Suppression of superfluid stiffness near Lifshitz-point instability to finite momentum superconductivity

We derive the effective Ginzburg-Landau theory for finite momentum (FFLO/PDW) superconductivity without spin population imbalance from a model with local attraction and repulsive pair-hopping. We find that the GL free energy must include up to sixth order derivatives of the order parameter, providing a unified description of the interdependency of zero and finite momentum superconductivity. For weak pair-hopping the phase diagram contains a line of Lifshitz points where vanishing superfluid stiffness induces a continuous change to a long wavelength Fulde-Ferrell (FF) state. For larger pair-hopping there is a bicritical region where the pair-momentum changes discontinuously. Here the FF type state is near degenerate with the Larkin-Ovchinnikov (LO) or Pair-Density-wave (PDW) type state. At the intersection of these two regimes there is a "Super-Lifshitz" point with extra soft fluctuations. The instability to finite momentum superconductivity occurs for arbitrarily weak pair-hopping for sufficiently large attraction suggesting that even a small repulsive pair-hopping may be significant in a microscopic model of strongly correlated superconductivity. Several generic features of the model may have bearing on the cuprate superconductors, including the suppression of superfluid stiffness in proximity to a Lifshitz point as well as the existence of subleading FFLO order (or vice versa) in the bicritical regime

Fluctuating superconductivity and pair-density wave order in the cuprate superconductors

High-temperature superconductors are some of nature’s most enigmatic materials. Besides carrying a supercurrent, these materials manifest a range of electronic and structural orders. A state of modulated superconductivity, called a pair-density wave (PDW), has been suggested to occur in copper-based (cuprate) high-temperature superconductors, with the possibility of explaining these various orders, and perhaps even superconductivity itself. This thesis is based upon four appended papers and concerns the nature of the PDWstate and the cuprate superconductors. In the first two papers, we consider a so-called pair-hopping interaction that can stabilize a (mean-field) PDWstate. In the first paper, we use this interaction to study the supercurrent carried by a PDW state, which, due to it being a multiplecomponent order, can lead to phase-separation and additional symmetry breaking. In the second paper, we study the competition between a PDWstate and an ordinary uniform superconducting state in the context of a BCS-BEC crossover. We find a suppressed superfluid stiffness in the vicinity of a PDWinstability, with implications on the nature of the underdoped cuprates. The third paper includes an experimental study on thin films of La_2-x Sr_xCuO_4, which above Tc develops a highly anisotropic resistive response, especially pronounced for underdoped samples, pointing towards an exotic pseudogap phase in the underdoped cuprates with quasi-1D phase superfluid stiffness. We interpret these results in terms of nematic order manifested in the superconducting fluctuations. In the last paper of this thesis, we consider a scenario where the cuprate pseudogap phase consists of a thermally disorder PDW state with vestigial order. We show that a vestigial PDWnematic order coexisting with a uniformsuperconducting order yields an anisotropic superconductor on a formconsistent with the fluctuations seen in La_2-x Sr_xCuO_4. Finally, in addition to providing background for the appended papers, this thesis contains an introduction to the general phenomenology of the cuprate superconductors

Nematic single-component superconductivity and loop-current order from pair-density wave instability

We investigate the nematic and loop-current type orders that may arise as vestigial precursor phases in a model with an underlying pair-density wave (PDW) instability. We discuss how such a vestigial phase gives rise to a highly anisotropic stiffness for a coexisting single-component superconductor with low intrinsic stiffness, as is the case for the underdoped cuprate superconductors. Next, focusing on a regime with a mean-field PDW ground state with loop-current and nematic $xy$ (B$_{2g}$) order, we find a preemptive transition into a low and high-temperature vestigial phase with loop-current and nematic order corresponding to $xy$ (B$_{2g}$) and $x^2-y^2$ (B$_{1g}$) symmetry respectively. Near the transition between the two phases, a state of soft nematic order emerges for which we expect that the nematic director is readily pinned away from the high-symmetry directions in the presence of an external field. Results are discussed in relation to findings in the cuprates, especially to the recently inferred highly anisotropic superconducting fluctuations W{\aa}rdh et al.[1], giving additional evidence for an underlying ubiquitous PDW instability in these materials.Comment: 19 pages, 9 figures, and 2 table

Colossal transverse magnetoresistance due to nematic superconducting phase fluctuations in a copper oxide

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 $0.02 \leq x \leq 0.25$. 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.Comment: 27 pages, 10 figures and 4 table