Anisotropic non-Fermi liquids

Sur, Shouvik; Lee, Sung-Sik

doi:10.1103/physrevb.94.195135

Cited by 29 publications

(22 citation statements)

References 76 publications

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“…We stress that our emergent anisotropic non-Fermiliquid fixed point is distinct from previously studied non-Fermi-liquid fixed points. Our fixed point is in 3d in sharp contrast to most of the previously studied fixed points including the very nice work by Sur and Lee where anisotropic non-Fermi liquid below 3d was found [37]. In 3d, quantum fluctuations are typically marginal or even irrelevant, so quasi-particles are usually welldefined.…”

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confidence: 54%

Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions

et al. 2019

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Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excitation in three spatial dimensions. Using the standard renormalization group methods, large N f theory and the = 4 − d method with fermion flavor number N f and spatial dimension d, we obtain the anomalous dimensions of electrons (η f = 0.366/N f ) in large N f theory and the associated anisotropic scaling relations of various physical observables. Our results may be observed in candidate materials for DWSMs such as HgCr2Se4 or SrSi2 when the system undergoes a TQPT.Introduction. -Quantum criticality and topology play key roles in modern condensed matter physics [1][2][3][4][5], and the two concepts become naturally important near TQPTs. Recently, there has been a surge of interest in TQPTs [6][7][8][9][10][11]. The simplest class is described by the weakly interacting Dirac fermions, and it is well understood that the sign of the Dirac mass terms determines adjacent topological phases [12][13][14]. Since quasiparticles are well defined, non-interacting tight-binding models are sufficient to describe TQPTs in this class.Beyond the simplest class, however, our understanding of TQPTs is far from complete. The long-range Coulomb interaction may drastically change the properties of non-interacting fermions near TQPTs, and the non-interacting tight-binding models cannot describe some classes of TQPTs. The interplay between critical electronic modes and the Coulomb interaction becomes significant, and quantum critical non-Fermi-liquid states may appear with emergent particle-hole and rotational symmetries [15][16][17][18][19]. Moreover, the interplay may also give rise to weakly coupled but infinitely anisotropic excitations in a class of TQPTs [20][21][22][23][24]. Thus, it is vital to deepen our understanding of TQPTs beyond the simplest class.In this work, we uncover a novel class of TQPTs which shows emergent anisotropic non-Fermi-liquid behaviors in three spatial dimensions (3d) associated with topological nature of electronic wave functions. Our target system is the DWSM adjacent to insulator phases under the long-range Coulomb interaction. The presence of either the fourfold (C 4 ) or sixfold (C 6 ) rotational symmetry allows a direct phase transition between DWSMs and insulators whose bare Hamiltonian has a quadratic band * These authors contributed equally to this work. † egmoon@kaist.ac.kr ‡ hmin@snu.ac.kr touching spectrum. Without the symmetries, double-Weyl nodes may split into two Weyl nodes. The longrange Coulomb inte...

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confidence: 54%

Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions

et al. 2019

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“…There are several examples of CFTs with fermionic degrees of freedom that can be studied in ϵ-expansion and to which the method we describe here is applicable, see for instance the recent works [18][19][20][21][22][23][24][25][26][27][28][29][30] and references therein. In our companion paper [31], we focus on 3d QED and use the NLO eigenvalues obtained here to estimate the scaling dimensions of four-fermion operators in d ¼ 3.…”

Section: Introductionmentioning

confidence: 99%

Operator mixing in the ε -expansion: Scheme and evanescent-operator independence

Pietro

Stamou

2018

Phys. Rev. D

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We consider theories with fermionic degrees of freedom that have a fixed point of Wilson-Fisher type in noninteger dimension d ¼ 4 − 2ϵ. Due to the presence of evanescent operators, i.e., operators that vanish in integer dimensions, these theories contain families of infinitely many operators that can mix with each other under renormalization. We clarify the dependence of the corresponding anomalous-dimension matrix on the choice of renormalization scheme beyond leading order in ϵ-expansion. In standard choices of scheme, we find that eigenvalues at the fixed point cannot be extracted from a finite-dimensional block. We illustrate in examples a truncation approach to compute the eigenvalues. These are observable scaling dimensions, and, indeed, we find that the dependence on the choice of scheme cancels. As an application, we obtain the IR scaling dimension of four-fermion operators in QED in d ¼ 4 − 2ϵ at order Oðϵ 2 Þ.

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“…This was argued by Abrikosov [15] in 1971, and re-examined closely more recently by Moon et al [1]. Hence, in addition to quantum critical Dirac systems, this seems to be a simple instance of emergent non-Fermi liquid behavior, as most other well-studied cases involve the presence of a finite Fermi surface [16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 81%

Search for plasmons in isotropic Luttinger semimetals

Mandal

2019

Annals of Physics

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Luttinger semimetals include materials like gray tin (α-Sn) and mercury telluride, which are three-dimensional gapless semiconductors having a quadratic band crossing point (QBCP). Due to a growing interest in QBCPs and new experimental efforts, it is essential to study the finite-temperature properties of such systems. In this paper, we investigate the emergence of plasmons in the presence of Coulomb interactions in isotropic Luttinger semimetals, for zero as well as generic nonzero temperatures. When the Fermi level lies right at the QBCP, which is the point where twofold degenerate conduction and valence bands touch each other quadratically, we find that plasmons cannot appear at zero temperature.However, for nonzero temperatures, thermal plasmons are generated. Whether they are long-lived or not depends on the values of temperature, effective electron mass and effective fine-structure constant, and the number of fermion flavors. We also numerically estimate the behavior of the inelastic scattering rate at nonzero temperatures, as a function of energy, where the signatures of the QBCP thermal plasmons show up as a sharp peak. Our results will thus serve as a guide to experimental probes on these systems.

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Anisotropic non-Fermi liquids

Cited by 29 publications

References 76 publications

Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions

Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions

Operator mixing in the ε -expansion: Scheme and evanescent-operator independence

Search for plasmons in isotropic Luttinger semimetals

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