New quantum transition in Weyl semimetals with correlated disorder

Louvet, Thibaud; Carpentier, David; Fedorenko, Andrei A.

doi:10.1103/physrevb.95.014204

Cited by 25 publications

(19 citation statements)

References 36 publications

(52 reference statements)

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“…Apart from short-range disorder, there might be disorder with long-range correlation in various SMs 50,107,[115][116][117][118][119] . The most frequently encountered is Coulomb impurity, which is defined in a similar way to that of RSP, but is spatially long-ranged.…”

Section: Influence Of Coulomb Impurity On Triple-wsmmentioning

confidence: 99%

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

2017

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The low-energy behaviors of gapless double-and triple-Weyl fermions caused by the interplay of long-range Coulomb interaction and quenched disorder are studied by performing a renormalization group analysis. It is found that an arbitrarily weak disorder drives the double-Weyl semimetal to undergo a quantum phase transition into a compressible diffusive metal, independent of the disorder type and the Coulomb interaction strength. In contrast, the nature of the ground state of triple-Weyl fermion system relies sensitively on the specific disorder type in the noninteracting limit: The system is turned into a compressible diffusive metal state by an arbitrarily weak random scalar potential or z component of random vector potential but exhibits stable critical behavior when there is only x or y component of random vector potential. In case the triple-Weyl fermions couple to random scalar potential, the system becomes a diffusive metal in the weak interaction regime but remains a semimetal if Coulomb interaction is sufficiently strong. Interplay of Coulomb interaction and x, or y, component of random vector potential leads to a stable infrared fixed point that is likely to be characterized by critical behavior. When Coulomb interaction coexists with the z component of random vector potential, the system flows to the interaction-dominated strong coupling regime, which might drive a Mott insulating transition. It is thus clear that double-and triple-Weyl fermions exhibit distinct low-energy behavior in response to interaction and disorder. The physical explanation of such distinction is discussed in detail. The role played by long-range Coulomb impurity in triple-Weyl semimetal is also considered. The main conclusion is that, Coulomb impurity always drives the system to become a compressible diffusive metal, whereas Coulomb interaction tends to suppress the Coulomb impurity, rendering the robustness of the semimetal phase.

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Section: Influence Of Coulomb Impurity On Triple-wsmmentioning

confidence: 99%

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

2017

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“…51 The effect of disorder correlations on the semimetal-diffusive metal transition was investigated in Ref. 52. It was found that for a < 2 the semimetal phase is always unstable while for 2 < a < a c ≈ 2.8 disorder drives the transition to a new universality class, whose critical exponents depend on a.…”

Section: Introductionmentioning

confidence: 99%

“…Stability regions of different FPs in the plane (a = 2 + δ, d = 2 + ε) 52. For a < 2 the Gaussian FP is unstable and the RG flow exhibits runaway reflecting instability of the semimetal phase in the case of very LR correlated disorder: a diffusive metal phase is settled for arbitrary weak disorder and the transition disappears.…”

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confidence: 97%

Multifractality at the Weyl-semimetal–diffusive-metal transition for generic disorder

2019

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A Weyl semimetal is a three dimensional topological gapless phase. In the presence of strong enough disorder it undergoes a quantum transition towards a diffusive metal phase whose universality class depends on the range of disorder correlations. Similar to other quantum transitions driven by disorder, the critical wave functions at the semimetal-diffusive metal transition exhibit multifractality. Using renormalization group methods we study the corresponding multifractal spectrum as a function of the range of disorder correlations for generic disorder including random scalar and vector potentials. We also discuss the relation between the geometric fluctuations of critical wave functions and the broad distribution of the local density of states (DOS) at the transition. We derive a new scaling relation for the typical local DOS and argue that it holds for other disorder-driven transitions in which both the average and typical local DOS vanish on one side of the transition. As an illustration we apply it to the recently discussed unconventional quantum transition in disordered semiconductors with power-law dispersion relation near the band edge.

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“…Hence we believe that our work sheds new light on the description of critical non-Gaussian disorder fluctuations in quantum systems beyond the disorderdriven semimetal-diffusive metal phase transition.Here we focus on the transition between a pseudoballistic semimetal phase with a vanishing density of states (DOS) at the nodal point and a diffusive metal phase with a finite DOS at zero energy [16][17][18][19][20][21][22][23]. The fieldtheoretic description of this transition using both replica and SUSY approaches [24][25][26][27] implies that in the absence of scattering between different nodal points the transition is controlled by a perturbative in ε = d − 2 FP of the d-dimensional U (N ) Gross-Neveu (GN) model taken in the unusual limit of a vanishing number of fermion flavors N → 0. As for the Anderson transition, numerical studies [28][29][30][31][32] demonstrate quantitative discrepancies with the predictions of the GN model [24][25][26] which grow with the order of approximation.…”

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confidence: 99%

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

2018

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In the presence of randomness, a relativistic semimetal undergoes a quantum transition towards a diffusive phase. A standard approach relates this transition to the U (N ) Gross-Neveu model in the limit of N → 0. We show that the corresponding fixed point is infinitely unstable, demonstrating the necessity to include fluctuations beyond the usual Gaussian approximation. We develop a functional renormalization group method amenable to include these effects and show that the disorder distribution renormalizes following the so-called porous medium equation. We find that the transition is controlled by a nonanalytic fixed point drastically different from that of the U (N ) Gross-Neveu model. Our approach provides a unique mechanism of spontaneous generation of a finite density of states and also characterizes the scaling behavior of the broad distribution of fluctuations close to the transition. It can be applied to other problems where nonanalytic effects may play a role, such as the Anderson localization transition.Introduction. -The interplay between disorder and quantum fluctuations leads to unique phenomena, the most remarkable being the Anderson localization. After more than half a century of intensive efforts, it remains a topical subject of research with applications to various domains of physics ranging from condensed matter to cold atoms and light propagation [1]. Remarkably, a different type of disorder-driven quantum phase transition was discovered recently when considering waves with a quantum relativistic dispersion relation [2]. This transition happens between a pseudoballistic phase and a diffusive metal as a function of the disorder strength (or the energy). It is predicted to occur in particular in the recently discovered three-dimensional (3D) Weyl [3,4] and Dirac semimetals [5][6][7] in which, respectively, two and four electronic bands cross linearly at isolated points. However we expect these phenomena to be relevant to other relativistic waves beyond condensed matter, such as ultracold atoms [8].In spite of numerous efforts, the understanding of this transition remains elusive. In this Letter we show that the fluctuations of the randomness beyond the standard Gaussian approximation invalidate previous fieldtheoretic descriptions of this transition. A very similar mechanism occurs in the context of the Anderson transition: there discrepancies between the results obtained using renormalization group (RG) and numerical simulations grow with the number of loops [9]. One may attribute them to the existence of infinitely many relevant operators of the associated field theory [10] which destabilize the fixed point (FP) usually considered to describe the transition [11][12][13]. We find that the same problem appears at the new semimetal-diffusive metal transition. We demonstrate how to overcome this obstacle by deriving and solving a functional renormalization group (FRG) for the whole (non-Gaussian) disorder distribution. To our knowledge this solution consti-tutes the only example of an analytical de...

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New quantum transition in Weyl semimetals with correlated disorder

Cited by 25 publications

References 36 publications

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

Multifractality at the Weyl-semimetal–diffusive-metal transition for generic disorder

Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium Equation

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