Nonlocal annihilation of Weyl fermions in correlated systems

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Nonlocal annihilation of Weyl fermions in correlated systems

L. Crippa, A. Amaricci, N. Wagner, G. Sangiovanni, J. C. Budich, and M. Capone

Phys. Rev. Research 2, 012023(R) – Published 22 January 2020

Abstract

Weyl semimetals (WSMs) are characterized by topologically stable pairs of nodal points in the band structure that typically originate from splitting a degenerate Dirac point by breaking symmetries such as time-reversal or inversion symmetry. Within the independent-electron approximation, the transition between an insulating state and a WSM requires the local creation or annihilation of one or several pairs of Weyl nodes in reciprocal space. Here, we show that strong electron-electron interactions may qualitatively change this scenario. In particular, we reveal that the transition to a Weyl semimetallic phase can become discontinuous, and, quite remarkably, pairs of Weyl nodes with a finite distance in momentum space suddenly appear or disappear in the spectral function. We associate this behavior with the buildup of strong many-body correlations in the topologically nontrivial regions, manifesting in dynamical fluctuations in the orbital channel. We also highlight the impact of electronic correlations on the Fermi arcs.

Received 26 April 2019
Revised 5 November 2019

DOI:https://doi.org/10.1103/PhysRevResearch.2.012023

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum phase transitions Surface states Topological phase transition Weyl fermions

Dynamical mean field theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

L. Crippa ¹, A. Amaricci^2,1, N. Wagner³, G. Sangiovanni³, J. C. Budich⁴, and M. Capone¹

¹Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
²CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Via Bonomea 265, I-34136 Trieste, Italy
³Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
⁴Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany

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Issue

Vol. 2, Iss. 1 — January - March 2020

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Images

Figure 1
(a) Band structure of (1) in the WSM phase on $k_{y} = 0$ plane including the $Γ$ point (orbital character in color). The circular insets show the Berry flux near the two Weyl points. (b)–(d) Position of Weyl nodes along $k_{z}$ (for $k_{x} = k_{y} = 0$ ) as a function of $M - M_{0}$ for increasing values of $U$ and $b_{z} = 0.1$ . Here $M_{0}$ is determined by the condition $M + Tr [σ_{0} τ_{z} Σ (0)] / 4 = 3$ , where $Σ (0)$ is the self-energy function at zero frequency. This condition, which in the case $b_{z} = 0$ [37] determines the topological transition point, is used here to center and compare data at different interactions strengths. The background colors in the panels reflect the behavior of the correlation strength $Ξ$ . For small $U$ ( $\approx 2.0$ ) the Weyl points form or annihilate continuously (b) at $Γ$ . At larger $U$ (c) they (dis)appear discontinuously at the boundary with an insulating state, while the width of the WSM phase reduces. Eventually (d), for large $U$ ( $> 5.7$ ) the WSM region disappears and the system undergoes a direct first-order transition between strong TI and BI.
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Figure 2
$M^{eff}$ behavior as a function of the bare mass for different values of interaction: (a) $U = 3.0$ , (b) $U = 5.5$ , (c) $U = 5.9$ . $M_{0}$ is defined as in Fig. 1. The shaded regions correspond to the WSM, that of the noninteracting system being the full width of the panels. The dotted lines represent (where significant) the expected width of the WSM region, spanning the interval $M^{eff} = [3 - b_{z}^{eff}, 3 + b_{z}^{eff}]$ . The blue lines represent the orbital compressibility $κ$ . The inset to panel (b) shows the behavior of $M^{eff}$ for $U = 5.5$ as a function of temperature.
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Figure 3
Phase diagram of the model for $b_{z} = 0.1$ . The regions (yellow) between the dotted lines are WSM. The inset shows the closing of the upper WSM region. Numerical results are represented by black symbols. At $U = 0$ , the widths of the semimetal regions are $2 b_{z}$ , centered around $M^{eff} = 1, 3$ . The first semimetal region remains open when increasing the interaction, and the transition from WTI to WSM to STI is always continuous. A second critical point signals the value of $U$ for which the upper WSM region closes.
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Figure 4
Electronic structure of a slab geometry near the $Γ$ point at $U = 5.6$ . The two panels report the behavior for two different values of the mass term $M$ across the WSM to BI transition (see inset of Fig. 3). (a) $M = 0.665$ ; the points (red and blue) indicate the Weyl nodes with opposite chirality. The band segment connecting them is the Fermi arc. (b) $M = 0.670$ ; the system is a band insulator.
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