives rise to two distinct features in conductance, Fabry-Perot resonances and Fano dips. The latter arise in the presence of a strong Zeeman field $B$ that removes a spin sector in the leads (\emph{helical} leads), but not in the central region. Conversely, a helical central r…
It is well known that the transport properties of single-electron transistors with a superconducting island and normal-conducting leads (NSN SET) may depend on whether or not there is a single quasiparticle on the island. This parity effect has pronounced consequences for the linear transport properties. Here we analyze the thermopower of NSN SET with and without parity effect, for entirely realistic values of device parameters. Besides a marked dependence of the thermopower on the superconducting gap $Δ$ we observe an enhancement in the parity regime which is accompanied by a dramatic increas…
