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Patel AA, Guo H, Esterlis I, Sachdev S. Universal theory of strange metals from spatially random interactions. Science 2023; 381:790-793. [PMID: 37590350 DOI: 10.1126/science.abq6011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 07/17/2023] [Indexed: 08/19/2023]
Abstract
Strange metals-ubiquitous in correlated quantum materials-transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures (T), such metals generically exhibit strange metal behavior with a T-linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/T) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.
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Affiliation(s)
- Aavishkar A Patel
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY 10010, USA
- Department of Physics, University of California Berkeley, Berkeley, CA 94720, USA
| | - Haoyu Guo
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Ilya Esterlis
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
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Rao P, Piazza F. Non-Fermi-Liquid Behavior from Cavity Electromagnetic Vacuum Fluctuations at the Superradiant Transition. PHYSICAL REVIEW LETTERS 2023; 130:083603. [PMID: 36898112 DOI: 10.1103/physrevlett.130.083603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Revised: 12/09/2022] [Accepted: 02/06/2023] [Indexed: 06/18/2023]
Abstract
We study two-dimensional materials where electrons are coupled to the vacuum electromagnetic field of a cavity. We show that, at the onset of the superradiant phase transition towards a macroscopic photon occupation of the cavity, the critical electromagnetic fluctuations, consisting of photons strongly overdamped by their interaction with electrons, can in turn lead to the absence of electronic quasiparticles. Since transverse photons couple to the electronic current, the appearance of non-Fermi-Liquid behavior strongly depends on the lattice. In particular, we find that in a square lattice the phase space for electron-photon scattering is reduced in such a way to preserve the quasiparticles, while in a honeycomb lattice the latter are removed due to a nonanalytical frequency dependence of the damping ∝|ω|^{2/3}. Standard cavity probes could allow us to measure the characteristic frequency spectrum of the overdamped critical electromagnetic modes responsible for the non-Fermi-liquid behavior.
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Affiliation(s)
- Peng Rao
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Francesco Piazza
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
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3
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Grossman O, Hofmann JS, Holder T, Berg E. Specific Heat of a Quantum Critical Metal. PHYSICAL REVIEW LETTERS 2021; 127:017601. [PMID: 34270320 DOI: 10.1103/physrevlett.127.017601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 05/30/2021] [Indexed: 06/13/2023]
Abstract
We investigate the specific heat c, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where c/T is close to the value expected from the noninteracting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of c/T, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of c/T onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.
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Affiliation(s)
- Ori Grossman
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Johannes S Hofmann
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Tobias Holder
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Huang KS, Raghu S, Kumar P. Numerical Study of a Dual Representation of the Integer Quantum Hall Transition. PHYSICAL REVIEW LETTERS 2021; 126:056802. [PMID: 33605754 DOI: 10.1103/physrevlett.126.056802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
We study the critical properties of the noninteracting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality CF states are delocalized at all energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain ν=2.56±0.02 and η=0.51±0.01, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.
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Affiliation(s)
- Kevin S Huang
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - 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
| | - Prashant Kumar
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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Damia JA, Kachru S, Raghu S, Torroba G. Two-Dimensional Non-Fermi-Liquid Metals: A Solvable Large-N Limit. PHYSICAL REVIEW LETTERS 2019; 123:096402. [PMID: 31524468 DOI: 10.1103/physrevlett.123.096402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Indexed: 06/10/2023]
Abstract
Significant effort has been devoted to the study of "non-Fermi-liquid" (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point. The problem has been extensively studied in a large-N limit (N corresponding to the number of fermion flavors) where universal behavior can be obtained by solving a set of coupled saddle-point equations. However, a remarkable study by Lee revealed the breakdown of such approximations in two spatial dimensions. We show that an alternate approach, in which the fermions belong to the fundamental representation of a global SU(N) flavor symmetry, while the order parameter fields transform under the adjoint representation (a "matrix large-N" theory), yields a tractable large N limit. At low energies, the system consists of an overdamped boson with dynamical exponent z=3 coupled to a non-Fermi-liquid with self-energy Σ(ω)∼ω^{2/3}, consistent with previous studies.
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Affiliation(s)
| | - Shamit Kachru
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - Srinivas Raghu
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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Abstract
We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of [Formula: see text] species of fermions at nonzero density coupled to a [Formula: see text] gauge field in two spatial dimensions and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters; i.e., the relationship is independent of [Formula: see text], the gauge-coupling constant, the Fermi velocity, the Fermi surface curvature, and high-energy details.
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Maslov DL, Chubukov AV. Optical response of correlated electron systems. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:026503. [PMID: 28002040 DOI: 10.1088/1361-6633/80/2/026503] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Recent progress in experimental techniques has made it possible to extract detailed information on dynamics of carriers in a correlated electron material from its optical conductivity, [Formula: see text]. This review consists of three parts, addressing the following three aspects of optical response: (1) the role of momentum relaxation; (2) [Formula: see text] scaling of the optical conductivity of a Fermi-liquid metal, and (3) the optical conductivity of non-Fermi-liquid metals. In the first part (section 2), we analyze the interplay between the contributions to the conductivity from normal and umklapp electron-electron scattering. As a concrete example, we consider a two-band metal and show that although its optical conductivity is finite it does not obey the Drude formula. In the second part (sections 3 and 4), we re-visit the Gurzhi formula for the optical scattering rate, [Formula: see text], and show that a factor of [Formula: see text] is the manifestation of the 'first-Matsubara-frequency rule' for boson response, which states that [Formula: see text] must vanish upon analytic continuation to the first boson Matsubara frequency. However, recent experiments show that the coefficient b in the Gurzhi-like form, [Formula: see text], differs significantly from b = 4 in most of the cases. We suggest that the deviations from Gurzhi scaling may be due to the presence of elastic but energy-dependent scattering, which decreases the value of b below 4, with b = 1 corresponding to purely elastic scattering. In the third part (section 5), we consider the optical conductivity of metals near quantum phase transitions to nematic and spin-density-wave states. In the last case, we focus on 'composite' scattering processes, which give rise to a non-Fermi-liquid behavior of the optical conductivity at T = 0: [Formula: see text] at low frequencies and [Formula: see text] at higher frequencies. We also discuss [Formula: see text] scaling of the conductivity and show that [Formula: see text] in the same model scales in a non-Fermi-liquid way, as [Formula: see text].
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Affiliation(s)
- Dmitrii L Maslov
- Department of Physics, University of Florida, PO Box 118440, Gainesville, FL 32611-8440, USA
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Geraedts SD, Zaletel MP, Mong RSK, Metlitski MA, Vishwanath A, Motrunich OI. The half-filled Landau level: The case for Dirac composite fermions. Science 2016; 352:197-201. [DOI: 10.1126/science.aad4302] [Citation(s) in RCA: 107] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2015] [Accepted: 02/16/2016] [Indexed: 11/03/2022]
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9
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She JH, Bishop AR. RKKY interaction and intrinsic frustration in non-Fermi-liquid metals. PHYSICAL REVIEW LETTERS 2013; 111:017001. [PMID: 23863021 DOI: 10.1103/physrevlett.111.017001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2013] [Revised: 05/16/2013] [Indexed: 06/02/2023]
Abstract
We study the RKKY interaction in non-Fermi-liquid metals. We find that the RKKY interaction mediated by some non-Fermi-liquid metals can be of much longer range than for a Fermi liquid. The oscillatory nature of the RKKY interaction thus becomes more important in such non-Fermi liquids, and gives rise to enhanced frustration when the spins form a lattice. Frustration suppresses the magnetic ordering temperature of the lattice spin system. Furthermore, we find that the spin system with a longer range RKKY interaction can be described by the Brazovskii model, where the ordering wave vector lies on a higher dimensional manifold. Strong fluctuations in such a model lead to a first-order phase transition and/or glassy phase. This may explain some recent experiments where glassy behavior was observed in stoichiometric heavy fermion material close to a ferromagnetic quantum critical point.
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Affiliation(s)
- Jian-Huang She
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, 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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Faulkner T, Iqbal N, Liu H, McGreevy J, Vegh D. Holographic non-Fermi-liquid fixed points. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2011; 369:1640-1669. [PMID: 21422019 DOI: 10.1098/rsta.2010.0354] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this 'holographic duality', various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS(2)) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.
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13
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Kim KS, Pépin C. Quantum Boltzmann equation study for the Kondo breakdown quantum critical point. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:025601. [PMID: 21386259 DOI: 10.1088/0953-8984/22/2/025601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We develop the quantum Boltzmann equation approach for the Kondo breakdown quantum critical point, involved with two bands for conduction electrons and localized fermions. Particularly, the role of vertex corrections in transport is addressed, crucial for non-Fermi liquid transport with temperature linear dependence. Only one band of spinons may be considered for scattering with gauge fluctuations, and their associated vertex corrections are introduced in the usual way, where the divergence of self-energy corrections is cancelled by that of vertex corrections, giving rise to a physically meaningful result in the gauge invariant expression for conductivity. On the other hand, two bands should be taken into account for scattering with hybridization excitations, giving rise to coupled quantum Boltzmann equations. We find that vertex corrections associated with hybridization fluctuations turn out to be irrelevant due to the heavy mass of spinons in the so called decoupling limit, consistent with the diagrammatic approach showing non-Fermi liquid transport.
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Affiliation(s)
- K-S Kim
- Asia Pacific Center for Theoretical Physics, Hogil Kim Memorial Building 5th floor, POSTECH, Hyoja-dong, Namgu, Pohang 790-784, Korea.
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Podolsky D, Paramekanti A, Kim YB, Senthil T. Mott transition between a spin-liquid insulator and a metal in three dimensions. PHYSICAL REVIEW LETTERS 2009; 102:186401. [PMID: 19518891 DOI: 10.1103/physrevlett.102.186401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2008] [Indexed: 05/27/2023]
Abstract
We study a bandwidth controlled Mott metal-insulator transition (MIT) from a Fermi-liquid metal to a quantum spin-liquid insulator in three dimensions. Using a slave rotor approach including gauge fluctuations, we obtain a continuous MIT and discuss finite temperature crossovers in its vicinity. We show that the specific heat C approximately Tlnln(1/T) at the MIT and that the metallic state near the MIT should exhibit a "conductivity minimum" as a function of temperature. We suggest Na4Ir3O8 as a candidate to test our predictions and compute its electron spectral function at the MIT.
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Affiliation(s)
- Daniel Podolsky
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
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Kim KS, Pépin C. Violation of the Wiedemann-Franz law at the Kondo breakdown quantum critical point. PHYSICAL REVIEW LETTERS 2009; 102:156404. [PMID: 19518660 DOI: 10.1103/physrevlett.102.156404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2008] [Indexed: 05/27/2023]
Abstract
We study the electrical and thermal transport near the heavy-fermion quantum critical point, identified with the breakdown of the Kondo effect. We show that the electrical conductivity comes mainly from conduction electrons while the thermal conductivity is given by both conduction electrons and localized fermions (spinons), scattered with hybridization fluctuations of dynamical exponent z = 3. As a result, we reveal that not only electrical but also thermal resistivity displays quasilinear temperature dependence in the intermediate temperature range, the main prediction of our transport study. An important feature turns out to be emergence of additional entropy carriers, that is, spinon excitations. We find that the Wiedemann-Franz ratio should be larger than the standard value, differentiating the Kondo breakdown scenario from the Hertz-Moriya-Millis framework.
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Affiliation(s)
- K-S Kim
- Institut de Physique Théorique, CEA, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette, France
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Galitski V, Kim YB. Spin-triplet pairing instability of the spinon fermi surface in a U(1) spin liquid. PHYSICAL REVIEW LETTERS 2007; 99:266403. [PMID: 18233593 DOI: 10.1103/physrevlett.99.266403] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2007] [Indexed: 05/25/2023]
Abstract
Recent experiments on the organic compound kappa-(ET)2Cu2(CN)3 have provided a promising example of a two-dimensional spin liquid state. This phase is described by a two-dimensional spinon Fermi sea coupled to a U(1) gauge field. We study Kohn-Luttinger-like pairing instabilities of the spinon Fermi surface due to singular interaction processes with twice-the-Fermi-momentum transfer. We find that under certain circumstances the pairing instability occurs in odd-orbital-angular momentum or spin-triplet channels. Implications to experiments are discussed.
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Affiliation(s)
- Victor Galitski
- Department of Physics and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
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17
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Ng TK, Lee PA. Power-law conductivity inside the Mott gap: application to kappa-(BEDT-TTF)2Cu2(CN){3}. PHYSICAL REVIEW LETTERS 2007; 99:156402. [PMID: 17995193 DOI: 10.1103/physrevlett.99.156402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2007] [Indexed: 05/25/2023]
Abstract
The charge dynamics of spin-liquid states described by U(1) gauge theory coupling to fermionic spinons is discussed in this paper. We find that the gapless spinons give rise to a power-law optical conductivity inside the charge gap. The theory is applied to explain the unusual optical conductivity observed recently in the organic compound kappa-(BEDT-TTF)2Cu2(CN){3}. We also propose an optical experiment to search for the in-gap excitations in the kagome spin-liquid insulator.
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Affiliation(s)
- Tai-Kai Ng
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay Road, Kowloon, Hong Kong
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Onoda M, Ichinose I, Matsui T. Finite-temperature properties of a gauge theory of nonrelativistic fermions. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:13674-13686. [PMID: 9985282 DOI: 10.1103/physrevb.54.13674] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kim YB, Lee PA. Specific heat and validity of the quasiparticle approximation in the half-filled Landau level. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:2715-2717. [PMID: 9986121 DOI: 10.1103/physrevb.54.2715] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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21
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Zhang L. Chern-Simons field theory of two-dimensional electrons in the lowest Landau level. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:3937-3951. [PMID: 9983946 DOI: 10.1103/physrevb.53.3937] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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22
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Kim YB, Lee PA, Wen XG. Quantum Boltzmann equation of composite fermions interacting with a gauge field. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:17275-17292. [PMID: 9981158 DOI: 10.1103/physrevb.52.17275] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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23
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Kopietz P, Hermisson J, Schönhammer K. Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:10877-10896. [PMID: 9980187 DOI: 10.1103/physrevb.52.10877] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Kwon H, Houghton A, Marston JB. Theory of fermion liquids. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:8002-8027. [PMID: 9979799 DOI: 10.1103/physrevb.52.8002] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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25
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Khveshchenko DV. Geometrical approach to bosonization of D>1 dimensional (non)-Fermi liquids. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:4833-4841. [PMID: 9981666 DOI: 10.1103/physrevb.52.4833] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Stern A, Halperin BI. Singularities in the Fermi-liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:5890-5906. [PMID: 9981779 DOI: 10.1103/physrevb.52.5890] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Schofield AJ. Upper critical field in the gauge model. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:11733-11738. [PMID: 9977912 DOI: 10.1103/physrevb.51.11733] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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28
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Kim YB, Lee PA, Wen XG, Stamp PC. Influence of gauge-field fluctuations on composite fermions near the half-filled state. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:10779-10788. [PMID: 9977774 DOI: 10.1103/physrevb.51.10779] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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