Incommensurate charge ordered states in thet–t′–Jmodel

Choubey, Peayush; Tu, Wei-Lin; Lee, Ting-Kuo; Hirschfeld, P. J.

doi:10.1088/1367-2630/19/1/013028

Cited by 32 publications

(56 citation statements)

References 45 publications

(127 reference statements)

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“…In fact, numerous different phases have been obtained by investigating Hubbard and t-J type Hamiltonians in attempts to find the proper theoretical description of high-T c cuprates [22][23][24][25][26][27][28][29][30][31][32], revealing low-energy intertwined inhomogeneous states, such as stripes, bidirectional charge-ordered states, checkerboard patterns, and so on. Recently, tensor network studies [33] and density matrix embedding theory [34] provided new evidence that the ground state (GS) of the Hubbard model could indeed be inhomogeneous at finite doping and that its phase diagram shows co-existence of d-wave superconducting (SC) order with other instabilities.…”

Section: Introductionmentioning

confidence: 99%

Competing orders in the Hofstadter t–J model

Schindler

Neupert

et al. 2018

Phys. Rev. B

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The Hofstadter model describes non-interacting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model including a Hubbard repulsion U . We investigate this model in the large-U limit corresponding to a t-J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly co-existing) charge, bond and superconducting orders. Topological properties of the states are also investigated and some of our results are compared to related experiments involving ultra-cold atoms loaded on optical lattices in the presence of a synthetic gauge field.

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Section: Introductionmentioning

confidence: 99%

Competing orders in the Hofstadter t–J model

Schindler

Neupert

et al. 2018

Phys. Rev. B

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“…This is consistent with the previous work of Capello et al [19] on the same model using variational Monte Carlo. Finally, the pair density wave (PDW) state has been the focus of many studies [20][21][22][23][24] (for a recent review, see Ref. [25]).…”

Section: Introductionmentioning

confidence: 99%

Interplay between d -wave superconductivity and a bond-density wave in the one-band Hubbard model

Faye

Sénéchal

2017

Phys. Rev. B

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It is now well established that superconducting cuprates support a charge density wave state in the socalled underdoped region of their phase diagram. We investigate the possibility of charge order in the square-lattice Hubbard model, both alone and in coexistence with d-wave superconductivity. The charge order has a period four in one direction, is centered on bonds and has a d form factor. We use the variational cluster approximation, an approach based on a rigorous variational principle that treats shortrange correlations exactly, with two clusters of size 2 × 6 that together tile the infinite lattice and provide a non-biased unit for a period-four bond density wave (BDW). We find that the BDW exists in a finite range of hole doping and increases in strength from U = 5 to U = 8. Its location and intensity depends strongly on the band dispersion. When probed simultaneously with d-wave superconductivity, the energy is sometimes lowered by the presence of both phases, depending on the interaction strength. Whenever they coexist, a pair-density wave (a modulation of superconducting pairing with the same period and form factor as the BDW) also exists.

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“…It was found that the superfluid density ρS(r) shows a checkerboard pattern indicative of the PDW state, and it shares a common wavevector with the checkerboard charge order. The most probable scenario was proposed to be the coexisting of d-wave symmetry superconductivity and d-symmetry form factor CDW.If the PDW state is such a pronounced feature as revealed in the SJTM, one would expect that it should also manifest itself in single particle tunneling spectroscopy probed by plain STM.An obvious strategy is to investigate the spatial distribution of SC gap size, but recent theories show that the SC gap size may not show spatial periodicity even if there is PDW order [24][25][26][30][31][32] . Here we propose that there are two other key characteristics associated with superconductivity in a single particle tunneling spectrum.…”

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confidence: 99%

“…An obvious strategy is to investigate the spatial distribution of SC gap size, but recent theories show that the SC gap size may not show spatial periodicity even if there is PDW order [24][25][26][30][31][32] . Here we propose that there are two other key characteristics associated with superconductivity in a single particle tunneling spectrum.…”

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confidence: 99%

Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor

Ruan

Cheng

et al. 2018

Nature Phys

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A major obstacle in understanding the mechanism of Cooper pairing in the cuprates is the existence of various intertwined orders associated with spin, charge, and Cooper pairs 1,2 . Of particular importance is the ubiquitous charge order features that have been observed in a variety of cuprates 2-12 , especially in the underdoped regime of the phase diagram. To explain the origin of the charge order and its implication to the superconducting phase, many theoretical models have been proposed, such as charge stripes 13 , electronic nematicity 13,14 , and Fermi surface instability 6,15 . A highly appealing physical picture is the so-called pair density wave (PDW), a periodic modulation of Cooper paring in space, which may also induce a charge order 2,16-32 . To elucidate the existence and nature of the PDW order, here we use scanning tunneling microscopy (STM) to investigate a severely underdoped Bi2Sr2CaCu2O8+δ, in which superconductivity just emerges on top of a pronounced checkerboard charge order. By analyzing the spatial distribution of the spectral features characteristic of superconductivity, we observe a periodic modulation of both the superconducting coherence peak and gap depth, demonstrating the existence of a density wave order of Cooper pairing. The PDW order has the same spatial periodicity as the charge order, and the amplitudes of the two orders exhibit clear positive correlation. These results shed important new lights on the origin of and interplay between the charge order and Cooper pairing modulation in the cuprates.The basic idea of PDW can date back to the original proposal of Fulde-Ferrell 33 and Larkin-Ovchinnikov 34,35 , in which the singlet pairing between the Zeeman-split Fermi surfaces will have a finite momentum Q, corresponding to periodic spatial modulations. For cuprates, several types of PDW orders have been proposed to be the origin of the charge order 16-30 , including unidirectional 16-22 , bidirectional 23 , and Ampere pairings 24 . More recently, theories involving the intertwinned PDW with d-form factor charge order and superconductivity have been extensively studied [25][26][27][28][29][30] , and it is proposed that both orders share a common wavevector.Although PDW in the cuprates has been predicted for more than 10 years, direct experimental proof of its existence has been lacking. The main challenge is how to probe the spatial distribution of Cooper pairing in the atomic scale. A significant recent progress is the detection of PDW state in optimally doped Bi2Sr2CaCu2O8+δ (Bi-2212) by using scanning Josephson tunneling microscopy (SJTM) 36 . In this technique, a scanning tip is decorated by a nanometer-sized superconducting (SC) Bi-2212 flake, and the tunneling of Cooper pairs between the tip and sample is utilized to map out the local distribution of Josephson critical current IJ(r). It was found that the superfluid density ρS(r) shows a checkerboard pattern indicative of the PDW state, and it shares a common wavevector with the checkerboard charge order. The most probab...

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Incommensurate charge ordered states in thet–t′–Jmodel

Cited by 32 publications

References 45 publications

Competing orders in the Hofstadter t–J model

Competing orders in the Hofstadter t–J model

Interplay between d -wave superconductivity and a bond-density wave in the one-band Hubbard model

Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor

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