Half-integer Flux Quantum Research Articles

Magnetotransport signatures of three-dimensional topological insulator nanostructures

We study the magnetotransport properties of patterned 3D topological insulator nanostructures with several leads, such as kinks or Y-junctions, near the Dirac point with analytical as well as numerical techniques. The interplay of the nanostructure geometry, the external magnetic field and the spin-momentum locking of the topological surface states lead to a richer magnetoconductance phenomenology as compared to straight nanowires. Similar to straight wires, a quantized conductance with perfect transmission across the nanostructure can be realized across a kink when the input and output channels are pierced by a half-integer magnetic flux quantum. Unlike for straight wires, there is an additional requirement depending on the orientation of the external magnetic field. A right-angle kink shows a unique $\pi$-periodic magnetoconductance signature as a function of the in-plane angle of the magnetic field. For a Y-junction, the transmission can be perfectly steered to either of the two possible output legs by a proper alignment of the external magnetic field. These magnetotransport signatures offer new ways to explore topological surface states and could be relevant for quantum transport experiments on nanostructures which can be realized with existing fabrication methods.

Asymmetric nanowire SQUID: Linear current-phase relation, stochastic switching, and symmetries

We study nanodevices based on ultrathin superconducting nanowires connected in parallel to form nanowire SQUIDs. The function of the critical current versus magnetic field, $I_{C}(B)$, is multivalued, asymmetric and its maxima and minima are shifted from the usual integer and half integer flux quantum points. The nanowire interference device is qualitatively distinct from conventional SQUIDs because nanowires do not obey the same current-phase relationship (CPR) as Josephson junctions. We demonstrate that the results can be explained assuming that (i) the CPR is linear and (ii) that each wire is characterized by a sample-specific critical phase, which is usually much larger than $\pi/2$. Our proposed model offers accurate fits to $I_{C}(B)$. It explains the single-valuedness regions where only one vorticity (i.e., the order parameter winding number) is stable as well as regions where multiple vorticity values are allowed for the SQUIDs. We also observe and explain regions in which the standard deviation of the switching current is independent of the magnetic field. We develop a technique that allows a reliable detection of hidden phase-slips. Using this technique we find that our model correctly predicts the boundaries of vorticity regions, even at low currents where $I_C(B)$ is not directly measurable.

Magnetic field-induced helical mode and topological transitions in a topological insulator nanoribbon.

The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.

Magnetic-field-influenced nonequilibrium transport through a quantum ring with correlated electrons in a photon cavity

We investigate magnetic-field influenced time-dependent transport of Coulomb interacting electrons through a two-dimensional quantum ring in an electromagnetic cavity under non-equilibrium conditions described by a time-convolutionless non-Markovian master equation formalism. We take into account the full electromagnetic interaction of electrons and cavity photons without resorting to the rotating wave approximation or reduction to two levels. A bias voltage is applied to semi-infinite leads along the x-axis, which are connected to the quantum ring. The magnetic field is tunable to manipulate the time-dependent electron transport coupled to a photon field with either x- or y-polarization. We find that the lead-system-lead current is strongly suppressed by the y-polarized photon field at magnetic field with two flux quanta due to a degeneracy of the many-body energy spectrum of the mostly occupied states. Furthermore, the current can be significantly enhanced by the y-polarized field at magnetic field with half integer flux quanta.

Thermal fluctuations and flux-tunable barrier in proximity Josephson junctions

The effect of thermal fluctuations in Josephson junctions is usually analysed using the Ambegaokar-Halperin (AH) theory in the context of thermal activation. "Enhanced" fluctuations, demonstrated by broadening of current-voltage characteristics, have previously been found for proximity Josephson junctions. Here we report measurements of micron-scale normal metal loops contacted with thin superconducting electrodes, where the unconventional loop geometry enables tuning of the junction barrier with applied flux; for some geometries, the barrier can be effectively eliminated. Stronger fluctuations are observed when the flux threading the normal metal loop is near an odd half-integer flux quantum, and for devices with thinner superconducting electrodes. These findings suggest that the activation barrier, which is the Josephson coupling energy of the proximity junction, is different from that of conventional Josephson junctions. Simple one dimensional quasiclassical theory can predict the interference effect due to the loop structure, but the exact magnitude of the coupling energy cannot be computed without taking into account the details of the sample dimensions. In this way, the physics of this system is similar to the phase slipping process in thin superconducting wires. Besides shedding light on thermal fluctuations in proximity junctions, the findings here also demonstrate a new type of superconducting interference device with two normal branches sharing the same SN interface on both sides of the device, which has technical advantages for making symmetrical interference devices.

π-phase shift at the interface of two pnictide superconductors with antiphases-wave pairing

We examine the nature of Josephson junction between two identical Fe-pnictides with anti-phase s-wave pairing. pi-phase shift is found if the junction barrier is thick and the two Fe-pnictides are oriented in certain directions relative to the interface. Our theory provides a possible explanation for the observed half integer flux quantum transitions in a niobium/polycrystal NdFeAsO loop, and attributes the pi-phase shift to intergrain junctions of Fe-pnictides.

MetastableπJunction between ans±-Wave and ans-Wave Superconductor

We examine a contact between a superconductor whose order parameter changes sign across the Brillioun zone, and an ordinary, uniform-sign superconductor. Within a Ginzburg-Landau-type model, we find that if the barrier between the two superconductors is not too high, the frustration of the Josephson coupling between different portions of the Fermi surface across the contact can lead to surprising consequences. These include time-reversal symmetry breaking at the interface and unusual energy-phase relations with multiple local minima. We propose this mechanism as a possible explanation for the half-integer flux quantum transitions in composite niobium-iron pnictide superconducting loops, which were discovered in recent experiments [C.-T. Chen et al., Nature Phys. 6, 260 (2010).].

Half-Integer Flux Quantization in a Superconducting Loop with a Ferromagnetic π-Junction

Superconducting loops containing a π-junction are predicted to show a spontaneous magnetic moment in zero external magnetic field. In order to confirm this longstanding prediction experimentally, we performed magnetization measurements on individual mesoscopic superconducting niobium loops with a ferromagnetic (PdNi) π-junction. The loops are prepared on top of the active area of a micro Hall-sensor based on high mobility GaAs/AlGaAs heterostructures. We observe switching of the loop between different magnetization states at very low-magnetic fields, which is asymmetric for positive and negative sweep direction. This is evidence for a spontaneous current induced by the intrinsic phase shift of the π-junction. In addition, the presence of the spontaneous current at zero applied field is directly revealed by an increase of the magnetic moment with decreasing temperature, which results in a half integer flux quantization in the loop at low temperatures.

Spontaneous supercurrent induced by ferromagnetic pi junctions.

We present magnetization measurements of mesoscopic superconducting niobium loops containing a ferromagnetic (PdNi) pi junction. The loops are prepared on top of the active area of a micro-Hall sensor based on high mobility GaAs/AlGaAs heterostructures. We observe asymmetric switching of the loop between different magnetization states when reversing the sweep direction of the magnetic field. This provides evidence for a spontaneous current induced by the intrinsic phase shift of the pi junction. In addition, the presence of the spontaneous current near zero applied field is directly revealed by an increase of the magnetic moment with decreasing temperature, which results in half integer flux quantization in the loop at low temperatures.

Analysis of ground states of0−πlong Josephson junctions

We investigate analytically a long Josephson $0\ensuremath{-}\ensuremath{\pi}$ junction with several $0$ and $\ensuremath{\pi}$ facets which are comparable to the Josephson penetration length ${\ensuremath{\lambda}}_{J}.$ Such junctions can be fabricated exploiting (a) the d-wave order-parameter symmetry of cuprate superconductors; (b) the spacial oscillations of the order parameter in superconductor-insulator-ferromagnet-superconductor structures with different thicknesses of ferromagnetic layer to produce 0 or $\ensuremath{\pi}$ coupling; or (c) the structure of the corresponding sine-Gordon equations and substituting the phase $\ensuremath{\pi}$ discontinuities by the artificial current injectors. We investigate analytically the possible ground states in such a system and show that there is a critical facet length ${a}_{c},$ which separates the states with half-integer flux quanta (semifluxons) from the trivial ``flat phase state'' without magnetic flux. We analyze different branches of the bifurcation diagram, derive a system of transcendental equations which can be effectively solved to find the crossover distance ${a}_{c}$ (bifurcation point), and present the solutions for different number of facets and the edge facets length.

The phase diagram for ultrathin dual superconducting cylinders

For superconducting cylinders with sufficiently small sizes, normal states exist around half-integer flux quanta even at zero temperature. Coupling between coaxial superconducting cylinders could merge the phase boundaries of the outer cylinder between n 2=0 and n 2=1 states and the zero resistance fields for the outer cylinder can be enhanced from around 0.5 φ 0 to around 1.5 φ 0.

Superconducting fluctuations in the destructive regime of ultrathin, superconducting cylinders

We have carried out experiments on ultrathin superconducting cylinders, which revealed the existence of a destructive regime predicted to occur around half-integer flux quanta in doubly connected samples with diameters smaller than the zero-temperature superconducting coherence length. At half-integer flux quanta, the resistance showed a broad resistance drop as the temperature was lowered, followed by a temperature independent resistance at the lowest temperatures. We show that the temperature dependence of the conductance at half-integer flux quanta can be attributed to superconducting fluctuations.

Destruction of the Global Phase Coherence in Ultrathin, Doubly Connected Superconducting Cylinders

In doubly connected superconductors, such as hollow cylinders, the fluxoid is known to be quantized, allowing the superfluid velocity to be controlled by an applied magnetic flux and the sample size. The sample-size-induced increase in superfluid velocity has been predicted to lead to the destruction of superconductivity around half-integer flux quanta. We report transport measurements in ultrathin Al and Au0.7In0.3 cylinders verifying the presence of this destructive regime characterized by the loss of the global phase coherence and reveal a phase diagram featuring disconnected phase coherent regions, as opposed to the single region seen in larger superconducting cylinders studied previously.

D-Wave pairing symmetry in cuprate superconductors—fundamental implications and potential applications

A combination of conventional and phase-sensitive probes has firmly established the prevalence of d-wave pairing symmetry in the superconducting state of high- T c cuprates. In this paper we first describe the basic ideas behind our tricrystal phase-sensitive pairing symmetry experiments, which we use the half-integer flux quantum effect as a definitive signature for d-wave pairing symmetry. We then argue that d-wave symmetry is universal in the cuprates, including as an example our recent results on the electron-doped high- T c superconductors. We consider the implications of this universal d-wave pairing symmetry for understanding the origin of high-temperature superconductivity, and on potential applications. In particular, we discuss the possibility of using the half-integer flux quantum effect for all d-wave single qubits and qubit arrays.

M-theory on [formula omitted]: new facts from a careful analysis

We carefully reexamine the issues of solving the modified Bianchi identity, anomaly cancellations and flux quantization in the S 1/ Z 2 orbifold of M-theory using the boundary-free “upstairs” formalism, avoiding several misconceptions present in earlier literature. While the solution for the four-form G to the modified Bianchi identity appears to depend on an arbitrary parameter b, we show that requiring G to be globally well-defined, i.e., invariant under small and large gauge and local Lorentz transformations, fixes b=1. This value also is necessary for a consistent reduction to the heterotic string in the small-radius limit. Insisting on properly defining all fields on the circle, we find that there is a previously unnoticed additional contribution to the anomaly inflow from the eleven-dimensional topological term. Anomaly cancellation then requires a quadratic relation between b and the combination λ 6/κ 4 of the gauge and gravitational coupling constants λ and κ. This contrasts with previous beliefs that anomaly cancellation would give a cubic equation for b. We observe that our solution for G automatically satisfies integer or half-integer flux quantization for the appropriate cycles. We explicitly write out the anomaly cancelling terms of the heterotic string as inherited from the M-theory approach. They differ from the usual ones by the addition of a well-defined local counterterm. We also show how five-branes enter our analysis.

PURE d-WAVE PAIRING SYMMETRY IN HIGH- Tc CUPRATE SUPERCONDUCTORS

We have directly observed the half-integer flux quantum effect in controlled-orientation tricrystal Bi 2Sr 2CaCu 2O 8+ x (Bi2212) and tetracrystal Tl 2Ba 2CuO 6+ δ (Tl2201) by using a high-resolution scanning SQUID microscope. The results of these phase-sensitive pairing symmetry tests, along with the recent ARPES data for Bi2212 by Ding et al., have definitively established the existence of pure d x 2– y 2 -wave pairing symmetry in both Bi2212 and Tl2201.

Phase-sensitive tests of pairing symmetry in cuprate superconductors

A new class of experiments, based on the macroscopic effects of pair tunneling and flux quantization, has been developed for determining pairing symmetry. These tests make use of the half-integer flux quantum effect in superconducting loops containing controlled orientation Josephson junctions as a probe of the internal symmetry of Cooper pairs. The novel phase-sensitive techniques include SQUID interferometry, tricrystal magnetometry, and single Josephson junction modulation. When combined with indirect evidence from experiments such as ARPES, penetration depth, NMR, and Raman measurements, the results of these phase sensitive experiments unambiguously establish the singlet d x 2− y 2 pairing symmetry in high- T c hole doped cuprate superconductors such as YBa 2Cu 3O 7, GdBa 2Cu 3O 7, Bi 2Sr 2CaCu 2O 8, and Tl 2Ba 2CuO 6.

Determination of pairing symmetry using phase-sensitive tunneling in tricrystal cuprates

An unambiguous determination of the pairing symmetry in cuprate superconductors is important in order to understand the origin of high-temperature superconductivity. By making use of the effects of pair tunneling and flux quantization, we have designed and implemented several tricrystal experiments for phase-sensitive determination of the order parameter symmetry in high-Tc superconductors such as YBa2Cu3O7 Tl2Ba2CuO6, GdBa2Cu3O7, and Bi2Sr2CaCu2O8. By using a high-resolution scanning SQUID microscope, we have made the first direct observation of spontaneously generated half-flux quanta at the tricrystal point. The half-integer flux quantum effect in various specially designed tricrystal cuprate systems provides strong evidence for d-wave pairing in high-Tc cuprates. Our various tricrystal experiments have demonstrated that this effect can be used as a general probe of the microscopic phase of the pair wavefunction in unconventional superconductors.

Tricrystal tunneling evidence for d-wave pairing symmetry in cuprate superconductors.

Strong evidence for d-wave pairing symmetry in high-temperature superconductors such as YBa2Cu3O7 and Tl2Ba2CuO6+δ has been obtained by monitoring the presence or absence of the half-integer flux quantum effect in various controlled—orientation tricrystal superconducting systems. New results of a tricrystal tunneling experiment with Gd Ba2Cu3O7 will also be presented.

Current-phase relation in an intermediately coupled superconductor-superconductor junction.

The limiting configuration of the S-N-S\ensuremath{'} junction in which the N-layer thickness is of the order of the screening length in metals (\ensuremath{\approxeq}1--2 \AA{}) may serve as a model for a clean S-S\ensuremath{'} interface. This configuration supports one N-layer-attached gap state (manifold), with eigenenergy close to and less than the smaller superconducting gap. This gap state is interpreted as the excitation associated with breakage of interface-attached Cooper pairs, comprised of one electron from each side of the thin-N layer. The corresponding junction's current-phase (\ensuremath{\psi}) relation is calculated. The gap state is shown to contribute an appreciable ``sin(2\ensuremath{\psi})'' correction term to the ``sin(\ensuremath{\psi})'' Josephson term. The corresponding maximum-current magnetic-flux dependence of a two-junction configuration (SQUID) is predicted to have zeros shifted from their common loci at half-integer flux quanta.