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Relations between Condensed Matter Physics and Relativistic Quantum Field Theory

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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (28 February 2021) | Viewed by 17694

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Special Issue Editor

Prof. Dr. Mikhail Zubkov

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Guest Editor

Physics Department, Ariel University, Ariel 40700, Israel
Interests: quantum field theory; lattice field theory; condensed matter physics; anomalous transport; emergent relativistic phenomena in condensed matter physics; quantum Hall effect; emergent gravity; composite Higgs bosons

Special Issue Information

Dear colleagues,

It has been known for a long time that certain features of high energy physics may be simulated in laboratory conditions using various condensed matter systems. In particular, the fermionic quasiparticles in superfluid Helium-3A are described by the (anisotropic) massless Dirac equation. In recent years, new materials have been discovered, where such an analogy is even more pronounced: graphene, Weyl semimetals, and Dirac semimetals. The quasiparticles in these materials also behave similarly to the elementary particles of high energy physics. Unlike the quasiparticles in Helium-3, they carry an ordinary electric charge, which facilitates simulation of electromagnetic phenomena specific to the physics of elementary particles. The mentioned analogy opens up the possibility to apply deep understanding of relativistic quantum field theories to the solution of various problems of condensed matter physics. In particular, the lattice field theory techniques may be applied to the physics of solids. In turn, various approaches of condensed matter physics theory may be applied to the high energy physics.

The corresponding mutual relationship of modern condensed matter physics and relativistic quantum field theory is the subject of the present Special Issue. Such features involve but are not reduced to the applications of relativistic quantum field theories (including lattice field theory) to physics of Dirac and Weyl semimetals, graphene, Quantum Hall Effects, fermionic superfluids, quark–gluon plasma, and anomalous transport effects.

Prof. Dr. Mikhail Zubkov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Weyl semimetals
Graphene
Fermionic superfluids
Relativistic quantum field theory
Quantum Hall Effect
Chiral Anomaly
Anomalous transport
Emergent gauge fields
Lattice field theory

Published Papers (7 papers)

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Research

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8 pages, 232 KiB

Open AccessArticle

Emission of Photons by Quasiparticles in Weyl Semimetals

by Alexander Andrianov, Roberto Soldati and Dmitri Vassilevich

Symmetry 2020, 12(5), 869; https://doi.org/10.3390/sym12050869 - 25 May 2020

Cited by 1 | Viewed by 1641

Abstract

We show that quasiparticles in Weyl semimetals may decay with emission of a single photon. We study the spectrum of emitted photons and estimate the decay rates. Full article

(This article belongs to the Special Issue Relations between Condensed Matter Physics and Relativistic Quantum Field Theory)

10 pages, 1003 KiB

Open AccessArticle

Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals

by Vicente Arjona, Juan Borge and María A. H. Vozmediano

Symmetry 2020, 12(5), 814; https://doi.org/10.3390/sym12050814 - 14 May 2020

Viewed by 2975

Abstract

Dirac and Weyl semimetals are three-dimensional electronic systems with the Fermi level at or near a band crossing. Their low energy quasi-particles are described by a relativistic Dirac Hamiltonian with zero effective mass, challenging the standard Fermi liquid (FL) description of metals. In FL systems, electrical and thermo–electric transport coefficient are linked by very robust relations. The Mott relation links the thermoelectric and conductivity transport coefficients. In a previous publication, the thermoelectric coefficient was found to have an anomalous behavior originating in the quantum breakdown of the conformal anomaly by electromagnetic interactions. We analyze the fate of the Mott relation in the system. We compute the Hall conductivity of a Dirac metal as a function of the temperature and chemical potential and show that the Mott relation is not fulfilled in the conformal limit. Full article

(This article belongs to the Special Issue Relations between Condensed Matter Physics and Relativistic Quantum Field Theory)

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Figure 1

17 pages, 1722 KiB

Open AccessArticle

Inflation in Supergravity from Field Redefinitions

by Michał Artymowski and Ido Ben-Dayan

Symmetry 2020, 12(5), 806; https://doi.org/10.3390/sym12050806 - 12 May 2020

Cited by 4 | Viewed by 1546

Abstract

Supergravity (SUGRA) theories are specified by a few functions, most notably the real Kähler function denoted by

G (T_{i}, {\bar{T}}_{i}) = K + log {| W |}^{2}

, where K is a real Kähler potential, and [...] Read more.

Supergravity (SUGRA) theories are specified by a few functions, most notably the real Kähler function denoted by

G (T_{i}, {\bar{T}}_{i}) = K + log {| W |}^{2}

, where K is a real Kähler potential, and W is a holomorphic superpotential. A field redefinition

T_{i} \to f_{1} (T_{i})

changes neither the theory nor the Kähler geometry. Similarly, the Kähler transformation,

K \to K + f_{2} + {\bar{f}}_{2}, W \to e^{- f_{2}} W

where

f_{2}

is holomorphic and leaves G and hence the theory and the geometry invariant. However, if we perform a field redefinition only in

K (T_{i}, {\bar{T}}_{i}) \to K (f (T_{i}), f ({\bar{T}}_{i}))

, while keeping the same superpotential

W (T_{i})

, we get a different theory, as G is not invariant under such a transformation while maintaining the same Kähler geometry. This freedom of choosing

f (T_{i})

allows construction of an infinite number of new theories given a fixed Kähler geometry and a predetermined superpotential W. Our construction generalizes previous ones that were limited by the holomorphic property of W. In particular, it allows for novel inflationary SUGRA models and particle phenomenology model building, where the different models correspond to different choices of field redefinitions. We demonstrate this possibility by constructing several prototypes of inflationary models (hilltop, Starobinsky-like, plateau, log-squared and bell-curve) all in flat Kähler geometry and an originally renormalizable superpotential W. The models are in accord with current observations and predict

r \in [10^{- 6}, 0.06]

spanning several decades that can be easily obtained. In the bell-curve model, there also exists a built-in gravitational reheating mechanism with

T_{R} \sim O (10^{7} G e V)

. Full article

(This article belongs to the Special Issue Relations between Condensed Matter Physics and Relativistic Quantum Field Theory)

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Figure 1

13 pages, 1778 KiB

Open AccessArticle

Non-Hermitian Chiral Magnetic Effect in Equilibrium

by Maxim N. Chernodub and Alberto Cortijo

Symmetry 2020, 12(5), 761; https://doi.org/10.3390/sym12050761 - 06 May 2020

Cited by 22 | Viewed by 2920

Abstract

We analyze the chiral magnetic effect for non-Hermitian fermionic systems using the bi-orthogonal formulation of quantum mechanics. In contrast to the Hermitian counterparts, we show that the chiral magnetic effect takes place in equilibrium when a non-Hermitian system is considered. The key observation is that for non-Hermitian charged systems, there is no strict charge conservation as understood in Hermitian systems, so the Bloch theorem preventing currents in the thermodynamic limit and in equilibrium does not apply. Full article

(This article belongs to the Special Issue Relations between Condensed Matter Physics and Relativistic Quantum Field Theory)

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Figure 1

29 pages, 930 KiB

Open AccessArticle

Elastic Deformations and Wigner–Weyl Formalism in Graphene

by I.V. Fialkovsky and M.A. Zubkov

Symmetry 2020, 12(2), 317; https://doi.org/10.3390/sym12020317 - 23 Feb 2020

Cited by 16 | Viewed by 2674

Abstract

We discuss the tight-binding models of solid state physics with the

Z_{2}

We discuss the tight-binding models of solid state physics with the

Z_{2}

sublattice symmetry in the presence of elastic deformations in an important particular case—the tight binding model of graphene. In order to describe the dynamics of electronic quasiparticles, the Wigner–Weyl formalism is explored. It allows the calculation of the two-point Green’s function in the presence of two slowly varying external electromagnetic fields and the inhomogeneous modification of the hopping parameters that result from elastic deformations. The developed formalism allows us to consider the influence of elastic deformations and the variations of magnetic field on the quantum Hall effect. Full article

(This article belongs to the Special Issue Relations between Condensed Matter Physics and Relativistic Quantum Field Theory)

9 pages, 269 KiB

Open AccessFeature PaperArticle

Quantum Hall Conductivity in the Presence of Interactions

by Xi Wu and Mikhail Zubkov

Symmetry 2020, 12(2), 200; https://doi.org/10.3390/sym12020200 - 01 Feb 2020

Viewed by 1920

Abstract

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that, irrespective of the interaction strength, the Hall conductivity is given by the filling fraction of Landau levels averaged over the ground state of the system. [...] Read more.

(This article belongs to the Special Issue Relations between Condensed Matter Physics and Relativistic Quantum Field Theory)

Review

Jump to: Research

12 pages, 2070 KiB

Open AccessReview

Magneto-Optical Tools to Study Effects in Dirac and Weyl Semimetals

by Dima Cheskis

Symmetry 2020, 12(9), 1412; https://doi.org/10.3390/sym12091412 - 25 Aug 2020

Cited by 4 | Viewed by 3325

Abstract

Research regarding topological Dirac and Weyl semimetals contributes to our understanding not only of the field of solid-state physics, but also the field of high-energy physics as the physics of Dirac and Weyl semimetals resembles the physics of Dirac and Weyl massless fermions. In condensed matter physics, the Weyl nodes are detached in momentum space and may be realized as emergent quasiparticles with a distinct chirality, left-handed or right-handed. These states lead to phenomena like the chiral anomaly and the anomalous Hall effect (AHE). Furthermore, the combination of quantum effects and magnetic effects in magnetic Weyl semimetals is very intriguing. Magneto-optical tools, which are usually used to study magnetic phenomena, also contribute to magnetic Weyl semimetals. Moreover, with the magneto-optical technique, it is possible to follow the dynamics of the processes and to study the lifetime of the Weyl states. In this work, we review and discuss the effects of using magneto-optical tools for studying quantum effects like the chiral anomaly or magnetic effects in magnetic Weyl and Dirac systems using the magneto-optical Kerr effect (MOKE) or Faraday systems including a single detection and imaging. Examples of using magneto-optical systems in the research of ultrafast magnetic dynamics of thin polycrystalline nickel and permaloy are reviewed as are the magnetic spatial dynamics by employing magneto-optical Kerr or Faraday microscopy tools with ferromagnetic thin films. Interestingly, the excitation of a circularly polarized femtosecond laser pulse could lead to the breakage of time-reversal symmetry and to the transformation of the Dirac state to the Floquet–Weyl semimetal state. The development of a suitable ultrafast magneto-optical system for Weyl systems is discussed, and the practical difficulties for the realization of such a system are considered. Full article

(This article belongs to the Special Issue Relations between Condensed Matter Physics and Relativistic Quantum Field Theory)

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