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The single-particle density of states and the tunneling conductance are studied for a two-dimensional BCS-like Hamiltonian with a d_{x^2-y^2}-gap and phase fluctuations. The latter are treated by a classical Monte Carlo simulation of an XY model. Comparison of our results with recent scanning tunneling spectra of Bi-based high-T_c cuprates supports the idea that the pseudogap behavior observed in these experiments can be understood as arising from phase fluctuations of a d_{x^2-y^2} pairing gap whose amplitude forms on an energy scale set by T_c^{MF} well above the actual superconducting transition.
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The opening of the pseudogap in underdoped cuprates breaks up the Fermi surface, which may lead to a breakup of the d-wave order parameter into two subband amplitudes and a low energy Leggett mode due to phase fluctuations between them. This causes a large increase in the temperature range of superconducting fluctuations with an overdamped Leggett mode. Almost resonant scattering of inter-subband phonons to a state with a pair of Leggett modes causes anomalously strong damping. In the ordered state, the Leggett mode develops a finite energy, suppressing the anomalous phonon damping but leading to an anomaly in the phonon dispersion.
Electron irradiation has been used to introduce point defects in a controlled way in the CuO2 planes of underdoped and optimally doped YBCO. This technique allows us to perform very accurate measurements of Tc and of the residual resistivity in a wide range of defect contents xd down to Tc=0. The Tc decrease does not follow the variation expected from pair breaking theories. The evolutions of Tc and of the transition width with xd emphasize the importance of phase fluctuations, at least for the highly damaged regime. These results open new questions about the evolution of the defect induced Tc depression over the phase diagram of the cuprates
A d-wave superconductor, its phase coherence progressively destroyed by unbinding of vortex-antivortex pairs, suffers an instability related to chiral symmetry breaking in two-flavor QED$_3$. The chiral manifold exhibits large degeneracy spanned by physical states acting as inherent ``competitors of d-wave superconductivity. Two of these states are associated with antiferromagnetic insulator and ``stripe phases, known to be stable in the pseudogap regime of cuprates near half-filling. The theory also predicts additional, yet unobserved state: a d+ip phase-incoherent superconductor.
The pseudogap (PG) regime of the underdoped cuprates arguably remains one of the most enigmatic phenomena of correlated quantum matter. Recent theoretical ideas suggest that fractionalized bosonic fields can lead to the PG phase, by opening a gap in the anti-nodal (AN) region of the Brillouin zone. Such fractionalized boson can originate from modulated particle-particle pairs or pair density wave (PDW), a magnetic stripe, or a modulated spin one particle-hole pair like a spin density wave (SDW) boson, among others. The main picture goes as follows. Electrons under strong coupling tend to form different types of unstable bosons at high temperatures. As the temperature goes down, the compact object gets extremely unstable, and to minimize the entropy, it finally fractionalizes into elementary components, linked by a constraint. The process of fractionalization involves, in this way, an emergent gauge field directly linked to the constraint. This, in turn, couples to the Fermi surface of electronic carriers and opens a gap in the AN region, which is partly responsible for the PG phase. Alternative theoretical approaches invoke a simple coexistence between the multiple quasi-degenerate orders like charge density wave (CDW), superconductivity (SC), and magnetic orders at low temperatures. This scenario attributes the PG formation as a vestigial order showing up at $T^{*}$, which acts as a precursor to the zero temperature orders. This intricate situation calls for a key experimental test, enabling us to discriminate between the various theoretical scenarios. In this paper, we focus on the case where the PDW boson has fractionalized into a CDW and SC order below $T^{*}$, and we compare this to the situation where the two orders simply coexist.
Evidence for intra-unit-cell (IUC) magnetic order in the pseudogap region of high-$T_c$ cuprates below a temperature $T^ast$ is found in several studies, but NMR and $mu$SR experiments do not observe the expected static local magnetic fields. It has been noted, however, that such fields could be averaged by fluctuations. Our measurements of muon spin relaxation rates in single crystals of YBa$_2$Cu$_3$O$_y$ reveal magnetic fluctuations of the expected order of magnitude that exhibit critical slowing down at $T^ast$. These results are strong evidence for fluctuating IUC magnetic order in the pseudogap phase.
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