Massive Dirac Fermions Research Articles

Trace anomalies and the graviton-dilaton amplitude

Abstract We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to ∆c − ∆a along any RG flow, where ∆c and ∆a are the differences of the UV and IR c- and a-trace anomalies respectively. This allows us to relate ∆c − ∆a to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.

Two-dimensional bilayer blue phosphorus Dirac-like material: a multi-orbital tight-binding investigation.

This study presents a theoretical examination of the electronic band structure of AA (AB) stacked bilayer blue phosphorus system within the fifth intralayer (5NN) and second interlayer nearest-neighbor (2NN) multi-orbital tight-binding (MOTB) approach. The variation of energy levels has been investigated through the symmetrical tensile strain of the low-buckled honeycomb lattice. Here, the primary objective is to examine the existence of Dirac electronic features in hexagonal stacked bilayer geometry. Our theoretical calculations predict that the AA bilayer is a new hexagonal two-dimensional material with px,y-orbital Dirac-like states at the high-symmetry K point. Consequently, these systems can host massless (massive) Dirac fermions. In particular, the AA bilayer exhibits zero-gap Dirac-like properties and manifests distinguishable Dirac-like cones in the presence of weak spin-orbit coupling when a modest stretch of 2.30% is achieved with a remarkably high Fermi velocity of approximately vf ≈ 0.12 × 105 m s-1. The behavior of the dispersion bands aligns reasonably well with recent experimental observations. Moreover, a stretch of 7.17% breaks some of the sublattice equivalence and enhances the spin-orbit interaction, resulting in the emergence of an electronic band gap of approximately ≈ 0.27 eV in the proximity of the high-symmetry K point. Furthermore, the tiny gap induced by the spin-orbit interaction implies topological nontriviality in the electronic state (quantum anomalous Hall state) of the honeycomb lattice. These findings categorize the AA bilayer as a rare two-dimensional Dirac-like material. This work provides, to the extent of our knowledge, a pioneering investigation into the existence of Dirac electronic properties in bilayer blue phosphorus. In addition, we present the first derivation of the MOTB model. However, the identified electronic characteristics designate this two-dimensional system as an ideal candidate for high-performance nanoelectronic devices.

Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect

Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect

No bulk thermal currents in massive Dirac fermions

We calculate the energy current flowing in the bulk of a (2+1)-dimensional system of massive Dirac fermions and along a (1+1)-dimensional domain wall generated by flipping the sign of the particle mass. We show that, at low temperatures and in the long-wavelength limit, the system does not support a bulk thermal Hall current proportional to the temperature gradient. The only such contribution is due to states localized at the domain wall. This puts an end to a controversy existing in the literature and amends previous results obtained via first-order perturbation calculations. Published by the American Physical Society 2024

Dominance of Extrinsic Scattering Mechanisms in the Orbital Hall Effect: Graphene, Transition Metal Dichalcogenides, and Topological Antiferromagnets.

The theory of the orbital Hall effect (OHE), a transverse flow of orbital angular momentum (OAM) in response to an electric field, has concentrated on intrinsic mechanisms. Here, using a quantum kinetic formulation, we determine the full OHE in the presence of short-range disorder using 2D massive Dirac fermions as a prototype. We find that, in doped systems, extrinsic effects associated with the Fermi surface (skew scattering and side jump) provide ≈95% of the OHE. This suggests that, at experimentally relevant transport densities, the OHE is primarily extrinsic.

First-order effect of electron-electron interactions on the anomalous Hall conductivity of massive Dirac fermions

We investigate the first-order correction to the anomalous Hall conductivity of 2D massive Dirac fermions arising from electron-electron interactions. In a fully gapped system in the limit of zero temperature, we find that this correction vanishes, confirming the absence of perturbative corrections to the topological Hall conductivity. At finite temperature or chemical potential, we find that the total Hall response decays faster than in the noninteracting case, depending on the strength of electron-electron interactions. These features, which could potentially be observed experimentally, show the importance of two-body interactions for anomalous Hall transport. Published by the American Physical Society 2024

Weyl Fermions on a Finite Lattice.

The phenomenon of unpaired Weyl fermions appearing on the sole 2n-dimensional boundary of a (2n+1)-dimensional manifold with massive Dirac fermions was recently analyzed in D. B. Kaplan [preceding Letter, Chiral gauge theory at the boundary between topological phases, Phys. Rev. Lett. 132, 141603 (2024).PRLTAO0031-900710.1103/PhysRevLett.132.141603]. In this Letter, we show that similar unpaired Weyl edge states can be seen on a finite lattice. In particular, we consider the discretized Hamiltonian for a Wilson fermion in (2+1) dimensions with a 1+1 dimensional boundary and continuous time. We demonstrate that the low lying boundary spectrum is indeed Weyl-like: it has a linear dispersion relation and definite chirality and circulates in only one direction around the boundary. We comment on how our results are consistent with Nielsen-Ninomiya theorem. This work removes one potential obstacle facing the program outlined in D. B. Kaplan, preceding Letter, for regulating chiral gauge theories.

Density Functional Theory Study of the Spin-Orbit Insulating Phase in SnTe Cubic Nanowires: Implications for Topological Electronics.

We investigate the electronic, structural, and topological properties of the SnTe and PbTe cubic nanowires using ab initio calculations. Using standard and linear-scale density functional theory, we go from the ultrathin limit up to the nanowire thicknesses observed experimentally. Finite-size effects in the ultrathin limit produce an electric quadrupole and associated structural distortions; these distortions increase the band gap, but they get reduced with the size of the nanowires and become less and less relevant. Ultrathin SnTe cubic nanowires are trivial band gap insulators; we demonstrate that by increasing the thickness, there is an electronic transition to a spin-orbit insulating phase due to trivial surface states in the regime of thin nanowires. These trivial surface states with a spin-orbit gap of a few meV appear at the same k-point of the topological surface states. Going to the limit of thick nanowires, we should observe the transition to the topological crystalline insulator phase with the presence of two massive surface Dirac fermions hybridized with the persistent trivial surface states. Therefore, we have the copresence of massive Dirac surface states and trivial surface states close to the Fermi level in the same region of the k-space. According to our estimation, the cubic SnTe nanowires are trivial insulators below the critical thickness tc1 = 10 nm, and they become spin-orbit insulators between tc1 = 10 nm and tc2 = 17 nm, while they transit to the topological phase above the critical thickness of tc2 = 17 nm. These critical thickness values are in the range of typical experimental thicknesses, making the thickness a relevant parameter for the synthesis of topological cubic nanowires. Pb1-xSnxTe nanowires would have both these critical thicknesses tc1 and tc2 at larger values depending on the doping concentration. We discuss the limitations of density functional theory in the context of topological nanowires and the consequences of our results on topological electronics.

The Anomalous Photo‐Nernst Effect of Massive Dirac Fermions In HfTe5

AbstractThe quantum geometric Berry curvature results in an anomalous correction to the band velocity of crystal electrons with a corresponding transverse (thermo)electric conductivity. However, time‐reversal symmetry typically constrains the direct observation and exploitation of anomalous transport to magnetic compounds. Here, it is demonstrated the anomalous Hall and Nernst conductivities are essential for describing the optoelectronic transport in thin films of the non‐magnetic, weakly gapped semimetal HfTe5 subject to an external magnetic field. A focused photoexcitation adresses the symmetries of the local Nernst conductivity, which unveils a hitherto hidden, anomalous photo‐Nernst effect of three‐dimensional (3D) massive Dirac fermions. The experimental temperature and density dependencies are compared with a semiclassical Boltzmann transport model. For HfTe5 thin films with the Fermi level close to the gap, the model suggests that the anomalous photo‐Nernst currents originate from an intrinsic Berry curvature mechanism, where the Zeeman interaction effectively breaks time‐reversal symmetry of the massive Dirac fermions already at moderate external magnetic fields.

Observation of anomalous Hall resonance of massive Dirac fermions in topological kagome-lattice magnet

The kagome-lattice materials promise emergence of Dirac fermions thanks to the special lattice geometry, which potentially realizes intriguing quantum topological states through various many-body interactions. The low-energy electromagnetic phenomena arising from such the Dirac fermions are expected to show the remarkable enhancement and, in certain conditions, to approach the universal responses, which, however, have remained elusive experimentally. Here, we show the resonantly enhanced magneto-optical response of massive Dirac fermions in kagome-lattice magnet TbMn6Sn6. The infrared magneto-optical spectroscopy reveals that the interband transition on massive Dirac bands significantly contributes to the observed resonance in the optical Hall conductivity. The analytical model expressed by a few band parameters reproduces the spectral characteristics of the resonance, which robustly produces almost 20 % of the quantized Hall conductance per one kagome layer even at room temperature. Our findings establish the general optical response of massive Dirac fermions, which is closely related to the universal electrodynamics in quantum anomalous Hall state.

Superlattice engineering of topology in massive Dirac fermions

Superlattice engineering of topology in massive Dirac fermions

Electrical, thermal and thermoelectric transport in open long-range Kitaev chain

We study electrical, thermal and thermoelectric transport in a hybrid device consisting of a long-range Kitaev (LRK) chain coupled to two metallic leads at two ends. Electrical and thermal currents are calculated in this device under both voltage and thermal bias conditions. We find that the transport characteristics of the LRK chain are distinguishably different from its short-range counterpart, which is well known for hosting zero energy Majorana edge modes under some specific range of values of the model parameters. The emergence of massive Dirac fermions, the absence of gap closing at the topological phase transition point and some special features of the energy spectrum which are unique to the LRK chain, significantly alter electrical/thermal current vs. voltage/temperature bias characteristics in comparison with that of the short-range Kitaev chain. These novel transport characteristics of the LRK model can be helpful in understanding nontrivial topological phases of the LRK chain.

Moiré Dirac fermions in transition metal dichalcogenides heterobilayers

Abstract Monolayer group-VIB transition metal dichalcogenides (TMDs) feature low-energy massive Dirac fermions, which have valley contrasting Berry curvature. This nontrivial local band topology gives rise to valley Hall transport and optical selection rules for interband transitions that open up new possibilities for valleytronics. However, the large bandgap in TMDs results in relatively small Berry curvature, leading to weak valley contrasting physics in practical experiments. Here, we show that Dirac fermions with tunable large Berry curvature can be engineered in moiré superlattice of TMD heterobilayers. These moiré Dirac fermions are created in a magnified honeycomb lattice with its sublattice degree of freedom formed by two local moiré potential minima. We show that applying an on-site potential can tune the moiré flat bands into helical ones. In short-period moiré superlattice, we find that the two moiré valleys become asymmetric, which results in a net spin Hall current. More interestingly, a circularly polarized light drives these moiré Dirac fermions into quantum anomalous Hall phase with chiral edge states. Our results open a new possibility to design the moiré-scale spin and valley physics using TMD moiré structures.

Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot.

We predict the existence of spontaneous spin and valley symmetry-broken states of interacting massive Dirac Fermions in a gated bilayer graphene quantum dot based on the exact diagonalization of the many-body Hamiltonian. The dot is defined by a vertical electric field and lateral gates, and its single-particle (SP) energies, wave functions, and Coulomb matrix elements are computed by using the atomistic tight-binding model. The effect of the Coulomb interaction is measured by the ratio of Coulomb elements to the SP level spacing. As we increase the interaction strength, we find the electrons in a series of spin and valley symmetry-broken phases with increasing valley and spin polarizations. The phase transitions result from the competition of the SP, exchange, and correlation energy scales. A phase diagram for N = 1-6 electrons is mapped out as a function of the Coulomb interaction strength.

Optical conductivity and orbital magnetization of Floquet vortex states

Motivated by recent experimental demonstrations of Floquet topological insulators, there have been several theoretical proposals for using structured light, either spatial or spectral, to create other properties such as flat bands and vortex states. In particular, the generation of vortex states in a massive Dirac fermion insulator irradiated by light carrying nonzero orbital angular momentum (OAM) has been proposed. Here, we evaluate the orbital magnetization and optical conductivity as physical observables for such a system. We show that the OAM of light induces nonzero orbital magnetization and current density. The orbital magnetization density increases linearly as a function of the OAM degree. In certain regimes, we find that orbital magnetization density is independent of the system size, width, and Rabi frequency of light. It is shown that the orbital magnetization arising from our Floquet theory is large and can be probed by magnetometry measurements. Furthermore, we study the optical conductivity for various types of electron transitions between different states such as vortex, edge, and bulk that are present in the system. Based on the peaks in conductance, a scheme for the detection of vortex states is proposed.

Characterization of charge-carrier dynamics at the Bi2Se3/MgF2 interface by multiphoton pumped UV–Vis transient absorption spectroscopy

Separate relaxation dynamics of electrons and holes in experiments on optical pumping-probing of semiconductors is rarely observed due to their overlap. Here we report the separate relaxation dynamics of long-lived (∼200 μs) holes observed at room temperature in a 10 nm thick film of the 3D topological insulator (TI) Bi2Se3 coated with a 10 nm thick MgF2 layer using transient absorption spectroscopy in the UV–Vis region. The ultraslow hole dynamics was observed by applying resonant pumping of massless Dirac fermions and bound valence electrons in Bi2Se3 at a certain wavelength sufficient for their multiphoton photoemission and subsequent trapping at the Bi2Se3/MgF2 interface. The emerging deficit of electrons in the film makes it impossible for the remaining holes to recombine, thus causing their ultraslow dynamics measured at a specific probing wavelength. We also found an extremely long rise time (∼600 ps) for this ultraslow optical response, which is due to the large spin–orbit coupling splitting at the valence band maximum and the resulting intervalley scattering between the splitting components. The observed dynamics of long-lived holes is gradually suppressed with decreasing Bi2Se3 film thickness for the 2D TI Bi2Se3 (film thickness below 6 nm) due to the loss of resonance conditions for multiphoton photoemission caused by the gap opening at the Dirac surface state nodes. This behavior indicates that the dynamics of massive Dirac fermions predominantly determines the relaxation of photoexcited carriers for both the 2D topologically nontrivial and 2D topologically trivial insulator phases.

The Coleman correspondence at the free fermion point

We prove that the truncated correlation functions of the charge and gradient fields associated with the massless sine-Gordon model on \mathbb{R}^2 with \beta=4\pi exist for all coupling constants and are equal to those of the chiral densities and vector current of free massive Dirac fermions. This is an instance of Coleman's prediction that the massless sine-Gordon model and the massive Thirring model are equivalent (in the above sense of correlation functions). Our main novelty is that we prove this correspondence starting from the Euclidean path integral in the nonperturbative regime of the infinite volume models. We use this correspondence to show that the correlation functions of the massless sine-Gordon model with \beta=4\pi decay exponentially and that the corresponding probabilistic field is localized.

Berry phase and topology in ultrastrongly coupled quantum light-matter systems

Strong coupling between matter and quantized electromagnetic fields in a cavity has emerged as a possible route toward controlling the phase of matter in the absence of an external drive. We develop a faithful and efficient theoretical framework to analyze quantum geometry and topology in materials ultrastrongly coupled to cavity electromagnetic fields in two dimensions. The formalism allows us to accurately evaluate geometrical and topological quantities, such as Berry phase and Chern number, in ultrastrong and deep strong-coupling regimes. We apply our general framework to analyze a concrete model of massive Dirac fermions coupled to a circularly polarized cavity mode. Surprisingly, in addition to an ordinary transition to the topological phase, our analysis reveals a unique feature in deep strong-coupling regimes, namely the emergence of a reentrant transition to the topologically trivial phase. We also demonstrate its intuitive understanding by showing the unitary mapping between the low-energy effective theory of strongly coupled light-matter systems and the Haldane honeycomb model.

Linear response of entanglement entropy to Toverline{T} in massive QFTs

We compute the leading correction to entanglement entropy in Toverline{T} deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy.

Observation of Weyl and Dirac fermions at smooth topological Volkov-Pankratov heterojunctions

Weyl and Dirac relativistic fermions are ubiquitous in topological matter. Their relativistic character enables high energy physics phenomena like the chiral anomaly to occur in solid state, which allows to experimentally probe and explore fundamental relativistic theories. Here we show that on smooth interfaces between a trivial and a topological material, massless Weyl and massive Dirac fermions intrinsically coexist. The emergence of the latter, known as Volkov-Pankratov states, is directly revealed by magneto-optical spectroscopy, evidencing that their energy spectrum is perfectly controlled by the smoothness of topological interface. Simultaneously, we reveal the optical absorption of the zero-energy chiral Weyl state, whose wavefunction is drastically transformed when the topological interface is smooth. Artificial engineering of the topology profile thus provides a novel textbook system to explore the rich relativistic energy spectra in condensed matter heterostructures.