Tilting of the magnetic field in Majorana nanowires: critical angle and zero-energy differential conductance

Semiconductor nanowires with strong spin-orbit coupling and proximity-induced s-wave superconductivity in an external magnetic field have been the most promising settings for approaches towards experimental evidence of topological Majorana zero-modes. We investigate the effect of tilting the magnetic field relative to the spin-orbit coupling direction in a simple continuum model and provide an analytical derivation of the critical angle, at which the topological states disappear. We also obtain the differential conductance characteristic of a junction with a normal wire for different tilting angles and propose the qualitative change of the dependence of the zero-energy differential conductance on the tunnel barrier strength at the critical angle as a new criterion for establishing the topological nature of the observed signal.Comment: 6 pages, 6 figures, submitted to Physical Review B. V2: Published versio

Thermodynamics of superconducting lattice fermions

We consider the Cooper-problem on a lattice model including onsite and near-neighbor interactions. Expanding the interaction in basis functions for the irreducible representation for the point group $C_{4v}$ yields a classification of the symmetry of the Cooper-pair wave function, which we calculate in real-space. A change of symmetry upon doping, from s-wave at low filling fractions, to $d_{x^2-y^2}$ at higher filling fractions, is found. Fermi-surface details are thus important for the symmetry of the superconducting wave function. Symmetry forbids mixing of s-wave and d-wave symmetry in the Cooper-pair wavefunction on a square lattice, unless accidental degeneracies occur. This conclusion also holds for the selfconsistent treatment of the many-body problem, at the critical temperature $T_c$. Below $T_c$, we find temperatures which are not critical points, where new superconducting channels open up in the order parameter due to bifurcations in the solutions of the nonlinear gap-equation. We calculate the free energy, entropy, coherence length, critical magnetic fields, and Ginzburg-Landau parameter $\kappa$. The model is of the extreme type-II variety. At the temperatures where subdominant channels condense, we find cusps in the internal energy and entropy, as well as as BCS-like discontinuities in the specific heat. The specific heat anomalies are however weaker than at the true superconducting critical point, and argued to be of a different nature.Comment: RevTex, 18 pages including 10 EPS figures; amstex, epsfig, subfigure require

Properties of the Virial Expansion and Equation of State of Ideal Quantum Gases in Arbitrary Dimensions

The virial expansion of ideal quantum gases reveals some interesting and amusing properties when considered as a function of dimensionality $d$. In particular, the convergence radius $\rho_c(d)$ of the expansion is particulary large at {\em exactly\/} $d=3$ dimensions, $\rho_c(3) = 7.1068\ldots \times \lim_{d\to3} \rho_c(d)$. The same phenomenon occurs in a few other special (non-integer) dimensions. We explain the origin of these facts, and discuss more generally the structure of singularities governing the asymptotic behavior of the ideal gas virial expansion.Comment: 23 pages, 13 figure

Dirac-fermions and conductance-oscillations in (s,d)-wave superconductor/normal graphene junctions

We investigate quantum transport in a normal/superconductor graphene heterostructure, including the possibility of an anisotropic pairing potential in the superconducting region. We find that under certain circumstances, the conductance displays an undamped, oscillatory behaviour as a function of applied bias voltage. Also, we investigate how the conductance spectra are affected by a d-wave pairing symmetry. These results combine unusual features of the electronic structure of graphene with the unconventional pairing symmetry found for instance in high-T_c superconductors.Comment: 4 pages, 2 figures. Accepted for publication in Phys. Rev. Let

Signatures of retroreflection and induced triplet electron-hole correlations in ferromagnet/s-wave superconductor structures

We present a theoretical study of a ferromagnet/s-wave superconductor junction to investigate the signatures of induced triplet correlations in the system. We apply the extended BTK-formalism and allow for an arbitrary magnetization strength/direction of the ferromagnet, a spin-active barrier, Fermi-vector mismatch, and different effective masses in the two systems. It is found that the phase associated with the $xy$-components of the magnetization in the ferromagnet couples with the superconducting phase and induces spin-triplet pairing correlations in the superconductor, if the tunneling barrier acts as a spin-filter. This feature leads to an induced spin-triplet pairing correlation in the ferromagnet, along with a spin-triplet electron-hole coherence due to an interplay between the ferromagnetic and superconducting phase. As our main result, we investigate the experimental signatures of retrorelection, manifested in the tunneling conductance of a ferromagnet/s-wave superconductor junction with a spin-active interface.Comment: 13 pages, accepted for publication in Phys. Rev.

Current-loops, phase transitions, and the Higgs mechanism in Josephson-coupled multi-component superconductors

The $N$-component London $\mathrm{U}(1)$ superconductor is expressed in terms of integer-valued supercurrents. We show that the inclusion of inter-band Josephson couplings introduces monopoles in the current fields, which convert the phase transitions of the charge-neutral sector to crossovers. The monopoles only couple to the neutral sector, and leave the phase transition of the charged sector intact. The remnant non-critical fluctuations in the neutral sector influence the one remaining phase transition in the charged sector, and may alter this phase transition from a $3DXY$ inverted phase transition into a first-order phase transition depending on what the values of the gauge-charge and the inter-component Josephson coupling are. This preemptive effect becomes more pronounced with increasing number of components $N$, since the number of charge-neutral fluctuating modes that can influence the charged sector increases with $N$. We also calculate the gauge-field correlator, and by extension the Higgs mass, in terms of current-current correlators. We show that the onset of the Higgs-mass of the photon (Meissner-effect) is given in terms of a current-loop blowout associated with going into the superconducting state as the temperature of the system is lowered.Comment: 12 pages, 3 figures. To appear in Physical Review

Calculation of Drag and Superfluid Velocity from the Microscopic Parameters and Excitation Energies of a Two-Component Bose-Einstein Condensate on an Optical Lattice

We investigate a model of a two-component Bose-Einstein condensate residing on an optical lattice. Within a Bogolioubov-approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laserlight wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.Comment: 11 pages, 5 figures. Accepted for publication in Phys. Rev.

Berry phases, current lattices, and suppression of phase transitions in a lattice gauge theory of quantum antiferromagnets

We consider a lattice model of two complex scalar matter fields $z_{a}, a=1,2$ under a CP1 constraint \abs{z_1}^2+\abs{z_2}^2=1, minimally coupled to a compact gauge field, with an additional Berry phase term. This model has been the point of origin for a large body of works addressing novel paradigms for quantum criticality, in particular spin-quark (spinon) deconfinement in S=1/2 quantum antiferromagnets. We map the model exactly to a link-current model, which permits the use of classical worm algorithms to study the model in large-scale Monte Carlo simulations on lattices of size L^3, up to L=360. We show that the addition of a Berry phase term to the lattice \CP-model suppresses the phase transition in the \groupO{3} universality class of the \CP-model. The link-current formulation of the model is useful in identifying the mechanism by which the phase transition is suppressed.Comment: 12 pages, 9 figures. Published in Physical Review

Fluctuation effects in phase-frustrated multiband superconductors

We compare the phase-diagrams of an effective theory of a three-dimensional multi-band superconductor obtained within standard and cluster mean-field theories, and in large-scale Monte Carlo simulations. In three dimensions, mean field theory fails in locating correctly the positions of the phase transitions, as well as the character of the transitions between the different states. A cluster mean-field calculations taking into account order-parameter fluctuations in a local environment improves the results considerably for the case of extreme type-II superconductors where gauge-field fluctuations are negligible. The large fluctuations in the multi-component superconducting order parameter originate with strong frustration due to interband Josephson-couplings. A novel chiral metallic phase found in previous works using large scale Monte-Carlo computations, is not obtained either within the single-site mean-field theory or the improved cluster mean-field theory of order parameter fluctuations. In three-dimensional superconductors, this unusual metallic phase originates with gauge-field fluctuations.Comment: 11 pages, 3 Figures. Submitted to Physical Review

Derivation of a Ginzburg-Landau free energy density containing mixed gradient terms of a p+ipp+ip superconductor with spin-orbit coupling

A Ginzburg-Landau free energy for a superconducting chiral p-wave order parameter is derived from a two-dimensional tight binding lattice model with weak spin-orbit coupling included as a general symmetry-breaking field. Superconductivity is accounted for by a BCS-type nearest neighbor opposite-spin interaction where we project the potential onto the $p$-wave irreducible representation of the square lattice symmetry group and assume this to be the dominating order. The resulting free energy contains kinetic terms that mix components of the order parameter as well as directional gradients --- so called mixed gradient terms --- as a virtue of the symmetry of the order parameter. Spin-orbit coupling and electron-hole anisotropy lead to additional contributions to the coefficients of these terms, increasing the number of necessary phenomenological parameters by one compared to previous work, and leading to an increase in the coefficient measuring Fermi surface anisotropy for Rashba spin-orbit coupling in the continuum limit