Modeling the pseudogap metallic state in cuprates: Quantum disordered pair density wave

Abstract

We present a way to quantum-disorder a pair density wave, and propose it to be a candidate of the effective low-energy description of the pseudogap metal which may reveal itself in a sufficiently high magnetic field to suppress the d-wave pairing. The ground state we construct is a small-pocket Fermi liquid with a hidden bosonic Mott insulator in the density-wave-enlarged unit cell. At low energy, the charge density is mainly carried by charge 2e bosons, which develop a small insulating gap. We discuss a number of experimental consequences. Optical excitation across the boson gap can explain the onset of mid infra-red absorption reported long ago. The interplay between the electron and the small-gap boson results in a characteristic electron spectral function consistent with ARPES. We also postulate a secondary magnetization density wave along (1,1) direction which breaks timereversal symmetry, mirror symmetry, and C4 rotation. Our treatment of fluctuating pair density wave provides a non-perturbative mechanism of gap generation on part of the Fermi surface, which can be generalized to other fluctuating orders. I. INTRODUCTIONPseudogap occupies a large region in the phase diagram of underdoped cuprates, up to a high temperature wellseparated from the superconductivity. Theoretically, it is desirable to kill the superconductivity and probe the pseudogap phenomena at zero temperature, where different quantum phases are sharply distinct. This line of thinking brings us to the study of high-field ground state of underdoped cuprates. At around 12% hole doping, the magnetic field needed to destroy long-range superconductivity corresponds to an energy scale well below the anti-nodal gap [1][2][3]; it is reasonable to expect the 'pseudogap' to be present in the high-field ground state. Surprisingly, as the superconductivity is destroyed, quantum oscillation of a small Fermi pocket was detected [4][5][6], and charge density wave (CDW) with correlation length hundreds of lattice spacing was discovered [7][8][9][10][11]. Harrison and Sebastian postulate that the CDW momentum connects the tips of 'Fermi arcs' and makes the closed pocket seen in quantum oscillations (for a review, see [12]). Another hint of the high-field ground state comes from the recent STM discovery of a new period 8 short-range but static CDW below T c in the 'vortex halo' [13][14][15], pointing to its possible origin in a pair density wave (PDW) with the same period. This experiment suggests the relevance of PDW to the high field pseudo-gap ground state in addition to the CDW. The possible relevance of PDW to the Cuprates have been under discussion for some time [16][17][18][19][20][21] and recently reviewed by Agterberg et al. [22] The large antinodal gap in the normal state and the decrease of low-energy fermionic carrier density, which are the most prominent phenomena of the pseudogap region, was initially attributed to fluctuating d-wave superconductivity. However, careful ARPES study [23,24] reported a momentum-dependence different from a d-wave su...

Unconventional quantum vortex matter state hosts quantum oscillations in the underdoped high-temperature cuprate superconductors

“…The observed coexistence can potentially be explained by nonuniform models of superconductivity that are spatially modulated at a finite wave vector, such as the pair density wave (PDW) recently reported in experiments such as scanning-tunneling microscopy (31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44). Unlike models of spatially uniform superconductivity that are characterized by nodal points (9, 19-21, 24, 29), models of finite wave vector superconductivity result in "nesting" over only a portion of the Fermi surface and consequently, yield a partially gapped Fermi surface and lines of gapless excitations (31).…”

Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity

“…2 B ), whose intensity may be below present X-ray detection limits. Alternatively, the PDW in YBa 2 Cu 3 O 7 may be fluctuating and thus unobservable ( 43 ). A distinct point is that a uniform DSC + PDW state should have clear spectroscopic signatures visible in angle-resolved photoemission spectroscopy (ARPES) ( 24 , 28 ).…”

Mirror symmetry breaking in a model insulating cuprate

“…Indeed, since Φ and Ψ break independent symmetries, they are not constrained to have the same critical temperature and a coupling term of the form Φ 2 Ψ 2 is allowed by symmetry in the free energy. More complex intra-unit-cell spin or spin-lattice coupled arrangements with higher multipole moments [27], intra-unit-cell orbital loop current configurations [28][29][30] possibly associated with topological order [31], or long wavelength orbital magnetization density waves [32] that break vertical mirror planes are plausible candidates for Φ. We note that the AFM form factor of Sr 2 CuO 2 Cl 2 measured from neutron diffraction reportedly deviates from that of a free Cu 2+ ion [33].…”