Pair-density waves, charge-density waves, and vortices in high-
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 cuprates

Dai, Zhehao; Zhang, Ya-Hui; Senthil, T.; Lee, Patrick A.

doi:10.1103/physrevb.97.174511

Cited by 77 publications

(70 citation statements)

References 55 publications

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“…40 The zero field PDW was only observed with the same vector as charge modulations. These observations inspired several theoretical works [41][42][43] indicating their importance in the PG phase, but with no consensus on whether the fundamental state is a PDW or a charge ordered state. In our formulation, we provide, for the first time, a viewpoint based on 'fractionalized' PDW which is the fundamental object.…”

Section: A General Introductionmentioning

confidence: 80%

“…We also note that the magnetic moments derived from microscopic mean field models are usually far smaller compared to what it is found in experiments. 42 The preemptive transition can also give way to nematicity 48,154 and the breaking of the inversion symmetry recently observed in the study of the optical second harmonic generation. 52…”

Section: Loop Current Statementioning

confidence: 88%

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Fractionalized pair density wave in the pseudogap phase of cuprate superconductors

et al. 2019

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The mysterious pseudo-gap (PG) phase of cuprate superconductors has been the subject of intense investigation over the last thirty years, but without a clear agreement about its origin. Owing to a recent observation in Raman spectroscopy, of a precursor in the charge channel, on top of the well known fact of a precursor in the superconducting channel, we present here a novel idea: the PG is formed through a Higgs mechanism, where two kinds of preformed pairs, in the particle-particle and particle-hole channels, become entangled through a freezing of their global phase. Remarkably, this entanglement is equivalent to fractionalizing a bond Cooper pair density wave (PDW) into its elementary parts; the particle-hole pair, giving rise to both density modulations and current modulations, and the particle-particle counterpart, leading to the formation of Cooper pairs. From this perspective, the "fractionalized PDW" becomes the central object around the formation of the pseudo-gap. The "locking" of phases between the charge and superconducting modes gives a unique explanation for the unusual global phase coherence of short-range charge modulations, observed below Tc on phase sensitive scanning tunneling microscopy (STM). A simple microscopic model enables us to estimate the mean-field values of the precursor gaps in each channel and the PG energy scale, and to compare them to the values observed in Raman scattering spectroscopy. We also discuss the possibility of a multiplicity of orders in the PG phase and give an overview of the phase diagram. arXiv:1906.01633v2 [cond-mat.supr-con]

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Section: A General Introductionmentioning

confidence: 80%

Section: Loop Current Statementioning

confidence: 88%

Fractionalized pair density wave in the pseudogap phase of cuprate superconductors

et al. 2019

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“…For more details, see Ref. [14,20]. We remark that the addition of the y-direction PDW contribution shown in Fig.…”

Section: A Mean-field Pdw Bands In Cupratesmentioning

confidence: 90%

“…[13].The mean-field PDW ansatz presented in Ref. [14,20] has many desired features: the fermion spectrum roughly resembles that observed by ARPES, CDW is generated as a subsidiary order at twice the PDW momentum, CDW connects the nodal arcs to form a gapless pocket, and the gapless Bogoliubov pocket is mostly electron-like, giving rise to the possibility of quantum oscillation. However, there is no PDW long range order in the majority of cuprates.…”

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confidence: 97%

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

2020

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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...

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“…This may be interpreted as a subsidiary PDW being generated by the period 4a 0 charge order together with the uniform d-wave pairing. In this sense the recent report [9] of short range period 8a 0 charge order in the vicinity of the vortex core is even more exciting, because it may be the signature of a hidden period 8a 0 PDW [10,11].Theoretically, there are very few microscopic models which are shown to have PDW ground states. Berg et al[12] studied a Kondo-Heisenberg model with 1D electron gas coupled to a spin chain.…”

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confidence: 99%

Pair Density Wave in the Doped t−J Model with Ring Exchange on a Triangular Lattice

Law

Lee

2019

Phys. Rev. Lett.

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In our previous work [Phys. Rev. Lett. 121, 046401 (2018)], we found a quantum spin liquid phase with a spinon Fermi surface in the two dimensional spin-1/2 Heisenberg model with four-spin ring exchange on a triangular lattice. In this work we dope the spinon Fermi surface phase by studying the t-J model with fourspin ring exchange. We perform density matrix renormalization group calculations on four-leg cylinders of a triangular lattice and find that the dominant pair correlation function is that of a pair density wave; i.e., it is oscillatory while decaying with distance with a power law. The doping dependence of the period is studied. This is the first example where pair density wave is the dominant pairing in a generic strongly interacting system where the pair density wave cannot be explained as a composite order and no special symmetry is required.A pair density wave (PDW) is a superconducting state in which Cooper pairs have finite momentum. The first example of PDW is the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [1, 2] which can arise in superconductors in strong magnetic fields when the Fermi surface is split by Zeeman effect. Recently PDW has come into prominence in the context of underdoped Cuprate superconductors. The striped PDW was proposed as a mechanism for dynamically inter-layer decoupling observed in 1/8 hole doped La 2−x Ba x CuO 4 [3-6]. One of us has proposed fluctuating bi-directional PDW as the "mother state" that is responsible for many of the anomalous properties of the pseudo-gap regime [7]. Experimentally a direct observation of PDW has been made via local Cooper pair tunnelling in Bi 2 Sr 2 CaCu 2 O 8+x [8]. They found Cooper pair density modulation with period 4a 0 where a 0 is the length of unit cell, and the magnitude of the modulation is five percent of the uniform pairing background. This may be interpreted as a subsidiary PDW being generated by the period 4a 0 charge order together with the uniform d-wave pairing. In this sense the recent report [9] of short range period 8a 0 charge order in the vicinity of the vortex core is even more exciting, because it may be the signature of a hidden period 8a 0 PDW [10,11].Theoretically, there are very few microscopic models which are shown to have PDW ground states. Berg et al.[12] studied a Kondo-Heisenberg model with 1D electron gas coupled to a spin chain. They found a spin gapped phase with PDW correlations oscillating with period 2a 0 , which matches the period of the ordering tendency of the spin chain. An extended two-leg Hubbard-Heisenberg model is also found to have a spin gapped phase with a PDW [13]. In all these examples, the PDW is commensurate and can either be interpreted as a composite order between short range spin order with the same commensurate period and another short range triplet pairing order, or requires the specially tuned symmetry of π flux through the ladder plaquette. Dodaro et al. [14] searched for PDW in a more standard t-J model for doped cuprates, but they did not find any evidence of PDW ordering ev...

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Pair-density waves, charge-density waves, and vortices in high- Tc cuprates

Cited by 77 publications

References 55 publications

Fractionalized pair density wave in the pseudogap phase of cuprate superconductors

Fractionalized pair density wave in the pseudogap phase of cuprate superconductors

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

Pair Density Wave in the Doped t−J Model with Ring Exchange on a Triangular Lattice

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