We report on transport properties of Josephson junctions in hybrid superconducting topological insulator devices, which show two striking departures from the common Josephson junction behavior: a characteristic energy that scales inversely with the width of the junction, and a low characteristic magnetic field for suppressing supercurrent. To explain these effects, we propose a phenomenological model which expands on the existing theory for topological insulator Josephson junctions.The Majorana fermion, a charge-neutral particle that is its own antiparticle, was proposed theoretically almost 75 years ago [1]. Electronic excitations in certain condensed matter systems have recently been predicted to act as Majorana fermions [1]. One such system is a three-dimensional topological insulator (TI) where superconducting correlations between particles are introduced, producing a "topological superconductor" [2]. When two superconductors are connected by a TI, the TI "weak link" superconducts due to its proximity to the superconducting leads. This produces a Josephson junction (JJ) but with several important distinctions compared to a conventional JJ, where the weak link is typically an ordinary metal or insulator. Fu and Kane have predicted [2] a one-dimensional (1D) mode of Majorana fermions at the interface between a conventional superconductor and a superconducting topological surface state. Hence, JJs formed with a TI weak link are expected to have two 1D modes at the two superconductor-TI interfaces [arrows in Fig. 1(a)], which fuse to form a 1D wire of Majorana fermions [shown in purple in Fig. 1(a)] running along the width of the device [2]. The energy spectrum of these Majorana fermions is characterized by states within the superconducting gap, which cross at zero energy when the phase difference ϕ between the two superconducting leads is π.To probe this exotic state, recent experiments have investigated transport in TI JJs, finding good agreement with conventional JJ behavior [3][4][5][6][7]. Two characteristic properties are typically reported for JJs. The first is the product I C R N , where I C is the critical current and R N is the normal state resistance. I C R N should be of order ∆/e (where ∆ is the superconducting gap of the leads and e is the charge of the electron) and independent of device geometry [8]. The second characteristic property is the "Fraunhofer-like" magnetic diffraction pattern, i.e. the decaying, oscillatory response of the supercurrent to the magnetic field B, applied perpendicular to the flow of the supercurrent. The first minimum in I C should occur at B = B C , when one quantum of flux Φ 0 = h/2e (where h is Planck's constant) is passed through the area of the device. Recent reports on TI JJs [6,7] match this expectation.In this Letter we report on transport properties of nanoscale Josephson junctions fabricated using Bi 2 Se 3 as the weak link material. The main experimental results of this Report are two departures from conventional Josephson junction behavior in these devices: a...

We report a nearly ideal quantum anomalous Hall effect in a three-dimensional topological insulator thin film with ferromagnetic doping. Near zero applied magnetic field we measure exact quantization in Hall resistance to within a part per 10,000 and longitudinal resistivity under 1 Ω per square, with chiral edge transport explicitly confirmed by non-local measurements. Deviations from this behavior are found to be caused by thermally-activated carriers, which can be eliminated by taking advantage of an unexpected magnetocaloric effect.PACS numbers: 73.43.Fj, 75.45.+j, 75.50.Pp The discovery of the quantum Hall effect (QHE) [1,2] led to a new understanding of electronic behavior in which topology plays a central role [3,4]. Initially, the critical experimental observation was the precise quantization of the Hall resistance to integer divisions of h/e 2 , where h is Planck's constant and e is the electron charge. This quantization, immune to sample-specific disorder, now forms the basis for a metrological standard [5]. A complementary feature-zero longitudinal resistance, reflecting resistanceless transport along sample edges-could also have technological applications, were it not for the demanding environmental requirements for achieving the QHE: a large magnetic field to break timereversal symmetry (TRS) and, in most cases, cryogenic temperatures. Ideas for producing a similar phenomenology without an external magnetic field have long been considered [6], often involving the interplay of symmetry and topology in new material systems.In the past decade, topological insulators (TIs) have emerged as a promising approach.In both twodimensional [7][8][9] and three-dimensional [10][11][12][13][14] forms, conduction in TIs is restricted to topologically-protected boundary states. In the 3D case, the presence of ferromagnetic exchange can break TRS, opening a gap in the otherwise Dirac-like surface states [15][16][17]. But topology adds a twist: even a uniformly magnetized sample will have, relative to the normal vector of the surface, a domain boundary where the magnetization switches from inward to outward. Along this line the gap should close, restoring conduction [16]. In a thin film geometry in which the easy axis of the magnetism is out-of-plane, confinement along the sample side wall should ensure conduction is one-dimensional while the surface gradient of the magnetism restricts it to only one direction, leading to ballistic, chiral transport. In a Hall bar geometry, this would be observed as the quantum anomalous Hall effect (QAHE), with a zero longitudinal resistance and a transverse resistance quantized to h/ne 2 , where n is typically ±1 but can in principle be a higher integer given sufficiently strong exchange [18].Experimental realization of the QAHE has been swift. Doping films of the ternary TI family (Bi,Sb) 2 Te 3 with Mn or Cr was found to produce robust out-of-plane ferromagnetism and a large anomalous Hall effect in transport [19][20][21]. Further growth optimization and chemical potential man...

). Electron-nuclear interaction in 13C nanotube double quantum dots. Nature Physics, 5(5), 321-326. https://doi.org

We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron 13 C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time, T1, first decreases with parallel magnetic field then goes through a minimum in a field of 1.4 T. We attribute both results to the spin-orbit-modified electronic spectrum of carbon nanotubes, which suppresses hyperfine mediated relaxation and enhances relaxation due to soft phonons. The inhomogeneous dephasing time, T * 2 , is consistent with previous data on hyperfine coupling strength in 13 C nanotubes.Few-electron double quantum dots have enabled the coherent manipulation and detection of individual and coupled electron spin states required to form qubits [1,2,3,4]. Although recent protocols mitigate decoherence due to hyperfine coupling in GaAs-based devices [5,6], an attractive alternative is to base spin qubits on group IV elements, which primarily comprise isotopes free of nuclear spins. Progress in this direction includes double quantum dots in Si/SiGe 2DEGs [7], P donors in Si [8], Ge/Si nanowires [9], and carbon nanotubes [10]. Recent advances in nanotube double dots include observation of singlet-triplet physics [11] and Pauli blockade [12]. Developing these systems as spin qubits depends crucially on understanding their modes of relaxation and dephasing.This Letter reports measurements of relaxation and dephasing times in a two-electron nanotube double quantum dot grown from isotopically enriched (99%) 13 C methane. Measurements use fast pulses applied to electrostatic gates combined with charge sensing measurements in the Pauli blockade regime, including spin and isospin quantum states. The relaxation time of these states, T 1 , initially decreases with parallel field and has a minimum in a field of 1.4 T. We interpret these results within the context of the recently observed [13] spinorbit interaction in carbon nanotubes [14,15]. We also measure a relatively short two-electron inhomogeneous dephasing time, T * 2 ∼ 3 ns, which presumably arises from hyperfine coupling. The implied hyperfine coupling strength is consistent with values measured recently by transport [16]. In contrast, the long T 1 does not show signatures of hyperfine coupling.The double dot studied here is based on a single-walled carbon nanotube grown by chemical vapor deposition using 99%13 CH 4 feedstock [17,18]. After deposition of two pairs of Pd contacts [ Fig. 1(a), red], the device is coated with a 30 nm functionalized Al 2 O 3 top-gate oxide using atomic layer deposition [19,20]. Aluminum top-gates (blue, yellow, and gray) define a double dot between contacts 1 and 2 and a single dot between contacts 3 and 4, capacitively coupled [orange wire in Fig. 1(a)] to the double dot to allow charge sensing [9,21]. The small bandgap (∼ 25 meV) nanotube is operated in the electron regime. Direct current and standard lock-in measurements are carried out in a dilution refrigerator (electron temperature ∼ 100 mK). Electron occupancies (N L , N R ) of the dou...