# SIMES Publications

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**"Enhanced Thermal Hall Effect in Nearly Ferroelectric Insulators"** — Jing-Yuan Chen: Steven A. Kivelson and Xiao-Qi Sun; Physical Review Letters, 04/21/20.

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Steven A. Kivelson and Xiao-Qi Sun

**Abstract**

In the context of recent experimental observations of an unexpectedly large thermal Hall conductivity, *κ*_{H}, in insulating La_{2}CuO_{4} (LCO) and SrTiO_{3} (STO), we theoretically explore conditions under which acoustic phonons can give rise to such a large *κ*_{H}. Both the intrinsic and extrinsic contributions to *κ*_{H} are large in proportion to the dielectric constant, ε, and the “flexoelectric” coupling, F. While the intrinsic contribution is still orders of magnitude smaller than the observed effect, an extrinsic contribution proportional to the phonon mean-free path appears likely to account for the observations, at least in STO. We predict a larger intrinsic *κ*_{H} in certain insulating perovskites.

**"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.

**"Disorder-induced suppression of charge density wave order: STM study of Pd-intercalated ErTe**_{3"} — Alan Fang: Joshua A. W. Straquadine, Ian R. Fisher, Steven A. Kivelson, and Aharon Kapitulnik; Physical Review B, 12/24/19.

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Joshua A. W. Straquadine, Ian R. Fisher, Steven A. Kivelson, and Aharon Kapitulnik

**Abstract**

Pd-intercalated ErTe_{3} is studied as a model system to explore the effect of increasing disorder on an incommensurate two-component charge density wave (CDW). The ordering vectors of the CDW components lie along the two in-plane principal axes of the nearly tetragonal crystal structure. Using scanning tunneling microscopy (STM), we show that introducing Pd intercalants (i.e., disorder) induces CDW dislocations, which appear to be associated with each CDW component separately. Increasing Pd concentration has a stronger effect on the secondary CDW order, manifested in a higher density of dislocations, and thus increases the anisotropy (nematic character) of the CDW. Suggestive evidence of Bragg glass phases at weak disorder is also discussed.

**"Observation of two types of charge-density-wave orders in superconducting La**_{2-x}Sr_{x}CuO_{4"} — J.-J. Wen: H. Huang, S.-J. Lee, H. Jang, J. Knight, Y.S. Lee, M. Fujita, K.M. Suzuki, S. Asano, S.A. Kivelson, C.-C. Kao & J.-S. Lee; Nature Communications, 07/22/19.

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H. Huang, S.-J. Lee, H. Jang, J. Knight, Y.S. Lee, M. Fujita, K.M. Suzuki, S. Asano, S.A. Kivelson, C.-C. Kao & J.-S. Lee

**Abstract**

The discovery of charge- and spin-density-wave (CDW/SDW) orders in superconducting cuprates has altered our perspective on the nature of high-temperature superconductivity (SC). However, it has proven difﬁcult to fully elucidate the relationship between the density wave orders and SC. Here, using resonant soft X-ray scattering, we study the archetypal cuprate La_{2-x}Sr_{x}CuO_{4} (LSCO) over a broad doping range. We reveal the existence of two types of CDW orders in LSCO, namely CDW stripe order and CDW short-range order (SRO). While the CDW-SRO is suppressed by SC, it is partially transformed into the CDW stripe order with developing SDW stripe order near the superconducting T_{c}. These ﬁndings indicate that the stripe orders and SC are inhomogeneously distributed in the superconducting CuO_{2} planes of LSCO. This further suggests a new perspective on the putative pair-density-wave order that coexists with SC, SDW, and CDW orders.

**"Pseudo-gap crossover in the electron-phonon system"** — I. Esterlis: S. A. Kivelson, and D. J. Scalapino; Physical Review B, 05/24/19.

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S. A. Kivelson, and D. J. Scalapino

**Abstract**

Thermodynamic properties of the square-lattice Holstein model of the electron-phonon problem with phonon frequencies small compared to the bare Fermi energy are obtained using Monte Carlo methods, a strong-coupling (bipolaronic) expansion, and a weak-coupling Migdal-Eliashberg approach. Already at elevated temperatures where the charge-density wave (CDW) and superconducting (SC) correlations are very short range, a crossover occurs as a function of increasing electron-phonon coupling, λ_{0}, from a normal metallic regime to a pseudogap regime. At sufficiently low *T*, a SC phase is found for small λ_{0} and a commensurate insulating CDW phase for large λ_{0}.

**"Fragile superconductivity in the presence of weakly disordered charge density waves"** — Yue Yu: S. A. Kivelson; Physical Review B, 04/06/19.

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S. A. Kivelson

**Abstract**

When superconducting (SC) and charge-density-wave (CDW) orders compete, novel low-temperature behaviors can result. From an analysis of the Landau-Ginzburg-Wilson theory of competing orders, we demonstrate the generic occurrence of a “fragile” SC phase at low temperatures and high fields in the presence of weak disorder. Here, the SC order is largely concentrated in the vicinity of dilute dislocations in the CDW order, leading to transition temperatures and critical currents that are parametrically smaller than those characterizing the zero-field SC phase. This may provide the outline of an explanation of the recently discovered “resilient” superconducting phase at high fields in underdoped YBa_{2}Cu_{3}O_{6+}_{δ}.

**"Colloquium: Anomalous metals: Failed superconductors"** — Aharon Kapitulnik: Steven A. Kivelson, Boris Spivak; Reviews of Modern Physics, 01/28/19.

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Steven A. Kivelson, Boris Spivak

**Abstract**

The observation of metallic ground states in a variety of two-dimensional electronic systems poses a fundamental challenge for the theory of electron fluids. Here evidence is analyzed for the existence of a regime, called the “anomalous metal regime,” in diverse 2D superconducting systems driven through a quantum superconductor to metal transition by tuning physical parameters such as the magnetic field, the gate voltage in the case of systems with a metal-oxide semiconductor field-effect transistor (MOSFET) geometry, or the degree of disorder. The principal phenomenological observation is that in the anomalous metal, as a function of decreasing temperature, the resistivity first drops as if the system were approaching a superconducting ground state, but then saturates at low temperatures to a value that can be orders of magnitude smaller than the Drude value. The anomalous metal also shows a giant positive magnetoresistance. Thus, it behaves as if it were a “failed superconductor.” This behavior is observed in a broad range of parameters. It will be moreover exhibited, by theoretical solution of a model of superconducting grains embedded in a metallic matrix, that as a matter of principle such anomalous metallic behavior can occur in the neighborhood of a quantum superconductor to metal transition. However, it will be also argued that the robustness and ubiquitous nature of the observed phenomena are difficult to reconcile with any existing theoretical treatment and speculate about the character of a more fundamental theoretical framework.

**"A bound on the superconducting transition temperature"** — I. Esterlis: S. A. Kivelson and D. J. Scalapino; npj Quantum Materials, 11/19/18.

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S. A. Kivelson and D. J. Scalapino

**Abstract**

It is notoriously difficult to make quantitative theoretical predictions of the superconducting transition temperature, *T*_{c}, either from first-principles or even from a knowledge of normal state properties. Ultimately, this reflects the fact that the energy scales involved in the superconducting state are extremely small in natural units, and that *T*_{c} depends exponentially on a subtle interplay between different interactions so that small uncertainties in microscopic processes can lead to order one effects on *T*_{c}. However, in some circumstances, it may be possible to determine (approximate) bounds on *T*_{c}. Here we propose such a bound for the conventional phonon-mediated mechanism of pairing with strongly retarded interactions, i.e. in the case in which ℏ*ω*¯≪*E*_{F}, where *ω*¯ is an appropriate characteristic phonon frequency and *E*_{F} is the Fermi energy. Specifically, drawing on both empirical results (shown in Fig. 2 below) and recent results^{1} of determinant quantum Monte Carlo (DQMC) studies of the paradigmatic Holstein model, we propose that *k*_{B}T_{c}≤*A*_{max}ℏ*ω*¯, where *A*_{max} is a dimensionless number of order one that we estimate to be *A*_{max} ≈ 1/10.

**"Generalization of Anderson's theorem for disordered superconductors"** — John F. Dodaro: Steven A. Kivelson; Physical Review B, 11/14/18.

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Steven A. Kivelson

**Abstract**

We show that at the level of BCS mean-field theory, the superconducting *T*_{c} is always increased in the presence of disorder, regardless of order parameter symmetry, disorder strength, and spatial dimension. This result reflects the physics of rare events—formally analogous to the problem of Lifshitz tails in disordered semiconductors—and arises from considerations of spatially inhomogeneous solutions of the gap equation. So long as the clean-limit superconducting coherence length, ξ0, is large compared to disorder correlation length, *a*, when fluctuations about mean-field theory are considered, the effects of such rare events are small (typically exponentially in [ξ0/a]^{d}); however, when this ratio is ∼1, these considerations are important. The linearized gap equation is solved numerically for various disorder ensembles to illustrate this general principle.