RECORD
Interplay between pair-density-wave and charge-density-wave orders in underdoped cuprates
Strongly Correlated Electrons · Submitted 15 Dec 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For the checkerboard state, we considered a situation when both CDW and PDW orders are present at low $T$ and show that the presence of both condensates induces a long sought chiral $s+id_{xy}$ superconductivity.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We analyze the interplay between charge-density-wave (CDW) and pair-density-wave (PDW) orders within the spin-fermion model for the cuprates. We specifically consider CDW order with transferred momenta $(\pm Q,0)$/$(0,\pm Q)$, and PDW order with total momenta $(0,\pm Q)/(\pm Q,0)$. We show that both emerge in the spin-fermion model near the onset of antiferromagnetism. We further argue that the two orders are nearly degenerate due to an approximate SU(2) particle-hole symmetry of the model. The ${\rm SU}(2)$ symmetry becomes exact if one neglects the curvature of the Fermi surface in hot regions, in which case ${\rm U}(1)$ CDW and PDW order parameters become components of an SO(4)-symmetric PDW/CDW "super-vector". We develop a Ginzburg-Landau theory for PDW/CDW order parameters and find two possible ground states: a "stripe" state, and a "checkerboard" state. We show that the ${\rm SO}(4)$ symmetry between CDW and PDW is broken by two effects. One is the inclusion of Fermi surface curvature, which selects a PDW order immediately below the instability temperature. Another is the overlap between different hot regions, which favors CDW order at low temperatures. For the stripe state, we show that the competition between the two effects gives rise to a first-order transition from PDW to CDW inside the ordered state. We also argue that beyond mean-field theory, the onset temperature for CDW order is additionally enhanced due to feedback from a preemptive breaking of ${\mathbb Z}_2$ time-reversal symmetry. We discuss the ground state properties of a pure PDW state and a pure CDW state, and show that the PDW checkerboard state yields a vortex-anti-vortex lattice. For the checkerboard state, we considered a situation when both CDW and PDW orders are present at low $T$ and show that the presence of both condensates induces a long sought chiral $s+id_{xy}$ superconductivity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We analyze the interplay between charge-density-wave (CDW) and pair-density-wave (PDW) orders within the spin-fermion model for the cuprates. | contribution 0.94 | 0.94 | 0.05 | asserted 0.77 |
| s1 | We specifically consider CDW order with transferred momenta $(\pm Q,0)$/$(0,\pm Q)$, and PDW order with total momenta $(0,\pm Q)/(\pm Q,0)$. | contribution 0.55 | 0.76 | 0.04 | asserted 0.94 |
| s2 | We show that both emerge in the spin-fermion model near the onset of antiferromagnetism. | result 0.99 | 0.92 | 0.16 | asserted 1.00 |
| s3 | We further argue that the two orders are nearly degenerate due to an approximate SU(2) particle-hole symmetry of the model. | result 0.57 | 0.84 | 0.20 | asserted 0.72 |
| s4 | The ${\rm SU}(2)$ symmetry becomes exact if one neglects the curvature of the Fermi surface in hot regions, in which case ${\rm U}(1)$ CDW and PDW order parameters become components of an SO(4)-symmetric PDW/CDW "super-vector". | interpretation 0.59 | 0.61 | 0.09 | asserted 0.99 |
| s5 | We develop a Ginzburg-Landau theory for PDW/CDW order parameters and find two possible ground states: a "stripe" state, and a "checkerboard" state. | result 0.55 | 0.97 | 0.16 | asserted 1.00 |
| s6 | We show that the ${\rm SO}(4)$ symmetry between CDW and PDW is broken by two effects. | result 0.81 | 0.90 | 0.09 | asserted 1.00 |
| s7 | One is the inclusion of Fermi surface curvature, which selects a PDW order immediately below the instability temperature. | result 0.96 | 0.86 | 0.12 | asserted 1.00 |
| s8 | Another is the overlap between different hot regions, which favors CDW order at low temperatures. | result 0.96 | 0.87 | 0.09 | asserted 0.98 |
| s9 | For the stripe state, we show that the competition between the two effects gives rise to a first-order transition from PDW to CDW inside the ordered state. | result 1.00 | 0.95 | 0.19 | asserted 1.00 |
| s10 | We also argue that beyond mean-field theory, the onset temperature for CDW order is additionally enhanced due to feedback from a preemptive breaking of ${\mathbb Z}_2$ time-reversal symmetry. | result 0.90 | 0.80 | 0.10 | hedged possibility 0.46 |
| s11 | We discuss the ground state properties of a pure PDW state and a pure CDW state, and show that the PDW checkerboard state yields a vortex-anti-vortex lattice. | result 0.94 | 0.93 | 0.10 | asserted 1.00 |
| s12 | For the checkerboard state, we considered a situation when both CDW and PDW orders are present at low $T$ and show that the presence of both condensates induces a long sought chiral $s+id_{xy}$ superconductivity. | result 0.99 | 0.91 | 0.24 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We analyze the interplay between charge-density-wave (CDW) and pair-density-wave (PDW) orders within the spin-fermion model for the cuprates. We specifically consider CDW order with transferred momenta $(\pm Q,0)$/$(0,\pm Q)$, and PDW order with total momenta $(0,\pm Q)/(\pm Q,0)$. We show that both emerge in the spin-fermion model near the onset of antiferromagnetism. We further argue that the two orders are nearly degenerate due to an approximate SU(2) particle-hole symmetry of the model. The ${\rm SU}(2)$ symmetry becomes exact if one neglects the curvature of the Fermi surface in hot regions, in which case ${\rm U}(1)$ CDW and PDW order parameters become components of an SO(4)-symmetric PDW/CDW "super-vector". We develop a Ginzburg-Landau theory for PDW/CDW order parameters and find two possible ground states: a "stripe" state, and a "checkerboard" state. We show that the ${\rm SO}(4)$ symmetry between CDW and PDW is broken by two effects. One is the inclusion of Fermi surface curvature, which selects a PDW order immediately below the instability temperature. Another is the overlap between different hot regions, which favors CDW order at low temperatures. For the stripe state, we show that the competition between the two effects gives rise to a first-order transition from PDW to CDW inside the ordered state. We also argue that beyond mean-field theory, the onset temperature for CDW order is additionally enhanced due to feedback from a preemptive breaking of ${\mathbb Z}_2$ time-reversal symmetry. We discuss the ground state properties of a pure PDW state and a pure CDW state, and show that the PDW checkerboard state yields a vortex-anti-vortex lattice. For the checkerboard state, we considered a situation when both CDW and PDW orders are present at low $T$ and show that the presence of both condensates induces a long sought chiral $s+id_{xy}$ superconductivity.
Human review
How the literature uses it
2 arXiv papers cite this in 2 sentences
What it cites · 11 sentences without a confident label
Cites as support 1 paper
-
Such a “orthogonal" configuration maximized the gain of energy due to the development of the secondary SC order and by this reason is a strong candidate for the actual CDW/PDW configuration in the state II [ref] .
Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates · Computation of the triple couplings within spin-fermion model · 0.98
Cites as background 4 papers
-
Known instabilities include $d$-wave superconductivity [ref] and charge orders of momentum $(Q,Q)$ (bond charge orders, Refs. [ref] ) and $(Q,0)/(0,Q)$ (CDW order, Refs. [ref] ).
Density-wave instabilities of fractionalized Fermi liquids · PDW and CDW instabilities in the spin-fermion model with linear dispersion · 0.88
-
This order can be either an incommensurate charge-density-wave order (CDW) [ref] defined as $ρ_k^Q ∝⟨c_α^†(k+Q/2) c_β(k-Q/2)⟩δ_αβ$ or an incommensurate pair-density-wave order (PDW) [ref] , $φ_Q^k∝⟨c_α(k-Q/2) c_β(-k-Q/2)⟩(iσ^y_αβ)$.
Theory of Intertwined Orders in High Temperature Superconductors · Introduction · 0.94
-
The CDW scenario has been proposed for the cuprates a while ago [ref] , but has recently gained momentum [ref] due to strong experimental evidence for charge order in the underdoped cuprates.
Charge Order in the Pseudogap Phase of Cuprate Superconductors · Introduction · 0.98
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.