We compare the effects of timelike, lightlike and spacelike one-dimensional inhomogeneities on the probability of nonperturbative pair production in strong fields. Using interpolating coordinates we give a unifying picture in which the effect of the inhomogeneity is encoded in branch cuts and poles circulated by complex worldline instantons. For spacelike inhomogeneities the length of the cut is related to the existence of critical points, while for lightlike inhomogeneities the cut contracts to a pole and the instantons become contractable to points, leading to simplifications particular to the lightlike case. We calculate the effective action in fields with up to three nonzero components, and investigate its behaviour under changes in field dependence.

We extend the standard effective model of d-wave superconductivity of a single band tight-binding Hamiltonian with nearest-neighbor attraction to include finite range periodically modulated pair-hopping. The pair-hopping is characterized by a fixed wave number $\pmb{\mathcal{Q}}=\mathcal{Q}\hat{x}$ breaking lattice rotational symmetry. Within self-consistent BCS theory we study the general variational state consisting of two incommensurate singlet pair amplitudes $\Delta_{{\bf Q}_1}$ and $\Delta_{{\bf Q}_2}$ and find two types of near degenerate ground states; of the Larkin-Ovchnnikov (LO) or pair-density wave (PDW) type with $\Delta_{{\bf Q}_1}=\Delta_{{\bf Q}_2}$ and ${\bf Q}_1=-{\bf Q}_2\approx \mathcal{Q}$ or of the Fulde-Ferrell (FF) type with $\Delta_{{\bf Q}_2}=0$ and ${\bf Q}_1\approx \pm \mathcal{Q}$. An anomalous term in the static current operator arising from the pair-hopping ensures that Bloch's theorem on zero current in the ground state is enforced also for the FF ground state, despite broken time-reversal symmetry without spin-population imbalance. We also consider a supercurrent by exploring the space of pair-momenta ${\bf Q}_1$ and ${\bf Q}_2$ and identify characteristics of a state with multiple finite momentum order-parameters. This includes the possibility of phase-separation of current densities and spontaneous mirror-symmetry breaking manifested in the directional dependence of the depairing current

We study nonperturbative pair production in electric fields with lightlike inhomogeneities, using complex worldline instantons. We show that the instanton contribution to the pair production probability is a complex contour integral over the instanton itself, and that pair production in the considered fields can be recast in terms of Cauchy's residue theorem. The instantons contribute residues from the poles they circulate (i.e. give local contributions), and the invariance of complex integrals under contour deformation manifests in the instanton contributions as invariance under a set of generalised, complex, reparameterisations.Comment: 6 pages, 3 pdf/png figures. Matches journal versio

FIG. 1. Transition temperatures for Q = 0 superconducting (SC, blue lines) and Q = 0 Fulde-Ferrell (FF, red lines) states of the model (1),(2) as a function of local attraction strength, g, and relative pair-hopping strength, α = gpair/g0. A line of Lifshitz points (given by (mB) −1 = 0 solutions of (11)), are shown in solid blue in the g, α-plane (dashed for subleading transition). The black solid line indicates a bicritical line. The black dot marks the super-Lifshitz point at the intersection of the bicritical and Lifshitz line. The red and green arrows indicate similar paths as in Figure 2.necessarily includes up to sixth order derivatives of the order parameter, and explore it in the context of the BCS to BEC crossover [33][34][35][36][37]. As seen in Figure 1, the homogeneous state becomes unstable to a finite momentum time-reversal breaking Fulde Ferrell (FF) type state (∆(r) = ∆ Q (r)e iQ·r ). This happens at arbitrarily small pair-hopping, α > 0, for a sufficiently large attraction, arXiv:1807.05303v2 [cond-mat.supr-con]

Electronic anisotropy (or 'nematicity') has been detected in all main families of cuprate superconductors by a range of experimental techniques -electronic Raman scattering, THz dichroism, thermal conductivity, torque magnetometry, second-harmonic generation -and was directly visualized by scanning tunneling microscope (STM) spectroscopy. Using angle-resolved transverse resistance (ARTR) measurements, a very sensitive and background-free technique that can detect 0.5% anisotropy in transport, we have observed it also in La 2-x Sr x CuO 4 (LSCO) for 0.02 ≤ x ≤ 0.25. Arguably the key enigma in LSCO is the rotation of the nematic director with temperature; this has not been seen before in any material. Here, we address this puzzle by measuring the angle-resolved transverse magnetoresistance (ARTMR) in LSCO. We report a discovery of colossal transverse magnetoresistance (CTMR) -an order-of-magnitude drop in the transverse resistivity in the magnetic field of 6 T, while none is seen in the longitudinal resistivity. We show that the apparent rotation of the nematic director is caused by superconducting phase fluctuations, which are much more anisotropic than the normal-electron fluid, and their respective directors are not parallel. This qualitative conclusion is robust and follows straight from the raw experimental data. We quantify this by modelling the measured (magneto-)conductivity by a sum of two conducting channels that correspond to distinct anisotropic Drude and Cooper-pair effective mass tensors. Strikingly, the anisotropy of Cooper-pair stiffness is significantly larger than that of the normal electrons, and it grows dramatically on the underdoped side, where the fluctuations become effectively quasi-one dimensional. Our analysis is deliberately general rather than model-dependent, but we also discuss some candidate microscopic models including coupled strongly-correlated ladders where the transverse (inter-ladder) phase stiffness is low compared to the longitudinal intra-ladder stiffness, as well as the anisotropic superconducting fluctuations expected close to the transition to a pair-density wave state. The results provide important clues about the pseudogap state in the cuprate superconductors.Apart from a high superconducting critical temperature (T c ), copper oxides show other striking features [1]. Unlike in standard metals, in the normal state the rotational symmetry of electron fluid is spontaneously broken ('electronic nematicity') [2][3][4][5][6][7][8][9][10][11]. Unlike in conventional superconductors, T c is set by the phase-ordering temperature rather than by the pairing-energy scale inferred from the measured single-particle response; consequently, above T c superconducting phase fluctuations abound [12][13][14][15][16][17][18][19][20]. The fact that nematicity is strongly enhanced in underdoped cuprates implies that there may be interesting, yet to be revealed, connections with other unusual properties such as the pseudogap, antiferromagnetic fluctuations, and charge-, spin-or pair-density w...