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1. Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions

   https://doi.org/10.21468/SciPostPhys.13.3.060  

   Yang, Luhang ; Weinberg, Phillip ; Feiguin, Adrian ( January 2022 , SciPost Physics)

   We study a generalized quantum spin ladder with staggered long rangeinteractions that decay as a power-law with exponent \alpha α .Using large scale quantum Monte Carlo (QMC) and density matrixrenormalization group (DMRG) simulations, we show that this modelundergoes a transition from a rung-dimer phase characterized by anon-local string order parameter, to a symmetry broken N'eel phase. Wefind evidence that the transition is second order. In the magneticallyordered phase, the spectrum exhibits gapless modes, while excitations inthe gapped phase are well described in terms of triplons – bound statesof spinons across the legs. We obtain the momentum resolved spin dynamicstructure factor numerically and find a well defined triplon band thatevolves into a gapless magnon dispersion across the transition. Wefurther discuss the possibility of deconfined criticality in thismodel.
2. Valence transition model of the pseudogap, charge order, and superconductivity in electron-doped and hole-doped copper oxides

   https://doi.org/DOI: 10.1103/PhysRevB.98.205153  

   Mazumdar, S. ( October 2018 , Physical review. B, Condensed matter)

   We present a valence transition model for electron- and hole-doped cuprates, within which there occurs a discrete jump in ionicity Cu2+ -> Cu1+ in both families upon doping, at or near optimal doping in the conventionally prepared electron-doped compounds and at the pseudogap phase transition in the hole-doped materials. In thin films of the T' compounds, the valence transition has occurred already in the undoped state. The phenomenology of the valence transition is closely related to that of the neutral-to-ionic transition in mixed-stack organic charge-transfer solids. Doped cuprates have negative charge-transfer gaps, just as rare-earth nickelates and BaBiO3. The unusually high ionization energy of the closed shell Cu1+ ion, taken together with the dopingdriven reduction in three-dimensional Madelung energy and gain in two-dimensional delocalization energy in the negative charge transfer gap state drives the transition in the cuprates. The combined effects of strong correlations and small d-p electron hoppings ensure that the systems behave as effective 1/2-filled Cu band with the closed shell electronically inactive O2- ions in the undoped state, and as correlated two-dimensional geometrically frustrated 1/4-filled oxygen hole band, now with electronically inactive closed-shell Cu1+ ions, in the doped state. The model thus gives microscopic justification for themore »two-fluid models suggested by many authors. The theory gives the simplest yet most comprehensive understanding of experiments in the normal states. The robust commensurate antiferromagnetism in the conventional T' crystals, the strong role of oxygen deficiency in driving superconductivity and charge carrier sign corresponding to holes at optimal doping are all manifestations of the same quantum state. In the hole-doped pseudogapped state, there occurs a biaxial commensurate period 4 charge density wave state consisting of O1- -Cu l(1+)-O1- spin singlets that coexists with broken rotational C-4 symmetry due to intraunit cell oxygen inequivalence. Finite domains of this broken symmetry state will exhibit twodimensional chirality and the polar Kerr effect. Superconductivity within the model results from a destabilization of the 1/4-filled band paired Wigner crystal [Phys. Rev. B 93, 165110 (2016) and ihid. 93, 205111 (2016)]. We posit that a similar valence transition, Ir4+ -> Ir3+, occurs upon electron doping Sr2IrO4. We make testable experimental predictions in cuprates including superoxygenated La2CuO4+delta and iridates. Finally, as indirect evidence for the valence bond theory of superconductivity proposed here, we note that there exist an unusually large number of unconventional superconductors that exhibit superconductivity proximate to exotic charge ordered states, whose band fillings are universally 1/4 or 3/4, exactly where the paired Wigner crystal is most stable.« less
3. Generic character of charge and spin density waves in superconducting cuprates

   https://doi.org/10.1073/pnas.2119429119  

   Lee, Sangjun ; Huang, Edwin W. ; Johnson, Thomas A. ; Guo, Xuefei ; Husain, Ali A. ; Mitrano, Matteo ; Lu, Kannan ; Zakrzewski, Alexander V. ; de la Peña, Gilberto A. ; Peng, Yingying ; et al ( April 2022 , Proceedings of the National Academy of Sciences)

   Charge density waves (CDWs) have been observed in nearly all families of copper-oxide superconductors. But the behavior of these phases across different families has been perplexing. In La-based cuprates, the CDW wavevector is an increasing function of doping, exhibiting the so-called Yamada behavior, while in Y- and Bi-based materials the behavior is the opposite. Here, we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched La 1.8 − x Eu 0.2 Sr x CuO 4 over a range of doping 0.07 ≤ x ≤ 0.20 . We find that the CDW amplitude is temperature independent and develops well above experimentally accessible temperatures. Further, the CDW wavevector shows a nonmonotonic temperature dependence, exhibiting Yamada behavior at low temperature with a sudden change occurring near the spin ordering temperature. We describe these observations using a Landau–Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and spin-CDW coupling. Extrapolating to high temperature, where the CDW amplitude is small and spin order is absent, our analysis predicts a decreasing wavevector with doping, similar to Y and Bi cuprates. Our study suggests that CDW order in allmore »families of cuprates forms by a common mechanism.« less
4. Pair-density-wave in the strong coupling limit of the Holstein-Hubbard model

   https://doi.org/10.1038/s41535-022-00426-w  

   Huang, Kevin S. ; Han, Zhaoyu ; Kivelson, Steven A. ; Yao, Hong ( February 2022 , npj Quantum Materials)

   A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effectivet-J-Vmodel, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around theKand$${K}^{\prime}$$$K^{\prime }$points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central chargec ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.
5. Weyl Fermions and broken symmetry phases of laterally confined ³ He films

   https://doi.org/10.1088/1361-648X/acf42b  

   Wu, Hao ; Sauls, J. A. ( September 2023 , Journal of Physics: Condensed Matter)

   Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)³He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,$L_z=(N/2)\hslash$, for$N/2$Cooper pairs. The power law suppression of the angular momentum,$L_z(T)\simeq (N/2)\hslash [1-\frac{2}{3}(\pi T/\mathrm{\Delta }{)}^2]$for$0⩽T\ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid³He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at$D_{c2}\sim 16{\xi }_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length$D\to D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, butmore »is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at$D_{c1}\sim 9{\xi }_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

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