# SIMES Publications

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**"Disruption of quantum oscillations by an incommensurate charge density wave"** — Yi Zhang: Akash V. Maharaj, and Steven Kivelson; Phys. Rev. B 91, 02/09/2015.

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Akash V. Maharaj, and Steven Kivelson

**Abstract**

Because a material with an incommensurate charge density wave (ICDW) is only quasiperiodic, Bloch’s theorem does not apply and there is no sharply defined Fermi surface. We will show that, as a consequence, there are no quantum oscillations which are truly periodic functions of 1/*B* (where *B* is the magnitude of an applied magnetic field). For a weak ICDW, there exist broad ranges of 1/*B* in which approximately periodic variations occur, but with frequencies that vary inexorably in an unending cascade with increasing 1/*B* . For a strong ICDW, e.g., in a quasicrystal, no quantum oscillations survive at all. Rational and irrational numbers really are different.

**"Dispersive charge density wave excitations in Bi**_{2}Sr_{2}CaCu_{2}O_{8+δ}" — L. Chaix: G. Ghiringhelli, Y. Y. Peng, M. Hashimoto, B. Moritz, K. Kummer, N. B. Brookes, Y. He, S. Chen, S. Ishida, Y. Yoshida, H. Eisaki, M. Salluzzo, L. Braicovich, Z.-X. Shen, T. P. Devereaux & W.-S. Lee; Nature Physics, 06/12/17.

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G. Ghiringhelli, Y. Y. Peng, M. Hashimoto, B. Moritz, K. Kummer, N. B. Brookes, Y. He, S. Chen, S. Ishida, Y. Yoshida, H. Eisaki, M. Salluzzo, L. Braicovich, Z.-X. Shen, T. P. Devereaux & W.-S. Lee

**Abstract**

Experimental evidence on high-*T*c cuprates reveals ubiquitous charge density wave (CDW) modulations^{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, which coexist with superconductivity. Although the CDW had been predicted by theory^{11, 12, 13}, important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap^{10, 14}. Here, we use ultrahigh-resolution resonant inelastic X-ray scattering to reveal new CDW character in underdoped Bi2.2Sr1.8Ca0.8Dy0.2Cu2O8+*δ*. At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature *T*^{∗}, the CDW persists, but the associated excitations significantly weaken with an indication of CDW wavevector shift. The dispersive CDW excitations, phonon anomaly, and analysis of the CDW wavevector provide a comprehensive momentum-space picture of complex CDW behaviour and point to a closer relationship with the pseudogap state.

**"Ideal charge-density-wave order in the high-field state of superconducting YBCO"** — H. Jang: W.-S. Lee, H. Nojiri, S. Matsuzawa, H. Yasumura, L. Nie, A. V. Maharaj, S. Gerber, Y.-J. Liu, A. Mehta, D. A. Bonn, R. Liang, W. N. Hardy, C. A. Burns, Z. Islam, S. Song, J. Hastings, T. P. Devereaux, Z.-X. Shen, S. A. Kivelson, C.-C. Kao, D. Zhu, and J.-S. Lee; Proceedings of the National Academy of Sciences, 12/20/16.

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W.-S. Lee, H. Nojiri, S. Matsuzawa, H. Yasumura, L. Nie, A. V. Maharaj, S. Gerber, Y.-J. Liu, A. Mehta, D. A. Bonn, R. Liang, W. N. Hardy, C. A. Burns, Z. Islam, S. Song, J. Hastings, T. P. Devereaux, Z.-X. Shen, S. A. Kivelson, C.-C. Kao, D. Zhu, and J.-S. Lee

**Abstract**

The existence of charge-density-wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the CDW ground state has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to only a dozen unit cells or less. Here we explore the field-induced 3D CDW correlations in extremely pure detwinned crystals of YBa_{2}Cu_{3}O_{2} (YBCO) ortho-II and ortho-VIII at magnetic fields in excess of the resistive upper critical field (Hc2Hc2) where superconductivity is heavily suppressed. We observe that the 3D CDW is unidirectional and possesses a long in-plane correlation length as well as significant correlations between neighboring CuO_{2}planes. It is significant that we observe only a single sharply defined transition at a critical field proportional to Hc2Hc2, given that the field range used in this investigation overlaps with other high-field experiments including quantum oscillation measurements. The correlation volume is at least two to three orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground state of an “ideal” disorder-free cuprate.

**"Ising Nematic Quantum Critical Point in a Metal: A Monte Carlo Study"** — Yoni Schattner: Samuel Lederer, Steven A. Kivelson, and Erez Berg; American Physical Society, 08/23/16.

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Samuel Lederer, Steven A. Kivelson, and Erez Berg

**Abstract**

The Ising nematic quantum critical point associated with the zero-temperature transition from a symmetric to a nematic metal is an exemplar of metallic quantum criticality. We carry out a minus-sign-free quantum Monte Carlo study of this quantum critical point for a two-dimensional lattice model with sizes up to 24×24 sites. For the parameters in this study, some (but not all) correlation functions exhibit scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance, and the system remains nonsuperconducting down to the lowest accessible temperatures. The observed scaling behavior has remarkable similarities to recently measured properties of the Fe-based superconductors proximate to their putative nematic quantum critical point.

**"Cold-spots and glassy nematicity in underdoped cuprates"** — Kyungmin Lee: Steven A. Kivelson, and Eun-Ah Kim; Physical Review B, 07/11/16.

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Steven A. Kivelson, and Eun-Ah Kim

**Abstract**

There is now copious direct experimental evidence of various forms of (short-range) charge order in underdoped cuprate high temperature superconductors, and spectroscopic signatures of a nodal-antinodal dichotomy in the structure of the single-particle spectral functions. In this context we analyze the Bogoliubov quasiparticle spectrum in a superconducting nematic glass. The coincidence of the superconducting “nodal points” and the nematic “cold-spots” on the Fermi surface naturally accounts for many of the most salient features of the measured spectral functions (from angle-resolved photoemission) and the local density of states (from scanning tunneling microscopy).

**"Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors"** — Hsueh-Hui Kuo: Jiun-Haw Chu, Johanna C. Palmstrom, Steven A. Kivelson, Ian R. Fisher; Science , 05/20/16.

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Jiun-Haw Chu, Johanna C. Palmstrom, Steven A. Kivelson, Ian R. Fisher

**Abstract**

## Discerning the nematic connection

The phase diagram of any given family of iron-based superconductors is complicated: Superconductivity competes with antiferromagnetism, with a structural transition often thrown in for good measure. Transport experiments have shown that in one of these families, Ba(Fe1-*x*Cox)2As2, a rotational electronic asymmetry, dubbed nematicity, drives the structural transition. Kuo *et al.* detected nematic fluctuations in five Fe-based superconductor families in the vicinity of optimal chemical doping: the doping that maximizes the superconducting transition temperature. Thus, nematicity may play a role in the mechanism of superconductivity in these compounds.

**"Electronic pair binding and Hund's rule violations in doped C**_{60"} — Hong-Chen Jiang: Steven Kivelson; Physical Review B, 04/05/16.

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Steven Kivelson

**Abstract**

We calculate the electronic properties of the *t**−**J* model on a C_{60} molecule using the density-matrix renormalization group and show that Hund’s first rule is violated and that for an average of three added electrons per molecule, an effective attraction (pair binding) arises for intermediate values of *t**/**J*. Specifically, it is energetically favorable to put four electrons on one C_{60} and two on a second rather than putting three on each. Our results show that a dominantly electronic mechanism of superconductivity is possible in doped C_{60}.

**"Quantum oscillations in a bilayer with broken mirror symmetry: A minimal model for YBa**_{2}Cu_{3}O_{6+δ"} — Akash V. Maharaj: Yi Zhang, B. J. Ramshaw, and S. A. Kivelson; Physical Review B, 03/01/16.

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Yi Zhang, B. J. Ramshaw, and S. A. Kivelson

**Abstract**

Using an exact numerical solution and semiclassical analysis, we investigate quantum oscillations (QOs) in a model of a bilayer system with an anisotropic (elliptical) electron pocket in each plane. Key features of QO experiments in the high temperature superconducting cuprate YBCO can be reproduced by such a model, in particular the pattern of oscillation frequencies (which reflect “magnetic breakdown” between the two pockets) and the polar and azimuthal angular dependence of the oscillation amplitudes. However, the requisite magnetic breakdown is possible only under the assumption that the horizontal mirror plane symmetry is spontaneously broken and that the bilayer tunneling t⊥ is substantially renormalized from its ‘bare’ value. Under the assumption that *t*_{⊥}=˜*Z**t*_{⊥}^{(o)}, where ˜Z is a measure of the quasiparticle weight, this suggests that ˜Z≲1/20. Detailed comparisons with new YBa_{2}Cu_{3}O_{6.58} QO data, taken over a very broad range of magnetic field, confirm specific predictions made by the breakdown scenario.

**"Critical spin fluctuations and the origin of nematic order in Ba(Fe**_{1−x}Co_{x})_{2}As_{2}" — F. Kretzschmar: T. Böhm, U. Karahasanović, B. Muschler, A. Baum, D. Jost, J. Schmalian, S. Caprara, M. Grilli, C. Di Castro, J. G. Analytis, J.-H. Chu, I. R. Fisher & R. Hackl; Nature Physics, 01/25/16.

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T. Böhm, U. Karahasanović, B. Muschler, A. Baum, D. Jost, J. Schmalian, S. Caprara, M. Grilli, C. Di Castro, J. G. Analytis, J.-H. Chu, I. R. Fisher & R. Hackl

**Abstract**

Nematic fluctuations and order play a prominent role in material classes such as the cuprates^{1}, some ruthenates^{2} or the iron-based compounds^{3, 4, 5, 6} and may be interrelated with superconductivity^{7, 8, 9, 10, 11}. In iron-based compounds^{12} signatures of nematicity have been observed in a variety of experiments. However, the fundamental question as to the relevance of the related spin^{13}, charge^{9, 14} or orbital^{8, 15, 16} fluctuations remains open. Here, we use inelastic light (Raman) scattering and study Ba(Fe1−*x*Co*x*)2As2 (0 ≤ *x* ≤ 0.085) for getting direct access to nematicity and the underlying critical fluctuations with finite characteristic wavelengths^{17, 18, 19, 20, 21}. We show that the response from fluctuations appears only in B1g (*x*^{2} − *y*^{2}) symmetry (1 Fe unit cell). The scattering amplitude increases towards the structural transition at *T*s but vanishes only below the magnetic ordering transition at *T*SDW < *T*s, suggesting a magnetic origin of the fluctuations. The theoretical analysis explains the selection rules and the temperature dependence of the fluctuation response. These results make magnetism the favourite candidate for driving the series of transitions.

**"Vestigial chiral and charge orders from bidirectional spin-density waves: Application to the iron-based superconductors"** — R. M. Fernandes: S. A. Kivelson, and E. Berg; Physical Review B, 01/19/16.

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**Additional Authors**

S. A. Kivelson, and E. Berg

**Abstract**

Recent experiments in optimally hole-doped iron arsenides have revealed a novel magnetically ordered ground state that preserves tetragonal symmetry, consistent with either a charge-spin density wave (CSDW), which displays a nonuniform magnetization, or a spin-vortex crystal (SVC), which displays a noncollinear magnetization. Here we show that, similarly to the partial melting of the usual stripe antiferromagnet into a nematic phase, either of these phases can also melt in two stages. As a result, intermediate paramagnetic phases with vestigial order appears: a checkerboard charge density wave for the CSDW ground state, characterized by an Ising-like order parameter, and a remarkable spin-vorticity density wave for the SVC ground state—a triplet *d*-density wave characterized by a vector chiral order parameter. We propose experimentally detectable signatures of these phases, show that their fluctuations can enhance the superconducting transition temperature, and discuss their relevance to other correlated materials