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Nosov PA, Burmistrov IS, Raghu S. Interaction-Induced Metallicity in a Two-Dimensional Disordered Non-Fermi Liquid. PHYSICAL REVIEW LETTERS 2020; 125:256604. [PMID: 33416393 DOI: 10.1103/physrevlett.125.256604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2020] [Accepted: 11/24/2020] [Indexed: 06/12/2023]
Abstract
The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. Instead, we start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.
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Affiliation(s)
- P A Nosov
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - I S Burmistrov
- L.D. Landau Institute for Theoretical Physics, Akademika Semenova Avenue 1-a, 142432 Chernogolovka, Russia
- Laboratory for Condensed Matter Physics, National Research University Higher School of Economics, 101000 Moscow, Russia
| | - S Raghu
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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2
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Schäfer T, Katanin AA, Held K, Toschi A. Interplay of Correlations and Kohn Anomalies in Three Dimensions: Quantum Criticality with a Twist. PHYSICAL REVIEW LETTERS 2017; 119:046402. [PMID: 29341780 DOI: 10.1103/physrevlett.119.046402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2016] [Indexed: 06/07/2023]
Abstract
A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that-in contradiction to the conventional Hertz-Millis-Moriya theory-its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electronic correlations become strong.
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Affiliation(s)
- T Schäfer
- Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna, Austria
| | - A A Katanin
- Institute of Metal Physics, 620990, Kovalevskaya str. 18, Ekaterinburg, Russia and Ural Federal University, Mira str. 19, 620002 Ekaterinburg, Russia
| | - K Held
- Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna, Austria
| | - A Toschi
- Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna, Austria
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Wang Y, Abanov A, Altshuler BL, Yuzbashyan EA, Chubukov AV. Superconductivity near a Quantum-Critical Point: The Special Role of the First Matsubara Frequency. PHYSICAL REVIEW LETTERS 2016; 117:157001. [PMID: 27768346 DOI: 10.1103/physrevlett.117.157001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2016] [Indexed: 06/06/2023]
Abstract
Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconducting T_{c} is nonzero even for strong incoherence and/or weak interaction due to the fact that the self-energy from dynamic critical fluctuations vanishes for the two lowest fermionic Matsubara frequencies ω_{m}=±πT. We obtain the analytic formula for T_{c}, which reproduces well earlier numerical results for the electron-phonon model at vanishing Debye frequency.
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Affiliation(s)
- Yuxuan Wang
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Artem Abanov
- Department of Physics, Texas A&M University, College Station, Texas 77843, USA
| | - Boris L Altshuler
- Department of Physics, Columbia University, New York, New York 10027, USA
| | - Emil A Yuzbashyan
- Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Andrey V Chubukov
- School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
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Wang Y, Chubukov AV. Superconductivity at the onset of spin-density-wave order in a metal. PHYSICAL REVIEW LETTERS 2013; 110:127001. [PMID: 25166835 DOI: 10.1103/physrevlett.110.127001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2012] [Indexed: 06/03/2023]
Abstract
We revisit the issue of superconductivity at the quantum-critical point (QCP) between a 2D paramagnet and a spin-density-wave metal with ordering momentum (π, π). This problem is highly nontrivial because the system at criticality displays a non-Fermi-liquid behavior and because the effective coupling constant λ for the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)] has found that the renormalizations of the pairing vertex are stronger than in BCS theory and hold in powers of log(2)(1/T). We analyze the full gap equation and argue that summing up of the leading logarithms does not lead to a pairing instability. Yet, we show that superconductivity has no threshold and appears even if λ is set to be small, because subleading logarithmical renormalizations diverge and give rise to a BCS-like result log1/T(c) ∝ 1/λ. We argue that the analogy with BCS is not accidental as at small λ superconductivity at a QCP predominantly comes from fermions that retain Fermi-liquid behavior at criticality. We compute T(c) for the actual λ ∼ O(1), and find that both Fermi-liquid and non-Fermi-liquid fermions contribute to the pairing.
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Affiliation(s)
- Yuxuan Wang
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Andrey V Chubukov
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Abstract
Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an X-ray diffraction study of the charge density wave (CDW) in 2H-NbSe(2) at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase; and in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the long-standing expectations of enhanced quantum fluctuations in low-dimensional systems, and may help to constrain theories of the quantum critical Fermi surface.
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Chubukov AV, Khveshchenko DV. Effect of fermi surface curvature on low-energy properties of fermions with singular interactions. PHYSICAL REVIEW LETTERS 2006; 97:226403. [PMID: 17155821 DOI: 10.1103/physrevlett.97.226403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2006] [Indexed: 05/12/2023]
Abstract
We discuss the effect of Fermi surface curvature on long-distance or time asymptotic behaviors of two-dimensional fermions interacting via a gapless mode described by an effective gauge-field-like propagator. By comparing the predictions based on the idea of multidimensional bosonization with those of the strong-coupling Eliashberg approach, we demonstrate that an agreement between the two requires a further extension of the former technique.
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Affiliation(s)
- A V Chubukov
- Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
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Krotkov P, Chubukov AV. Non-fermi liquid and pairing in electron-doped cuprates. PHYSICAL REVIEW LETTERS 2006; 96:107002. [PMID: 16605777 DOI: 10.1103/physrevlett.96.107002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2005] [Indexed: 05/08/2023]
Abstract
We study the normal state and pairing instability in electron-doped cuprates in a model with long-ranged antiferromagnetic spin fluctuations close to an antiferromagnetic quantum-critical point. We show that the fermionic self-energy has a non-Fermi-liquid form leading to peculiar frequency dependencies of the conductivity and the Raman response. We solve the pairing problem and demonstrate that T(c) is determined by the curvature of the Fermi surface, and the pairing gap delta (kappa, omega) is strongly nonmonotonic along the Fermi surface. The normal state frequency dependencies, the value of T(c) is approximately 10 K, and the kappa dependence of the gap agree with the experiment.
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Affiliation(s)
- P Krotkov
- Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, 20742, USA
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Maebashi H, Miyake K, Varma CM. Undressing the Kondo effect near the antiferromagnetic quantum critical point. PHYSICAL REVIEW LETTERS 2005; 95:207207. [PMID: 16384097 DOI: 10.1103/physrevlett.95.207207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2005] [Indexed: 05/05/2023]
Abstract
The problem of a spin-1/2 magnetic impurity near an antiferromagnetic transition of the host lattice is shown to transform to a multichannel problem. A variety of fixed points is discovered asymptotically near the antiferromagnetic critical point. Among these is a new variety of stable fixed point of a multichannel Kondo problem which does not require channel isotropy. At this point Kondo screening disappears but coupling to spin fluctuations remains. In addition to its intrinsic interest, the problem is an essential ingredient in the problem of quantum critical points in heavy fermions.
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Affiliation(s)
- H Maebashi
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
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Chubukov AV, Pépin C, Rech J. Instability of the quantum-critical point of itinerant ferromagnets. PHYSICAL REVIEW LETTERS 2004; 92:147003. [PMID: 15089567 DOI: 10.1103/physrevlett.92.147003] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2003] [Indexed: 05/24/2023]
Abstract
We study the stability of the quantum-critical point for itinerant ferromagnets commonly described by the Hertz-Millis-Moriya (HMM) theory. We argue that in D</=3 long-range spatial correlations associated with the Landau damping of the order parameter field generate a universal negative, nonanalytic |q|((D+1)/2) contribution to the static magnetic susceptibility chi(s)(q,0), which makes HMM theory unstable. We argue that the actual transition is either towards incommensurate ordering, or first order. We also show that singular corrections are specific to the spin problem, while charge susceptibility remains analytic at criticality.
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Affiliation(s)
- Andrey V Chubukov
- Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706-1390, USA
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Chubukov AV, Finkel'stein AM, Haslinger R, Morr DK. First-order superconducting transition near a ferromagnetic quantum critical point. PHYSICAL REVIEW LETTERS 2003; 90:077002. [PMID: 12633265 DOI: 10.1103/physrevlett.90.077002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2002] [Indexed: 05/24/2023]
Abstract
We address the issue of how triplet superconductivity emerges in an electronic system near a ferromagnetic quantum critical point (FQCP). Previous studies found that the superconducting transition is of second order, and T(c) is strongly reduced near the FQCP due to pair-breaking effects from thermal spin fluctuations. In contrast, we demonstrate that near the FQCP, the system avoids pair-breaking effects by undergoing a first order transition at a much larger T(c). A second order superconducting transition emerges only at some distance from the FQCP.
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Affiliation(s)
- Andrey V Chubukov
- Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA
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Caprara S, Di Castro C, Werner P, Zwerger W. Vertex corrections near the stripe phase. PHYSICAL REVIEW LETTERS 2002; 88:066403. [PMID: 11863830 DOI: 10.1103/physrevlett.88.066403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2001] [Indexed: 05/23/2023]
Abstract
We calculate the vertex corrections within a model for fermion quasiparticles coupled with charge and spin fluctuations, which provide the relevant scattering mechanism near the stripe instability in high- T(c) cuprates. The logarithmic divergence of the vertex, which characterizes the spin-fermion model near the antiferromagnetic instability, is ruled out, due to the incommensuration of the charge and spin modulation within the stripe phase, as revealed by neutron scattering. This simplifies the skeleton structure of the problem. The vertex is negative in the relevant kinematical regime, effectively reducing the interaction strength. Our results apply to generic incommensurate instabilities of electronic origin.
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Affiliation(s)
- S Caprara
- Dipartimento di Fisica, Università di Roma "La Sapienza" and Istituto Nazionale per la Fisica della Materia, SMC and UdR Roma 1, Piazzale Aldo Moro 2, 00185 Roma, Italy
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Buhler C, Yunoki S, Moreo A. Magnetic domains and stripes in a spin-fermion model for cuprates. PHYSICAL REVIEW LETTERS 2000; 84:2690-2693. [PMID: 11017301 DOI: 10.1103/physrevlett.84.2690] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/1999] [Indexed: 05/23/2023]
Abstract
Monte Carlo simulations applied to a model of interacting fermions and classical spins show the existence of antiferromagnetic spin domains and charge stripes upon hole doping. The stripes have a filling of approximately 1/2 hole per site, and they separate spin domains with a pi phase shift among them. The observed stripes run either along the x or y axes. No particular boundary conditions or external fields are needed to stabilize these structures. When magnetic incommensurate peaks are observed at momentum pi(1,1-delta), charge incommensurate peaks appear at (0,2delta). The charge fluctuations responsible for the stripe formation also induce a pseudogap in the density of states.
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Affiliation(s)
- C Buhler
- Department of Physics, National High Magnetic Field Lab and MARTECH, Florida State University, Tallahassee, Florida 32306, USA
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Perali A, Castellani C, Grilli M. d-wave superconductivity near charge instabilities. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16216-16225. [PMID: 9985700 DOI: 10.1103/physrevb.54.16216] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ioffe LB, Millis AJ. Effect of van Hove singularities on a spin liquid. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:3645-3654. [PMID: 9986273 DOI: 10.1103/physrevb.54.3645] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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