Holstein polaron: the effect of multiple phonon modes

We generalize the Momentum Average approximations MA$^{(0)}$ and MA$^{(1)}$ to study the effects of coupling to multiple optical phonons on the properties of a Holstein polaron. As for a single phonon mode, these approximations are numerically very efficient. They become exact for very weak or very strong couplings, and are highly accurate in the intermediate regimes, {\em e.g.} the spectral weights obey exactly the first six, respectively eight, sum rules. Our results show that the effect on ground-state properties is cumulative in nature. In particular, if the effective coupling to one mode is much larger than to the others, this mode effectively determines the GS properties. However, even very weak coupling to a second phonon mode has important non-perturbational effects on the higher energy spectrum, in particular on the dispersion and the phonon statistics of the polaron band

Using magnetic stripes to stabilize superfluidity in electron-hole double monolayer graphene

Experiments have confirmed that double monolayer graphene cannot generate finite temperature electron-hole superfluidity. This has been shown to be due to very strong screening of the electron-hole pairing attraction. The linear dispersing energy bands in monolayer graphene prevent attempts to reduce the strength of the screening. We propose a new hybrid device in which the two sheets of monolayer graphene are placed in a modulated periodic perpendicular magnetic field. Such a magnetic field preserves the isotropic Dirac cones of the original monolayers but it reduces the slope of the cones so that the monolayer Fermi velocity $v_F$ is smaller. We show that with current experimental techniques, this reduction in $v_F$ can sufficiently weaken the screening to permit electron-hole superfluidity at measurable temperatures.Comment: Revised version. MultiSuper collaboration: http://www.multisuper.or

Superconducting proximity effect in graphene under inhomogeneous strain

The interplay between quantum Hall states and Cooper pairs is usually hindered by the suppression of the superconducting state due to the strong magnetic fields needed to observe the quantum Hall effect. From this point of view graphene is special since it allows the creation of strong pseudo-magnetic fields due to strain. We show that in a Josephson junction made of strained graphene, Cooper pairs will diffuse into the strained region. The pair correlation function will be sub-lattice polarized due to the polarization of the local density of states in the zero pseudo-Landau level. We uncover two regimes; 1) one in which the cyclotron radius is larger than the junction length in which case the supercurrent will be enhanced, and 2) the long junction regime where the supercurrent is strongly suppressed because the junction becomes an insulator. In the latter case quantized Hall states form and Andreev scattering at the normal/superconducting interface will induce edge states. Our numerical calculation has become possible due to an extension of the Chebyshev Bogoliubov-de Gennes method to computations on video cards (GPUs).Comment: to appear in PR

Adatoms and Anderson localization in graphene

We address the nature of the disordered state that results from the adsorption of adatoms in graphene. For adatoms that sit at the center of the honeycomb plaquette, as in the case of most transition metals, we show that the ones that form a zero-energy resonant state lead to Anderson localization in the vicinity of the Dirac point. Among those, we show that there is a symmetry class of adatoms where Anderson localization is suppressed, leading to an exotic metallic state with large and rare charge droplets, that localizes only at the Dirac point. We identify the experimental conditions for the observation of the Anderson transition for adatoms in graphene.Comment: 8 pages, 5 figures, 2 appendixes, Final versio

Proximity induced pseudogap in mesoscopic superconductor/normal-metal bilayers

Recent scanning tunneling microscopy measurements of the proximity effect in Au/La$_{2-x}$Sr$_{x}$CuO$_{4}$ and La$_{1.55}$Sr$_{0.45}$CuO$_{4}$/La$_{2-x}$Sr$_{x}$CuO$_{4}$ bilayers showed a proximity-induced pseudogap [Yuli et al., Phys. Rev. Lett. {\bf 103}, 197003 (2009)]. We describe the proximity effect in mesoscopic superconductor/normal-metal bilayers by using the Bogoliubov-de Gennes equations for a tight-binding Hamiltonian with competing antiferromagnetic and d-wave superconductivity orders . The temperature dependent local density of states is calculated as a function of the distance from the interface. Bound state due to both d-wave and spin density wave gaps are formed in the normal metal for energies less than the respective gaps. If there is a mismatch between the Fermi velocities in the two layers we observe that these states will shift in energy when spin density wave order is present, thus inducing a minigap at finite energy. We conclude that the STM measurement in the proximity structures is able to distinguish between the two scenarios proposed for the pseudogap (competing or precursor to superconductivity)

Giant proximity effect in a phase-fluctuating superconductor

When a tunneling barrier between two superconductors is formed by a normal material that would be a superconductor in the absence of phase fluctuations, the resulting Josephson effect can undergo an enormous enhancement. We establish this novel proximity effect by a general argument as well as a numerical simulation and argue that it may underlie recent experimental observations of the giant proximity effect between two cuprate superconductors separated by a barrier made of the same material rendered normal by severe underdoping.Comment: 4 pages, 3 figures; version to appear in PRL (results of simulations in 3d added). For related work and info visit http://www.physics.ubc.ca/~fran

Real-space calculation of the conductivity tensor for disordered topological matter

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.Comment: 5 pages, 3 figures and a supplementary material (3 pages

Emerging Nonequilibrium Bound State in Spin-Current-Local-Spin Scattering

Magnetization reversal is a well-studied problem with obvious applicability in computer hard drives. One can accomplish a magnetization reversal in at least one of two ways: application of a magnetic field or through a spin current. The latter is more amenable to a fully quantum-mechanical analysis. We formulate and solve the problem whereby a spin current interacts with a ferromagnetic Heisenberg spin chain, to eventually reverse the magnetization of the chain. Spin flips are accomplished through both elastic and inelastic scattering. A consequence of the inelastic-scattering channel, when it is no longer energetically possible, is the occurrence of a nonequilibrium bound state, which is an emergent property of the coupled local plus itinerant spin system. For certain definite parameter values the itinerant spin lingers near the local spins for some time, before eventually leaking out as an outwardly diffusing state. This phenomenon results in spin-flip dynamics and filtering properties for this type of system

Proximity effect in clean strong/weak/strong superconducting tri-layers

Recent measurements of the Josephson critical current through LSCO/LCO/LSCO thin films showed an unusually large proximity effect. Using the Bogoliubov-de Gennes (BdG) equations for a tight binding Hamiltonian we describe the proximity effect in weak links between a superconductor with critical temperature $T_c$ and one with critical temperature $T_c$', where $T_c>T_c$'. The weak link (N') is therefore a superconductor above its own critical temperature and the superconducting regions are considered to have either s-wave or d-wave symmetry. We note that the proximity effect is enhanced due to the presence of superconducting correlations in the weak link. The dc Josephson current is calculated, and we obtain a non-zero value for temperatures greater than $T_c$' for sizes of the weak links that can be almost an order of magnitude greater than the conventional coherence length. Considering pockets of superconductivity in the N' layer, we show that this can lead to an even larger effect on the Josephson critical current by effectively shortening the weak link.Comment: submitted to Physical Review