Signatures of Topological Superconductors

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.

The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.

This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.

As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.

Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

Plasma loop and strapping field dynamics: reproducing solar eruptions in the laboratory

Coronal mass ejections (CMEs) are dramatic eruptions of large, plasma structures from the Sun. These eruptions are important because they can harm astronauts, damage electrical infrastructure, and cause auroras. A mysterious feature of these eruptions is that plasma-filled solar flux tubes first evolve slowly, but then suddenly erupt. One model, torus instability, predicts an explosive-like transition from slow expansion to fast acceleration, if the spatial decay of the ambient magnetic field exceeds a threshold.

We create arched, plasma filled, magnetic flux ropes similar to CMEs. Small, independently-powered auxiliary coils placed inside the vacuum chamber produce magnetic fields above the decay threshold that are strong enough to act on the plasma. When the strapping field is not too strong and not too weak, expansion force build up while the flux rope is in the strapping field region. When the flux rope moves to a critical height, the plasma accelerates quickly, corresponding to the observed slow-rise to fast-acceleration of most solar eruptions. This behavior is in agreement with the predictions of torus instability.

Historically, eruptions have been separated into gradual CMEs and impulsive CMEs, depending on the acceleration profile. Recent numerical studies question this separation. One study varies the strapping field profile to produce gradual eruptions and impulsive eruptions, while another study varies the temporal profile of the voltage applied to the flux tube footpoints to produce the two eruption types. Our experiment reproduced these different eruptions by changing the strapping field magnitude, and the temporal profile of the current trace. This suggests that the same physics underlies both types of CME and that the separation between impulsive and gradual classes of eruption is artificial.

I. Nuclear spin-internal-rotation-coupling. II. Fluorine spin-rotation interaction and magnetic shielding in fluorobenzene

Part I.

The interaction of a nuclear magnetic moment situated on an internal top with the magnetic fields produced by the internal as well as overall molecular rotation has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written

H_SR = Ῑ · M · Ĵ + Ῑ · M” · Ĵ”

Where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling.

The F¹⁹ nuclear spin-lattice relaxation time (T₁) of benzotrifluoride and several chemically substituted benzotrifluorides, have been measured both neat and in solution, at room temperature by pulsed nuclear magnetic resonance. From these experimental results it is concluded that in benzotrifluoride the internal rotation is crucial to the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction.

Part II.

The radiofrequency spectrum corresponding to the reorientation of the F¹⁹ nuclear moment in flurobenzene has been studied by the molecular beam magnetic resonance method. A molecular beam apparatus with an electron bombardment detector was used in the experiments. The F¹⁹ resonance is a composite spectrum with contributions from many rotational states and is not resolved. A detailed analysis of the resonance line shape and width by the method of moments led to the following diagonal components of the fluorine spin-rotational tensor in the principal inertial axis system of the molecule:

F/Caa = -1.0 ± 0.5 kHz

F/Cbb = -2.7 ± 0.2 kHz

F/Ccc = -1.9 ± 0.1 kHz

From these interaction constants, the paramagnetic contribution to the F¹⁹ nuclear shielding in C₆H₅F was determined to be -284 ± ppm. It was further concluded that the F¹⁹ nucleus in this molecule is more shielded when the applied magnetic field is directed along the C-F bond axis. The anisotropy of the magnetic shielding tensor, σ_” - σ_⊥, is +160 ± 30 ppm.

I. Anisotropy and crystal structure of ferromagnetic thin films. II. Investigations into magnetic microstructure by Lorentz microscopy

The induced magnetic uniaxial anisotropy of Ni-Fe alloy films has been shown to be related to the crystal structure of the film. By use of electron diffraction, the crystal structure or vacuum-deposited films was determined over the composition range 5% to 85% Ni, with substrate temperature during deposition at various temperatures in the range 25° to 500° C. The phase diagram determined in this way has boundaries which are in fair agreement with the equilibrium boundaries for bulk material above 400°C. The (α+ ɤ) mixture phase disappears below 100°C.

The measurement of uniaxial anisotropy field for 25% Ni-Fe alloy films deposited at temperatures in the range -80°C to 375°C has been carried out. Comparison of the crystal structure phase diagram with the present data and those published by Wilts indicates that the anisotropy is strongly sensitive to crystal structure. Others have proposed pair ordering as an important source of anisotropy because of an apparent peak in the anisotropy energy at about 50% Ni composition. The present work shows no such peak, and leads to the conclusion that pair ordering cannot be a dominant contributor.

Width of the 180° domain wall in 76% Ni-Fe alloy films as a function of film thickness up to 1800 Å was measured using the defocused mode of Lorentz microscopy. For the thinner films, the measured wall widths are in good agreement with earlier data obtained by Fuchs. For films thicker than 800 Å, the wall width increases with film thickness to about 9000 Å at 1800 Å film thickness. Similar measurements for polycrystalline Co films with thickness from 200 to 1500 Å have been made. The wall width increases from 3000 Å at 400 Å film thickness to about 6000 Å at 1500 Å film thickness. The wall widths for Ni-Fe and Co films are much greater than predicted by present theories. The validity of the classical determination of wall width is discussed, and the comparison of the present data with theoretical results is given.

Finally, an experimental study of ripple by Lorentz microscopy in Ni-Fe alloy films has been carried out. The following should be noted: (1) the only practical way to determine experimentally a meaningful wavelength is to find a well-defined ripple periodicity by visual inspection of a photomicrograph. (2) The average wavelength is of the order of 1µ. This value is in reasonable agreement with the main wavelength predicted by the theories developed by others. The dependence of wavelength on substrate deposition temperature, alloy composition and the external magnetic field has been also studied and the results are compared with theoretical predictions. (3) The experimental fact that the ripple structure could not be observed in completely epitaxial films gives confirmation that the ripple results from the randomness of crystallite orientation. Furthermore, the experimental observation that the ripple disappeared in the range 71 and 75% Ni supports the theory that the ripple amplitude is directly dependent on the crystalline anisotropy. An attempt to experimentally determine the order of magnitude of the ripple angle was carried out. The measured angle was about 0.02 rad. The discrepancy between the experimental data and the theoretical prediction is serious. The accurate experimental determination of ripple angle is an unsolved problem.

Surface impedance theory for superconductors in large static magnetic fields

A theory of electromagnetic absorption is presented to explain the changes in surface impedance for Pippard superconductors (ξ_o ≫λ) due to large static magnetic fields. The static magnetic field penetrating the metal near the surface induces a momentum dependent potential in Bogolubov's equations. Such a potential modifies a quasiparticle's wavefunction and excitation spectrum. These changes affect the behavior of the surface impedance in a way that in large measure agrees with available observations.

Microwave dynamics of quasiparticles and critical fields in superconducting films

The microwave response of the superconducting state in equilibrium and non-equilibrium configurations was examined experimentally and analytically. Thin film superconductors were mostly studied in order to explore spatial effects. The response parameter measured was the surface impedance.

For small microwave intensity the surface impedance at 10 GHz was measured for a variety of samples (mostly Sn) over a wide range of sample thickness and temperature. A detailed analysis based on the BCS theory was developed for calculating the surface impedance for general thickness and other experimental parameters. Experiment and theory agreed with each other to within the experimental accuracy. Thus it was established that the samples, thin films as well as bulk, were well characterised at low microwave powers (near equilibrium).

Thin films were perturbed by a small dc supercurrent and the effect on the superconducting order parameter and the quasiparticle response determined by measuring changes in the surface resistance (still at low microwave intensity and independent of it) due to the induced current. The use of fully superconducting resonators enabled the measurement of very small changes in the surface resistance (< 10^-9 Ω/sq.). These experiments yield information regarding the dynamics of the order parameter and quasiparticle systems. For all the films studied the results could be described at temperatures near T_c by the thermodynamic depression of the order parameter due to the static current leading to a quadratic increase of the surface resistance with current.

For the thinnest films the low temperature results were surprising in that the surface resistance decreased with increasing current. An explanation is proposed according to which this decrease occurs due to an additional high frequency quasiparticle current caused by the combined presence of both static and high frequency fields. For frequencies larger than the inverse of the quasiparticle relaxation time this additional current is out of phase (by π) with the microwave electric field and is observed as a decrease of surface resistance. Calculations agree quantitatively with experimental results. This is the first observation and explanation of this non-equilibrium quasiparticle effect.

For thicker films of Sn, the low temperature surface resistance was found to increase with applied static current. It is proposed that due to the spatial non-uniformity of the induced current distribution across the thicker films, the above purely temporal analysis of the local quasiparticle response needs to be generalised to include space and time non-equilibrium effects.

The nonlinear interaction of microwaves arid superconducting films was also examined in a third set of experiments. The surface impedance of thin films was measured as a function of the incident microwave magnetic field. The experiments exploit the ability to measure the absorbed microwave power and applied microwave magnetic field absolutely. It was found that the applied surface microwave field could not be raised above a certain threshold level at which the absorption increased abruptly. This critical field level represents a dynamic critical field and was found to be associated with the penetration of the app1ied field into the film at values well below the thermodynamic critical field for the configuration of a field applied to one side of the film. The penetration occurs despite the thermal stability of the film which was unequivocally demonstrated by experiment. A new mechanism for such penetration via the formation of a vortex-antivortex pair is proposed. The experimental results for the thinnest films agreed with the calculated values of this pair generation field. The observations of increased transmission at the critical field level and suppression of the process by a metallic ground plane further support the proposed model.

Optimizing the Curie temperature of pseudo-binary RxR2-x ' Fe-17 (R, R ' = rare earth) for magnetic refrigeration

Several pseudo-binary RxR2-x'Fe-17 alloys (with R = Y, Ce, Pr, Gd and Dy) were synthesized with rhombohedral Th2Zn17-type crystal structure determined from x-ray and neutron powder diffraction. The choice of compositions was done with the aim of tuning the Curie temperature (T-C) in the 270 +/- 20 K temperature range, in order to obtain the maximum magneto-caloric effect around room temperature. The investigated compounds exhibit broad isothermal magnetic entropy changes, Delta S-M(T), with moderate values of the refrigerant capacity, even though the values of Delta S-M(Peak) are relatively low compared with those of the R2Fe17 compounds with R = Pr or Nd. The reduction on the Delta S-M(Peak) is explained in terms of the diminution in the saturation magnetization value. Furthermore, the Delta S-M(T) curves exhibit a similar caret-like behavior, suggesting that the magneto-caloric effect is mainly governed by the Fe-sublattice. A single master curve for Delta S-M/Delta S-M(Peak)(T) under different values of the magnetic field change are obtained for each compound by rescaling of the temperature axis.

Development of an Active Superconducting Magnetic Bearing

The potential use of YBa2Cu3C7as an active component in a magnetic bearing is being investigated. Measurements are being made of the load bearing capacity and related stiffnesses in comparison to predictions from the critical state model. Although the load bearing capacity is high and increases with the square of the magnetic field trapped the stiffness is low. We report on a novel design concept to overcome this problem. © 1995 IEEE

Dynamic properties of superconducting magnetic bearings

The potential use of YBa2j as an active component in a magnetic bearing is being investigated. Although the load bearing capacity is high and increases with the square of the magnetic field trapped, the stiffness is low. Both the stiffness and the lévitation height are a function of the loading history of the bearing. At Cambridge we have been investigating the effects of dynamic loading such as single large excursions from steady state loads and cyclically applied loads such as vibrations. Since a superconducting bearing has little inherent damping cyclic loads applied at or near its natural frequency can have catastrophic effects. The information being gathered at Cambridge will be used to enable these effects to be mitigated in the bearing design process. © 1997 IEEE.

Behavior of bulk melt-textured YBCO single domains subjected to crossed magnetic fields

We have experimentally investigated the crossed magnetic field effects on bulk melt-processed YBCO single domains. The samples were first permanently magnetized along their c-axis and then subjected to several cycles of a transverse magnetic field parallel to the ab planes. The magnetic properties along the c and ab directions were simultaneously measured using a couple of orthogonal pick-up coils as well as a Hall probe placed against the sample surface. The effects of both sweep amplitude and polarity were investigated. Field sweeps of alternate polarities are shown to affect the decay of the c-axis magnetization much more strongly than field sweeps of unique polarity do. However, the c-axis magnetization does not show any saturation even after a large number of field sweeps. Next, a micro-Hall probe scanning system was used to measure the distribution of magnetic induction over the top surface of the single domain subjected to the same combination of magnetic fields. The results are shown to be consistent with those determined with the sensing coils and bring out the role played by geometric effects.

Characterization of nano-composite M-2411/Y-123 thin films by electron backscatter diffraction and in-field critical current measurements

Thin films of nano-composite Y-Ba-Cu-O (YBCO) superconductors containing nano-sized, non-superconducting particles of Y2Ba 4CuMOx (M-2411 with M = Ag and Nb) have been prepared by the PLD technique. Electron backscatter diffraction (EBSD) has been used to analyze the crystallographic orientation of nano-particles embedded in the film microstructure. The superconducting YBa2Cu3O7 (Y-123) phase matrix is textured with a dominant (001) orientation for all samples, whereas the M-2411 phase exhibits a random orientation. Angular critical current measurements at various temperature (T) and applied magnetic field (B) have been performed on thin films containing different concentration of the M-2411 second phase. An increase in critical current density J c at T < 77 K and B < 6 T is observed for samples with low concentration of the second phase (2 mol % M-2411). Films containing 5 mol % Ag-2411 exhibit lower Jc than pure Y-123 thin films at all fields and temperatures. Samples with 5 mol % Nb-2411 show higher Jc(B) than phase pure Y-123 thin films for T < 77 K. © 2010 IOP Publishing Ltd.

Pulsed field magnetization of a high temperature superconducting motor

As we known, the high temperature (77 K) superconducting (HTS) motor is considered as a competitive electrical machine by more and more people. There have been various of designs for HTS motor in the world. However, most of them focus on HTS tapes rather than bulks. Therefore, in order to investigate possibility of HTS bulks on motor application, a HTS magnet synchronous motor which has 75 pieces of YBCO bulks surface mounted on the rotor has been designed and developed in Cambridge University. After pulsed field magnetization (PFM) process, the rotor can trap a 4 poles magnetic field of 375 mT. The magnetized rotor can provide a maximum torque of 49.5 Nm and a maximum power of 7.8 kW at 1500 rpm. © 2010 IEEE.

Magnetophonon resonance in graphite: High-field Raman measurements and electron-phonon coupling contributions

We perform Raman scattering experiments on natural graphite in magnetic fields up to 45 T, observing a series of peaks due to interband electronic excitations over a much broader magnetic field range than previously reported. We also explore electron-phonon coupling in graphite via magnetophonon resonances. The Raman G peak shifts and splits as a function of magnetic field, due to the magnetically tuned coupling of the E 2g optical phonons with the K- and H-point inter-Landau-level excitations. The analysis of the observed anticrossing behavior allows us to determine the electron-phonon coupling for both K- and H-point carriers. In the highest field range (>35 T) the G peak narrows due to suppression of electron-phonon interaction. © 2012 American Physical Society.

Alternating current loss of second-generation high-temperature superconducting coils with magnetic and non-magnetic substrate

It is widely believed that the second-generation high-temperature superconducting (2G HTS) tapes with magnetic substrates suffer higher transport loss compared to those with non-magnetic substrates. To test this, we prepared two identical coils with magnetic and non-magnetic substrates, respectively. The experimental result was rather surprising that they generated roughly the same amount of transport loss. We used finite element method to understand this result. It is found that, unlike in the single tape where the magnetic field-dependent critical current characteristic can be neglected and the effect of magnetic substrate dominates, the magnetic field-dependent critical current characteristic of 2G tape plays as an equally important role as magnetic substrate in terms of HTS coils. © 2012 American Institute of Physics.

The experiment to evaluate the AC loss of 2G HTS windings in the application of rotating electric machines

This paper presents the design of an AC loss experiment using nitrogen boil-off method. This experiment is aimed at exploring the AC loss of HTS double race-track coils which will be installed on the rotor of a wind turbine generator. The operating environment is simulated by designing a cryostat with rotating magnetic field windings. Apart from the fact that the alternating magnetic field causes most of AC loss on the HTS coils, we also believe that the DC background field would be another important factor causing AC loss if the HTS coil is experiencing by both alternating magnetic field in the perpendicular direction and DC background field in the parallel direction. In order to perform the boil-off measurement, we present the method to estimate the heat leakage in the cryostat which might cause errors to the measurement. © 2011 IEEE.