Translational symmetry breaking and valence-bond-solid (VBS) order in doped antiferromagnets

The theoretical strategy of these works is summarized in Figure 1.

Figure 1. Experimentally, the high temperature superconductors are produced by doping the insulating compound La2CuO4 with mobile holes. However, in this process, one crosses a quantum phase transition at which long-range magnetic order disappears. Theoretically it is more convenient to first destroy the magnetic long-range order in the insulator by some other mechanism (e.g. by adding frustrating magnetic interactions), and to then dope with mobile carriers: this two-step theoretical process is sketched above. Details of the first step are discussed elsewhere in these web pages, while the second step is described in the papers below.

The first theoretical step in Figure 1 was discussed elsewhere in these web pages: it was predicted in early work that destroying Neel order in insulating, square lattice antiferromagnets leads to the appearance of spin-Peierls order (or more generally valence-bond-solid (VBS) order). In addition, such paramagnetic insulators also necessarily possess a sharp S=1 collective spin resonance, and the confinement of a S=1/2 moment near each non-magnetic impurity (discussed elsewhere). The papers below discuss the consequences of doping such a VBS state by mobile holes: VBS order, confinement of S=1/2 moments near non-magnetic impurities, and the sharp S=1 resonance survive for a finite range of doping, and co-exist with d-wave-like superconductivity.

A first analysis of the doping of the non-magnetic VBS-ordered Mott insulator appeared in paper 2, and the results are summarized in Figure 2 below.


Figure 2. Phase diagram from paper 2 of the doping of a VBS-ordered Mott insulator, as described by the t-J model. It is instructive to follow the phases as a function of the doping d for large values of t/J. Initially, there is a superconducting state which coexists with VBS ordering. Here the superconducting order is d-wave like (that is, the pairing amplitudes in the x and y directions have opposite signs) and it coexists with VBS order: such a state was first discussed in paper 2. With increasing doping, the amplitude of the VBS order decreases and gapless fermionic excitations appear at nodal points, which are first generated at the edges of the Brillouin zone. Eventually there is a phase transition to an isotropic d-wave superconductor. The computation also found an instability to phase separation below the dotted line.

A more complete analysis of the phase diagram requires a more careful consideration of the influence of the long-range Coulomb interactions, and of the possibility of VBS-ordered states with larger periods. Such an analysis was carried out in papers 3,4, and the results are summarized in Figure 3 below.


Figure 3. Phase diagram analogous to Figure 1 above from papers 3,4. The vertical axis represents an arbitrary short-range exchange interaction which can destroy the long-range Neel order in the insulator. A specific example is the study of A. W. Sandvik, S. Daul, R. R. P. Singh, and D. J. Scalapino, Physical Review Letters 89, 247201 (2002), which used a ring exchange interaction: as expected from the arguments in this web page, the large ring exchange phase had VBS order, as shown in the figure above. The computations of papers 3,4 were carried out in the unhatched region (which has no long range magnetic order) and sample configurations of the VBS order are shown; the states shown pick one directions as special, but "checkerboard" states also appear (M. Vojta, Physical Review B 66, 104505 (2002)). The physics of the transition from the hatched to the unhatched regions (involving restoration of spin rotation invariance) is discussed in the web pages on collinear magnetic order, non-collinear magnetic order, quantum criticality, and the influence of an applied magnetic field . While the mean-field studies of VBS order lead to a bond-centered modulation of the lattice spacings (shown above), there can be "resonance" between different mean-field configurations, and the symmetry of bond modulations can also be such that the reflection symmetry is about a site.

Notice the more elaborate types of VBS order in the non-magnetic superconductor. It is expected that the primary modulation in these VBS-ordered states will be in the exchange, kinetic, and pairing energies between sites, rather than the on-site charge densities. This issue should be distinguished from the issue of the lattice symmetry of the modulation, which could have a plane of reflection symmetry about either the bonds or the sites.

While the VBS states discussed above break the symmetry between the x and y lattice directions, they are not necessarily ``quasi one-dimensional'' i.e. the basic instability leading to VBS ordering in the undoped paramagnet is genuinely two-dimensional. Furthermore, "checkerboard" states can also appear (M. Vojta, Physical Review B 66, 104505 (2002)).

See also the article by Barbara Levi in Physics Today, volume 57, number 9, page 24 (2004).

PAPERS

  1. Large N limit of the square lattice t-J model at 1/4 and other filling fractions, S. Sachdev, Phys. Rev. B 41, 4502 (1990).
  2. Large N expansion for frustrated and doped quantum antiferromagnets, S. Sachdev and N. Read, International Journal of Modern Physics B 5, 219 (1991); cond-mat/0402109.
  3. Charge order, superconductivity, and a global phase diagram of doped antiferromagnets, M. Vojta and S. Sachdev, Physical Review Letters 83, 3916 (1999); cond-mat/9906104.
  4. Competing orders and quantum criticality in doped antiferromagnets, M. Vojta, Y. Zhang, and S. Sachdev, Physical Review B 62, 6721 (2000); cond-mat/0003163.
  5. Translational symmetry breaking in two-dimensional antiferromagnets and superconductors, S. Sachdev and M. Vojta, Journal of the Physical Society of Japan 69, Suppl. B, 1 (2000); cond-mat/9910231.
  6. Quantum phase transitions, S. Sachdev, Physics World 12, No 4, 33 (April 1999).
  7. Quantum phase transitions in antiferromagnets and superfluids, S. Sachdev and M. Vojta, Physica B 280, 333 (2000); cond-mat/9908008.
  8. Quantum criticality: competing ground states in low dimensions, S. Sachdev, Science 288, 475 (2000); cond-mat/0009456.
  9. Bond operator theory of doped antiferromagnets: from Mott insulators with bond-centered charge order, to superconductors with nodal fermions, K. Park and S. Sachdev, Physical Review B 64, 184510 (2001); cond-mat/0104519.
  10. Spin and charge order in Mott insulators and d-wave superconductors, S. Sachdev, Proceedings of Spectroscopies of Novel Superconductors, Chicago, May 13-17, 2001, Journal of Physics and Chemistry of Solids 63, 2269 (2002); cond-mat/0108238.
  11. Pinning of dynamic spin density wave fluctuations in the cuprate superconductors, A. Polkovnikov, M. Vojta, and S. Sachdev, Physical Review B 65, 220509 (2002); cond-mat/0203176.
  12. Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes, S. Sachdev and T. Morinari, Physical Review B 66, 235117 (2002); cond-mat/0207167.
  13. Spin collective mode and quasiparticle contributions to STM spectra of d-wave superconductors with pinning, A. Polkovnikov, S. Sachdev, and M. Vojta, Proceedings of the 23rd International Conference on Low Temperature Physics, August 20-27, 2002, Hiroshima, Japan, Physica C 388-389, 19 (2003) (Erratum: 391, 381 (2003)); cond-mat/0208334.
  14. Order and quantum phase transitions in the cuprate superconductors, S. Sachdev, Reviews of Modern Physics 75, 913 (2003); cond-mat/0211005.
  15. Order and quantum phase transitions in the cuprate superconductors (summary), S. Sachdev, Solid State Communications 127, 169 (2003), Proceedings of the Euroconference on Quantum Phases at the Nanoscale, Erice, Italy, 15-20 July 2002.
  16. Understanding correlated electron systems by a classification of Mott insulators, S. Sachdev, Annals of Physics 303, 226 (2003); cond-mat/0211027.
  17. Field theories of paramagnetic Mott insulators, S. Sachdev, Proceedings of the International Conference on Theoretical Physics, Paris, UNESCO, 22-27 July 2002, Annales Henri Poincare 4, 559 (2003); cond-mat/0304137.
  18. Putting competing orders in their place near the Mott transition, L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Physical Review B 71, 144508 (2005); cond-mat/0408329.
  19. Phenomenological lattice model for dynamic spin and charge fluctuations in the cuprates, M. Vojta and S. Sachdev, Proceedings of Spectroscopies of Novel Superconductors, Sitges, Spain, July 11-16, 2004, Journal of the Physics and Chemistry of Solids, 67, 11 (2006); cond-mat/0408461.
  20. Putting competing orders in their place near the Mott transition II: The doped quantum dimer model, L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Physical Review B 71, 144509 (2005); cond-mat/0409470.
  21. Thermal melting of density waves on the square lattice, A. Del Maestro and S. Sachdev, Physical Review B 71, 184511 (2005); cond-mat/0412498.
  22. Estimating the mass of vortices in the cuprate superconductors, L. Bartosch, L. Balents, and S. Sachdev, cond-mat/0502002.
  23. Competing Orders and non-Landau-Ginzburg-Wilson Criticality in (Bose) Mott transitions , L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Proceedings of ``Physics of Strongly Correlated Electron Systems'', YKIS2004 workshop, Yukawa Institute, Kyoto, Japan, November 2004, Progress of Theoretical Physics Supplement 160, 314 (2005); cond-mat/0504692.
  24. Detecting the quantum zero-point motion of vortices in the cuprate superconductors, L. Bartosch, L. Balents, and S. Sachdev, Annals of Physics 321, 1528 (2006); cond-mat/0602429.
  25. From stripe to checkerboard order on the square lattice, in the presence of quenched disorder, A. Del Maestro, B. Rosenow, and S. Sachdev, Physical Review B 74, 024520 (2006); cond-mat/0603029.
  26. Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory, C. Xu and S. Sachdev, Physical Review B 79, 064405 (2009); arXiv:0811.1220.
  27. Bond order in two-dimensional metals with antiferromagnetic exchange interactions, S. Sachdev and R. La Placa, Physical Review Letters 111, 027202 (2013); arXiv:1303.2114.
  28. Angular fluctuations of a multi-component order describe the pseudogap regime of the cuprate superconductors, L. E. Hayward, D. G. Hawthorn, R. G. Melko, and S. Sachdev, Science 343 , 1336 (2014); arXiv:1309.6639.
  29. Mean field theory of competing orders in metals with antiferromagnetic exchange interactions, J. D. Sau and S. Sachdev, Physical Review B 89, 075129 (2014); arXiv:1311.3298.
  30. Quantum quenches and competing orders, Ling-Yan Hung, Wenbo Fu, and S. Sachdev, Physical Review B 90, 024506 (2014); arXiv:1402.0875.
  31. Bond order instabilities in a correlated two-dimensional metal, A. Allais, J. Bauer, and S. Sachdev, Physical Review B 90, 155114 (2014); arXiv:1402.4807.
  32. Auxiliary-boson and DMFT studies of bond ordering instabilities of t-J-V models on the square lattice, A. Allais, J. Bauer, and S. Sachdev, Indian Journal of Physics 88, 905 (2014); arXiv:1402.6311.
  33. Fermi Surface and Pseudogap Evolution in a Cuprate Superconductor, Yang He, Yi Yin, M. Zech, A. Soumyanarayanan, I. Zeljkovic, M. M. Yee, M. C. Boyer, K. Chatterjee, W. D. Wise, Takeshi Kondo, T. Takeuchi, H. Ikuta, P. Mistark, R. S. Markiewicz, A. Bansil, S. Sachdev, E. W. Hudson, and J. E. Hoffman, Science 344, 608 (2014); arXiv:1305.2778.
  34. Direct phase sensitive identification of a d-form factor density wave in underdoped cuprates, K. Fujita, M. H. Hamidian, S. D. Edkins, Chung Koo Kim, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, H. Eisaki, S. Uchida, A. Allais, M. J. Lawler, E.-A. Kim, S. Sachdev, and J. C. Seamus Davis, Proceedings of the National Academy of Sciences 111, E3026 (2014); arXiv:1404.0362.
  35. Feedback of superconducting fluctuations on charge order in the underdoped cuprates, D. Chowdhury and S. Sachdev, Physical Review B 90, 134516 (2014); arXiv:1404.6532.
  36. Connecting high-field quantum oscillations to the pseudogap in the underdoped cuprates, A. Allais, D. Chowdhury, and S. Sachdev, Nature Communications 5, 5771 (2014); arXiv:1406.0503.
  37. Diamagnetism and density wave order in the pseudogap regime of YBa2Cu3O6+x, L. E. Hayward, A. J. Achkar, D. G. Hawthorn, R. G. Melko, and S. Sachdev, Physical Review B 90, 094515 (2014); arXiv:1406.2694.
  38. Renormalization Group Analysis of a Fermionic Hot Spot Model, S. Whitsitt and S. Sachdev, Physical Review B 90, 104505 (2014); arXiv:1406.6061.
  39. Comment on "Symmetry classification of bond order parameters in cuprates", A. Allais, J. Bauer, and S. Sachdev, arXiv:1407.3281.
  40. Density wave instabilities of fractionalized Fermi liquids, D. Chowdhury and S. Sachdev, Physical Review B 90, 245136 (2014); arXiv:1409.5430.
  41. Charge ordering in three-band models of the cuprates, A. Thomson and S. Sachdev, Physical Review B 91, 115142 (2015); arXiv:1410.3483.
  42. The enigma of the pseudogap phase of the cuprate superconductors, D. Chowdhury and S. Sachdev, in Quantum Criticality in Condensed Matter: Phenomena, Materials and Ideas in Theory and Experiment: 50th Karpacz Winter School of Theoretical Physics, J. Jedrzejewski Editor, World Scientific (2015), arXiv:1501.00002
  43. Fluctuating orders and quenched randomness in the cuprates, Laimei Nie, L. E. H. Sierens, R. G. Melko, S. Sachdev, and S. A. Kivelson, Physical Review B 92, 174505 (2015); arXiv:1505.06206.
  44. Real space Eliashberg approach to charge order of electrons coupled to dynamic antiferromagnetic fluctuations, J. Bauer and S. Sachdev, Physical Review B 92, 085134 (2015); arXiv:1506.06136.
  45. Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State, M. H. Hamidian, S. D. Edkins, Chung Koo Kim, J. C. Davis, A. P. Mackenzie, H. Eisaki, S. Uchida, M. J. Lawler, E.-A. Kim, S. Sachdev, and K. Fujita, Nature Physics 12, 150 (2016); arXiv:1507.07865
  46. Magnetic-field Induced Interconversion of Cooper Pairs and Density Wave States within Cuprate Composite Order, M. H. Hamidian, S. D. Edkins, K. Fujita, A. Kostin, A. P. Mackenzie, H. Eisaki, S. Uchida, M. J. Lawler, E.-A. Kim, S. Sachdev, and J. C. Davis, arXiv:1508.00620
  47. Emergent gauge fields and the high temperature superconductors, S. Sachdev, Philosophical Transactions of the Royal Society A 374, 20150248 (2016); arXiv:1512.00465.
  48. Confinement transition to density wave order in metallic doped spin liquids, Physical Review B 93, 165139 (2016); A. A. Patel, D. Chowdhury, A. Allais, and S. Sachdev, arXiv:1602.05954.
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