Quasiparticles and vortices in unconventional superconductors

Abstract

Quasiparticles in the vortex lattice of strongly type-II superconductors are investigated by means of a singular gauge transformation applied to the tight binding lattice Bogoliubov-de Gennes Hamiltonian. We present a detailed derivation of the gauge invariant effective low energy Hamiltonian for the quasiparticle-vortex system and show how the physics of the "Doppler shift" and "Berry phase" can be incorporated at the Hamiltonian level by working in the singular gauge. In particular, we show that the "Berry phase" effect manifests itself in the effective Hamiltonian through a half-flux Aharonov-Bohm scattering of quasiparticles off vortices and stress the important role that this effect plays in the quasiparticle dynamics. Full numerical solutions in the regime of intermediate fields Hc1 ≪ B ≪ Hc2 are presented for model superconductors with s-, p-and d-wave symmetries and with square and triangular vortex lattices. For s-and p-wave cases we obtain low energy bound states in the core, in agreement with the existing results. For d-wave case only extended quasiparticle states exist. We investigate in detail the nature of these extended states and provide comparison to the previous results within linearized "Dirac fermion" model. We also investigate internodal interference effects when vortex and ionic lattices have high degree of commensurability and discuss various specific choices for the singular gauge transformation.

Berry phases and the intrinsic thermal Hall effect in high-temperature cuprate superconductors

“…This model has been discussed extensively elsewhere 6,11,15 : c r,s is the electron annihilation operator, the sum over the spin projection s ¼ m or k in the first and the last terms is implicit, 24×24 28×28 32×32 36×36 40×40 44×44 48×48 52×52 20×20 24×24 28×28 32×32 36×36 40×40 44×44 48×48 20×20 24×24 28×28 32×32 36×36 40×40 44×44 48×48 20×28 24×34 28×40 32×44 36×50 40×56 44×62 16×28 20×34 24×42 28×48 32×56 36×62 40×70 3. 6 7.1 14.3 7.1 …”

“…Because such large gauge invariance must hold, the validity of the results has been in doubt. A tight-binding lattice regularization was found to remove such problems 6 . The initial model calculation 10 of k xy using such regularization was limited to unrealistically large values of H, indeed finding that for a space inversion symmetric vortex lattice, the QP spectrum is generally gapped and that lim T!0 k xy =T ¼ npk 2 B =ð6' Þ, albeit the values of n ranged from À 2 to 12.…”

“…Unfortunately, the linearized approximation, on which these conclusions rest, has been found to be problematic. Within the linearized approximation, the QP spectrum is not 6,7 invariant under the large (singular) gauge transformations 8,9 , which were being employed in the calculations 5 of k xy . Because such large gauge invariance must hold, the validity of the results has been in doubt.…”

Model of phase fluctuations in a latticed-wave superconductor: Application to the Cooper-pair charge-density wave in underdoped cuprates

“…2). The simplest starting point is the lattice d-wave superconductor (LdSC) model discussed in detail by Vafek et al 18 . The model describes fermions hopping between nearest neighbor sites ij on a square lattice with a renormalized matrix element t * and contains a nearest neighbor spin-singlet pairing term with an effective coupling constant λ eff adjusted to stabilize the d x 2 −y 2 state with the maximum pairing gap ∆:…”

Quasiparticle scattering from vortices ind-wave superconductors. I. Superflow contribution

“…Note that when considering a system of many vortices, the resulting sea of branch cuts can be problematic. In response, Franz and Tesanovic introduced an alternate gauge transformation better suited to the vortex lattice 19,20 . However, for the single vortex case that we consider, the Anderson gauge described above is most convenient.…”