arXiv subjects

A. A. Burkov

Publications and source records attributed to A. A. Burkov.

At least 19 recordsLinked to original sources

arXiv2026

Anderson localization in topological metals

We address the question of whether topological metals (TM) retain their nontrivial characteristics in the presence of disorder. While in the clean case, the issue is what protects the gaplessness of the spectrum, i.e. the band-touching nodes in TM, this question needs to be reformulated in the presence of disorder. The concept of gaplessness loses its sharp meaning in this case, since spectral gaps can be filled in by disorder-induced states. What is still meaningful is entanglement: one may ask whether the long-range entanglement of the clean gapless TM survives in the presence of disorder or, in other words, whether nontrivial topology protects the TM from Anderson localization. We demonstrate that such a protection exists in the case of three-dimensional (3D) Weyl semimetals, but not in 2D and 3D (type-I) Dirac or 3D nodal line semimetals. We establish this by combining the idea of unquantized anomaly as the topological response of TM with the decorated domain wall construction, used previously to discuss average symmetry-protected topological insulating phases.

cond-mat.mes-hall↗

arXiv2026

Modeling strained Cd$_3$As$_2$ thin films and their behavior in magnetic fields

We present a systematic analysis of the behavior of thin films of Cd$_3$As$_2$ under different strain profiles and in magnetic fields. In each case, we construct effective $k \cdot p$ models by considering the reduction of symmetry and all constraints imposed by the remaining symmetries. Our analysis naturally describes both in-plane biaxial and uniaxial strain. Biaxial strain is expected to preserve in-plane $C_4$ rotational symmetry while breaking inversion, allowing for a description in terms of the $4mm$ point group. Uniaxial strain, on the other hand, breaks $C_4$ symmetry. For this case, we consider two scenarios: one preserving inversion, described by the $mmm$ group, and one breaking it, leading to $2mm$ symmetry. After deriving the models, we examine the effects of out-of-plane magnetic fields, identifying two possible microscopic mechanisms that can account for the experimental results reported in Ahadi et al. (2025). Importantly, our analysis proposes a new method for differentiating between them. By incorporating the effects of multiple subbands along the confinement direction, we show that the opening of a gap in the lowest Landau level requires either reducing the symmetry down to $2mm$, breaking both inversion and $C_4$ rotations, or a topological transition of the band structure due to strain-induced band renormalization. Furthermore, we demonstrate that a two-dimensional Dirac semimetal phase can be induced by sufficiently large in-plane magnetic fields. This phase is highly sensitive to different strain profiles, with band touchings occurring when the field is applied perpendicular to preserved mirror planes, serving as a powerful probe of the material's strain profile.

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arXiv2026

Quantum geometric contribution to the diffusion constant

We discuss the quantum geometric contribution to the diffusion constant and the DC conductivity in metals and semimetals with linear Dirac dispersion. We demonstrate that, for systems with perfectly linear dispersion, there exists a clear and rigorous separation of the quantum geometric from the ordinary band velocity contributions to the diffusion constant, which turns out to be directly related to the separation of a rank two tensor into transverse and longitudinal parts. We also demonstrate that, within the self-consistent Born approximation and for Gaussian-distributed disorder, the diffusion constant of three-dimensional Dirac fermions at charge neutrality is entirely quantum geometric in origin, which is not the case for two-dimensional Dirac fermions. This is the result of an accidental perfect cancellation of the band velocity contribution in three dimensions.

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arXiv2025

Chiral charge conservation and ballistic magnetotransport in a disordered Weyl semimetal

We demonstrate that in an ideal Weyl semimetal, in which the Fermi energy coincides with the band-touching nodes, weak direct inter-nodal scattering is irrelevant and, as a result, the chiral charge is (almost) exactly conserved. This leads to an experimentally-observable effect: in an applied magnetic field, the charge transport along the field becomes purely ballistic, with the conductance given by $e^2/h$ per magnetic flux quantum through the sample cross-section. This is the strongest experimental manifestation of nontrivial topology in Weyl and Dirac semimetals.

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arXiv2025

Disordered Weyl semimetal as an array of coupled Hubbard chains

We demonstrate that a disordered magnetic Weyl semimetal may be mapped onto a two-dimensional array of coupled replicated Hubbard chains, where the Hubbard $U$ is directly related to the variance of the disorder potential. This is a three-dimensional generalization of a similar mapping of the two-dimensional quantum Hall plateau transition to a one-dimensional Hubbard chain. We demonstrate that this mapping leads to the conclusion that the Weyl semimetal becomes a diffusive metal with a nonzero density of states at arbitrarily weak disorder, in agreement with recent work. We also discuss the absence of localization in strongly disordered Weyl semimetals from the viewpoint of this mapping.

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arXiv2024

Absence of localization in Weyl semimetals

One of the fundamental facts of condensed matter physics is that sufficient amount of disorder always turns a Fermi liquid metal into an Anderson insulator: a compressible, but non-conducting phase of matter. Recently, topological semimetals have emerged as another way a metallic phase may be realized. In this paper we point out that, unlike ordinary metals, at least some topological semimetals are immune to localization, provided certain conditions are satisfied. We present several physical arguments, based on diagrammatic perturbation theory and Keldysh field theory, as well as domain wall network construction, to back up this claim.

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arXiv2024

Theory for Cd$_3$As$_2$ thin films in the presence of magnetic fields

We present a theory for thin films of the Dirac semimetal Cd$_3$As$_2$ in the presence of magnetic fields. We show that, above a critical thickness, specific subbands $n$ of thin film Cd$_3$As$_2$ are in a quantum spin Hall insulator regime and study their response to in- and out-of-plane magnetic fields. We find that sufficiently large in-plane Zeeman fields drive the system toward a 2D Dirac semimetal regime, provided the field is directed perpendicular to a high-symmetry mirror plane. For other directions, we find the Dirac points to be weakly gapped. We further investigate how the system responds to finite out-of-plane field components, both starting from the quantum spin Hall regime at small in-plane fields and from the 2D Dirac semimetal regimes at larger in-plane fields, addressing recent experimental observations in [A. C. Lygo et al., Phys. Rev. Lett. 130 046201 (2023)] and [B. Guo et al., Phys. Rev. Lett. 131, 046601(2023)].

cond-mat.mes-hall↗

arXiv2023

Current-Induced Spin Accumulation and Magnetoresistance in Chiral Semimetals

Weyl fermions possess the property of spin-momentum locking: the expectation value of the spin is parallel or antiparallel to the momentum at any given point in the Brillouin zone in the vicinity of a Weyl node. This is a direct consequence of the fact that Weyl nodes are monopoles of the Berry curvature, and in this sense an expression of the nontrivial Weyl electronic structure topology. Thanks to this property, an isolated Weyl node produces a large spin accumulation in response to a charge current, $\hbar/2$ per electron, similar to surface states of time-reversal invariant topological insulators. However, in bulk Weyl semimetals, the nodes must occur in pairs of opposite chirality and, when the nodes are at the same energy, the effect cancels out. Here we show that this cancellation is avoided in chiral semimetals, in which Weyl nodes of opposite chirality occur at different energies due to broken mirror symmetry. We find that the spin accumulation is maximized when the Fermi energy coincides with one of the nodes in a pair and reaches the same value as for an isolated node in this case. Moreover, we demonstrate the existence of a distinct magnetoresistance mechanism, closely related to this current-induced spin accumulation.

cond-mat.mes-hall↗

arXiv2023

Topological order in interacting semimetals

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a nonabelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. This may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED$_3$ to $3+1$ dimensions. In addition we discuss a $(3+1)$-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

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arXiv2022

Dynamical Effects from Anomaly: Modified Electrodynamics in Weyl Semimetal

We discuss the modified quantum electrodynamics from a time-reversal-breaking Weyl semimetal coupled with a $U(1)$ gauge (electromagnetic) field. A key role is played by the soft dispersion of the photons in a particular direction, say $\hat{z}$, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in $\hat{z}$ is logarithmically reduced under renormalization group flow, together with the fine structure constant. Meanwhile, fermions acquire a finite lifetime from spontaneous emission of the soft photon, namely the Cherenkov radiation. At low energy $E$, the inverse of the fermion lifetime scales as $τ^{-1}\sim E/{\rm PolyLog}(E)$. Therefore, even though fermion quasiparticles are eventually well-defined at very low energy, over a wide intermediate energy window the Weyl semimetal behaves like a marginal Fermi liquid. Phenomenologically, our results are more relevant for emergent Weyl semimetals, where the fermions and photons all emerge from strongly correlated lattice systems. Possible experimental implications are discussed.

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arXiv2022

Topological properties of Dirac and Weyl semimetals

This chapter describes topological (Dirac and Weyl) semimetals from the viewpoint of their observable electromagnetic response. We argue that this response may be represented by topological terms with unquantized (non-integer) coefficients and make a connection with the Luttinger's theorem, which relates the size of the Fermi surface of an ordinary metal to the number of electrons per unit cell. We discuss observable transport phenomena, associated with this topological response.

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arXiv2021

Emergent anomalies and generalized Luttinger theorems in metals and semimetals

Luttinger's theorem connects a basic microscopic property of a given metallic crystalline material, the number of electrons per unit cell, to the volume, enclosed by its Fermi surface, which defines its low-energy observable properties. Such statements are valuable since, in general, deducing a low-energy description from microscopics, which may perhaps be regarded as the main problem of condensed matter theory, is far from easy. In this paper we present a unified framework, which allows one to discuss Luttinger theorems for ordinary metals, as well as closely analogous exact statements for topological (semi)metals, whose low-energy description contains either discrete point or continuous line nodes. This framework is based on the 't Hooft anomaly of the emergent charge conservation symmetry at each point on the Fermi surface, a concept recently proposed by Else, Thorngren and Senthil [Phys. Rev. X 11, 021005 (2021)]. We find that the Fermi surface codimension $p$ plays a crucial role for the emergent anomaly. For odd $p$, such as ordinary metals ($p=1$) and magnetic Weyl semimetals ($p=3$), the emergent symmetry has a generalized chiral anomaly. For even $p$, such as graphene and nodal line semimetals (both with $p=2$), the emergent symmetry has a generalized parity anomaly. When restricted to microscopic symmetries, such as $U(1)$ and lattice symmetries, the emergent anomalies imply (generalized) Luttinger theorems, relating Fermi surface volume to various topological responses. The corresponding topological responses are the charge density for $p=1$, Hall conductivity for $p=3$, and polarization for $p=2$. As a by-product of our results, we clarify exactly what is anomalous about the surface states of nodal line semimetals.

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arXiv2021

Signal power and energy-per-bit optimization problems in systems mMTC

Currently, the issues of the operation of the Internet of Things technology are being actively studied. The operation of a large number of different self-powered sensors is within the framework of a massive machine-type communications scenario using random access methods. Topical issues in this type of communication are: reducing the transmission signal power and increasing the duration of the device by reducing the consumption energy per bit. Formulation and analysis of the tasks of minimizing transmission power and spent energy per bit in systems without retransmissions and with retransmissions to obtain achievability bounds. A model of the system is described, within which four problems of minimizing signal power and energy consumption for given parameters (the number of information bits, the spectral efficiency of the system, and the Packet Delivery Ratio) are formulated and described. The numerical results of solving these optimization problems are presented, which make it possible to obtain the achievability bounds for the considered characteristics in systems with and without losses. The lower bounds obtained by the Shannon formula are presented, assuming that the message length is not limited. The results obtained showed that solving the minimization problem with respect to one of the parameters (signal power or consumption energy per bit) does not minimize the second parameter. This difference is most significant for small information message lengths, which corresponds to IoT scenarios. The results obtained allow assessing the potential for minimizing transmission signal power and consumption energy per bit in random multiple access systems with massive machine-type communications scenarios. The presented problems were solved without taking into account the average delay of message transmission.

cs.IT↗

arXiv2021

Unquantized anomalies in topological semimetals

Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial topology in momentum space and crystal symmetry, wherein topological charges may be assigned to point band-touching nodes, preventing gap opening, unless protecting crystal symmetries are violated. These topological charges, however, are defined from noninteracting band eigenstates, which raises the possibility that the physics of topological semimetals may be modified qualitatively by electron-electron interactions. Here we ask the following question: what makes the topological semimetals nontrivial beyond band theory? Alternatively, can strong electron-electron interactions open a gap in topological semimetals without breaking the protecting symmetries or introducing topological order? We demonstrate that the answer is generally no, and what prevents it is their topological response, or quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses are detectable as fractional symmetry charges induced on certain gauge defects. We discuss the cases of type-I Dirac semimetals and time-reversal invariant Weyl semimetals in detail. For type-I Dirac semimetals, we also show that the anomaly vanishes, in a nontrivial manner, if the momenta of the Dirac nodes satisfy certain exceptional conditions.

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arXiv2020

Charge density waves in Weyl semimetals

We present a theory of charge density wave (CDW) states in Weyl semimetals and their interplay with the chiral anomaly. In particular, we demonstrate a special nature of the shortest-period CDW state, which is obtained when the separation between the Weyl nodes equals exactly half a primitive reciprocal lattice vector. Its topological properties are shown to be distinct from all other Weyl CDW states. We make a connection between this observation and the three-dimensional fractional quantum Hall state, which was recently proposed to exist in magnetic Weyl semimetals.

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arXiv2020

Theory of the fractional quantum Hall effect in Weyl semimetals

We develop a hydrodynamic field theory of the three-dimensional fractional quantum Hall effect, which was recently proposed to exist in magnetic Weyl semimetals, when the Weyl nodes are gapped by strong repulsive interactions. This theory takes the form of a BF theory, which contains both one-form and two-form gauge fields, coupling to quasiparticle and loop excitations correspondingly. It may be regarded as a generalization of the Chern-Simons theory of two-dimensional fractional quantum Hall liquids to three dimensions.

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arXiv2020

Fractional Quantum Hall Effect in Weyl Semimetals

Weyl semimetal may be thought of as a gapless topological phase protected by the chiral anomaly, where the symmetries involved in the anomaly are the $U(1)$ charge conservation and the crystal translational symmetry. The absence of a band gap in a weakly-interacting Weyl semimetal is mandated by the electronic structure topology and is guaranteed as long as the symmetries and the anomaly are intact. The nontrivial topology also manifests in the Fermi arc surface states and topological response, in particular taking the form of an anomalous Hall effect in magnetic Weyl semimetals, whose magnitude is only determined by the location of the Weyl nodes in the Brillouin zone. Here we consider the situation when the interactions are not weak and ask whether it is possible to open a gap in a magnetic Weyl semimetal while preserving its nontrivial electronic structure topology along with the translational and the charge conservation symmetries. Surprisingly, the answer turns out to be yes. The resulting topologically ordered state provides a nontrivial realization of the fractional quantum Hall effect in three spatial dimensions in the absence of an external magnetic field, which cannot be viewed as a stack of two dimensional states. Our state contains loop excitations with nontrivial braiding statistics when linked with lattice dislocations.

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arXiv2018

Dirac fermion duality and the parity anomaly

We present a derivation of the recently discovered duality between the free massless (2+1)-dimensional Dirac fermion and QED$_3$. Our derivation is based on a regularized lattice model of the Dirac fermion and is similar to the more familiar derivation of the boson-vortex duality. It also highlights the important role played by the parity anomaly, which is somewhat less obvious in other discussions of this duality in the literature.

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