Dirac Electrons Research Articles

Valley switch effect in an α-T3 lattice-based superconducting interferometer

Abstract Dirac electrons possess a valley degree of freedom, which is currently under investigation as a potential information carrier. We propose an approach to generate and manipulate the valley-switching current (VSC) through Andreev reflection using an interferometer-based superconductor hybrid junction. The interferometer comprises a ring-shaped structure formed by topological kink states in the α-T3 lattice via carefully designed electrostatic potentials. Our results demonstrate the feasibility of achieving a fully polarized VSC in this device without contamination from cotunneling electrons sharing the same valley as the incident electron. Furthermore, we show that control over the fully polarized VSC can be achieved by applying a nonlocal gate voltage or modifying the global parameter α. The former alters the dynamic phase of electrons while the latter provides an α-dependent Berry phase, both directly influencing quantum interference and thereby affecting performance in terms of generating and manipulating VSC, crucial for advancements in valleytronics.

Dirac Electrons in Graphene Flakes

Dirac Electrons in Graphene Flakes

Viscous terahertz photoconductivity of hydrodynamic electrons in graphene.

Light incident upon materials can induce changes in their electrical conductivity, a phenomenon referred to as photoresistance. In semiconductors, the photoresistance is negative, as light-induced promotion of electrons across the bandgap enhances the number of charge carriers participating in transport. In superconductors and normal metals, the photoresistance is positive because of the destruction of the superconducting state and enhanced momentum-relaxing scattering, respectively. Here we report a qualitative deviation from the standard behaviour in doped metallic graphene. We show that Dirac electrons exposed to continuous-wave terahertz (THz) radiation can be thermally decoupled from the lattice, which activates hydrodynamic electron transport. In this regime, the resistance of graphene constrictions experiences a decrease caused by the THz-driven superballistic flow of correlated electrons. We analyse the dependencies of the negative photoresistance on the carrier density, and the radiation power, and show that our superballistic devices operate as sensitive phonon-cooled bolometers and can thus offer, in principle, a picosecond-scale response time. Beyond their fundamental implications, our findings underscore the practicality of electron hydrodynamics in designing ultra-fast THz sensors and electron thermometers.

Dirac Electrons with Molecular Relaxation Time at Electrochemical Interface between Graphene and Water.

The time dynamics of charge accumulation at the electrochemical interface between graphene and water is important for supercapacitors, batteries, and chemical and biological sensors. By using impedance spectroscopy, we have found that measured capacitance (Cm) at this interface with the gate voltage Vgate ≈ 0.1 V follows approximate laws Cm~T1.2 and Cm~T0.11 (T is Vgate period) in frequency ranges (1000-50,000) Hz and (0.02-300) Hz, respectively. In the first range, this dependence demonstrates that the interfacial capacitance (Cint) is only partially charged during the charging period. The observed weaker frequency dependence of the measured capacitance (Cm) at frequencies below 300 Hz is primarily determined by the molecular relaxation of the double-layer capacitance (Cdl) and by the graphene quantum capacitance (Cq), and it also implies that Cint is mostly charged. We have also found a voltage dependence of Cm below 10 Hz, which is likely related to the voltage dependence of Cq. The observation of this effect only at low frequencies indicates that Cq relaxation time is much longer than is typical for electron processes, probably due to Dirac cone reconstruction from graphene electrons with increased effective mass as a result of their quasichemical bonding with interfacial molecular charges.

Nernst effect of the dice lattice in a strong magnetic field

The dice lattice bears a similar honeycomb lattice structure to graphene but with a non-dispersive flat band intersecting the Dirac bands at the band center. In this work, we investigate Nernst effect of the dice lattice in a strong magnetic field, focusing on the role of the flat band. By using the Chebyshev polynomial Green’s function method, we show that no Nernst effect (Sxy=0) is around the Dirac point in the clean limit contrary to the graphene case because of the existence of a zero Hall conductivity platform. However, an unconventional negative Sxy of the double-peak structure emerges instead when the flat band is broadened by disorder and temperature. In addition, when a mass term of Dirac electrons is introduced in the system to open an energy gap, a negative single peak of Sxy appears at the Dirac point and this is due to the derivative quantum Hall effect of non-Dirac electrons in the flat band appearing in the energy gap.

Sub-Sharvin Conductance and Incoherent Shot-Noise in Graphene Disks at Magnetic Field.

Highly doped graphene samples show reduced conductance and enhanced shot-noise power compared with standard ballistic systems in two-dimensional electron gas. These features can be understood within a model that assumes incoherent scattering of Dirac electrons between two interfaces separating the sample and the leads. Here we find, by adopting the above model for the edge-free (Corbino) geometry and by computer simulation of quantum transport, that another graphene-specific feature should be observable when the current flow through a doped disk is blocked by a strong magnetic field. When the conductance drops to zero, the Fano factor approaches the value of F≈0.56, with a very weak dependence on the ratio of the disk radii. The role of finite source-drain voltages and the system behavior when the electrostatic potential barrier is tuned from a rectangular to a parabolic shape are also discussed.

Ultralow lattice thermal conductivity in type-I Dirac MBene TiB2

MBenes, the emergent novel two-dimensional family of transition metal borides have recently attracted remarkable attention. Transport studies of such two-dimensional structures are very rare and are of sparking interest. In this paper Using Boltzmann transport theory with ab-initio inputs from density functional theory, we examined the transport in TiB2 MBene system, which is highly dependent on number of layers. We have shown that the addition of an extra layer (as in bilayer BL) destroys the formation of type-I Dirac state by introducing the positional change and tilt to the Dirac cones, thereby imparting the type-II Weyl metallic character in contrast to Dirac-semimetallic character in monolayer ML. Such non-trivial electronic ordering significantly impacts the transport behavior. We further show that the anisotropic room temperature lattice thermal conductivity κ L for ML (BL) is observed to be 0.41 (0.52) and 2.00 (2.04) W m−1 K−1 for x and y directions, respectively, while the high temperature κ L (ML 0.13 W m−1 K−1 and BL 0.21 W m−1 K−1 at 900 K in x direction) achieves ultralow values. Our analysis reveals that such values are attributed to enhanced anharmonic phonon scattering, enhanced weighted phase space and co-existence of electronic and phononic Dirac states. We have further calculated the electronic transport coefficients for TiB2 MBene, where the layer dependent competing behavior is observed at lower temperatures. Our results further unravels the layer dependent thermoelectric performance, where ML is shown to have promising room-temperature thermoelectric figure of merit (ZT) as 1.71 compared to 0.38 for BL.

Topological superfluid responses of superconducting Dirac semimetals

We demonstrate that topological constraints do not only dictate the geometric part of the superfluid stiffness, but can also govern the superfluid stiffness. By introducing a general adiabatic approach for superfluid responses, we showcase such a possibility by proving that the stiffness of a superconducting Dirac cone in two dimensions (2D) is proportional to its topological charge. By relying on the emergent Lorentz invariance of Dirac electrons, we unify the superfluid stiffness and quantum capacitance in these systems. Based on this connection, we further predict a topological origin for the quantum capacitance of a Josephson junction where 2D massless Dirac electrons are sandwiched between two conventional superconductors. We show that the topological responses persist upon effecting strain, are resilient against weak disorder, and can be experimentally controlled via a Zeeman field. Remarkably, the nonuniversal topological quantization of the two superfluid responses, yet implies the universal topological quantization of the admittance modulus of the superconducting Dirac system in units of conductance. The quantum admittance effect arises when embedding the superconducting Dirac system in an ac electrical circuit with a frequency tuned at the absorption edge. These findings are in principle experimentally observable in graphene-superconductor hybrids. Published by the American Physical Society 2024

Seebeck Effect of Dirac Electrons in Organic Conductors under Hydrostatic Pressure Using a Tight-Binding Model Derived from First Principles

Seebeck Effect of Dirac Electrons in Organic Conductors under Hydrostatic Pressure Using a Tight-Binding Model Derived from First Principles

Exploring the effects of a one-dimensional periodic potential on a three-dimensional topological insulator

High mobility two-dimensional systems with superposed 1D lateral periodic potentials exhibit characteristic commensurability (Weiss) oscillations that reflect the interplay of the cyclotron radius at the Fermi level and the superlattice period. Here, we impose a one-dimensional periodic potential on strained HgTe, which is a strong 3D topological insulator. By tuning the Fermi level with top gates, the effects of the artificial potential can be studied in the bulk gap, where only Dirac surface states exist, in the conduction band, and in the valence band, where Dirac electrons and holes coexist. On the electron side, we observe clear commensurability oscillations whose period is governed by the carrier density of the top-surface Dirac electrons. Unexpectedly, weak commensurability oscillations are also observed in the valence band with a period that depends on both electron and hole density. Published by the American Physical Society 2024

Nanophotonic route to control electron behaviors in 2D materials

Abstract Two-dimensional (2D) Dirac materials, e.g., graphene and transition metal dichalcogenides (TMDs), are one-atom-thick monolayers whose electronic behaviors are described by the Dirac equation. These materials serve not only as test beds for novel quantum physics but also as promising constituents for nanophotonic devices. This review provides a brief overview of the recent effort to control Dirac electron behaviors using nanophotonics. We introduce a principle of light-2D Dirac matter interaction to offer a design guide for 2D Dirac material–based nanophotonic devices. We also discuss opportunities for coupling nanophotonics with externally perturbed 2D materials.

Nonspreading relativistic electron wavepacket in a strong laser field

A solution of the Dirac equation in a strong laser field presenting a nonspreading wave packet of the electron is derived. It consists of a generalization of the self-accelerating free electron wavepacket [I. Kaminer , ] to the case with the background of a strong laser field. Built upon the notion of nonspreading for an extended relativistic wavepacket, the concept of Born rigidity for accelerated motion in relativity is the key ingredient of the solution. At its core, the solution comes from the connection between the self-accelerated free electron wavepacket and the eigenstate of a Dirac electron in a constant and homogeneous gravitational field via the equivalence principle. The solution is an essential step towards the realization of the laser-driven relativistic collider [S. Meuren , ], where the large spreading of a common Gaussian wavepacket during the excursion in a strong laser field strongly limits the expectable yields. Published by the American Physical Society 2024

Observation of Kekulé vortices around hydrogen adatoms in graphene

Fractional charges are one of the wonders of the fractional quantum Hall effect. Such objects are also anticipated in two-dimensional hexagonal lattices under time reversal symmetry—emerging as bound states of a rotating bond texture called a Kekulé vortex. However, the physical mechanisms inducing such topological defects remain elusive, preventing experimental realization. Here, we report the observation of Kekulé vortices in the local density of states of graphene under time reversal symmetry. The vortices result from intervalley scattering on chemisorbed hydrogen adatoms. We uncover that their 2π winding is reminiscent of the Berry phase π of the massless Dirac electrons. We can also induce a Kekulé pattern without vortices by creating point scatterers such as divacancies, which break different point symmetries. Our local-probe study thus confirms point defects as versatile building blocks for Kekulé engineering of graphene’s electronic structure.

Strain-induced modulation of electronic structure in correlated Dirac semimetal Pv-CaIrO3 epitaxial thin films

Perovskite CaIrO3 is theoretically predicted to be a Dirac node semimetal near the Mott transition, which possesses a considerable interplay between electron correlations and spin–orbit coupling. Electron correlations can significantly tune the behavior of relativistic Dirac fermions. Here, we have grown high-quality perovskite CaIrO3 thin films on different substrates using oxide molecular beam epitaxy to modulate both electron correlations and Dirac electron states. Through in situ angle-resolved photoemission spectroscopy, we demonstrate a systematic evolution of the bandwidth and effective mass of Jeff=1/2 band in perovskite CaIrO3 induced by strain. The bandwidth of the Jeff=1/2 band undergoes an evident increase under in-plane compressive strain, which could be attributed to the weakening of electron correlations. The compressive strain can potentially shift the position of the Dirac node relative to the Fermi level and play a vital role in the transition from hole-type to electron-type transport characteristics. Our work provides a feasible approach for manipulating the topological Dirac electron states by engineering the strength of electron correlations.

Emergence of quantum confinement in topological kagome superconductor CsV3Sb5

Quantum confinement is a restriction on the motion of electrons in a material to specific region, resulting in discrete energy levels rather than continuous energy bands. In certain materials, quantum confinement could dramatically reshape the electronic structure and properties of the surface with respect to the bulk. Here, in the recently discovered kagome superconductors CsV3Sb5, we unveil the dominant role of quantum confinement in determining their surface electronic structure. Combining angle-resolved photoemission spectroscopy (ARPES) measurement and density-functional theory simulation, we report the observations of two-dimensional quantum well states due to the confinement of bulk electron pocket and Dirac cone to the nearly isolated surface layer. The theoretical calculations on the slab model also suggest that the ARPES observed spectra are almost entirely contributed by the top two layers. Our results not only explain the disagreement of band structures between the recent experiments and calculations, but also suggest an equally important role played by quantum confinement, together with strong correlation and band topology, in shaping the electronic properties of this material.

Emission of twisted photons by a Dirac electron in a strong magnetic field

We study the spontaneous emission of a photon during the transitions between relativistic Landau states of an electron in a constant magnetic field that can reach the Schwinger value of Hc=4.4×109 T. In contrast to the conventional method, in which detection of both the final electron and the photon are implied in a certain basis, here we derive the photon state as it evolves from the process itself. It is shown that the emitted photon state represents a twisted Bessel beam propagating along the field axis with a total angular momentum (TAM) projection onto this axis ℓ−ℓ′, where ℓ and ℓ′ are the TAM of the initial electron and of the final one, respectively. Thus, the majority of the emitted photons turn out to be twisted, with ℓ−ℓ′≳1, even when the magnetic field reaches the critical value of H∼Hc. The transitions without a change of the electron angular momentum, ℓ′=ℓ, are possible, yet much less probable. We also compare our findings with those for a spinless charged particle and demonstrate their good agreement for the transitions without change of the electron spin projection even in the critical fields, while the spin-flip transitions are generally suppressed. In addition, we argue that whereas the ambiguous choice of an electron spin operator affects the differential probability of emission, this problem can partially be circumvented for the photon evolved state because it is the electron TAM rather than the spin alone that defines the TAM of the emitted twisted photon. Published by the American Physical Society 2024

Spatial quasi-bound states of Dirac electrons in graphene monolayer

Our study investigated the emergence of spatial quasi-bound states (QBSs) in graphene monolayers induced by rectangular potential barriers. By solving the time-independent Dirac equation and using the transfer matrix formalism, we calculated the resonance energies and identify the QBSs based on probability density functions (PDF). We analyzed two types of structures: single and double barriers, and we find that the QBSs are located within the barrier region, at energies higher than the single barrier. Additionally, we observe QBSs in the double barrier and their position depends on the distance and width of the well between the two barriers. The width and height of the barrier significantly impact the QBSs while the well width influences the resonance energy levels of the QBSs in the double barrier. Interestingly, the QBSs can be manipulated in the graphene system, offering potential for optoelectronic devices. Finally, our results demonstrated that the spatial localization of these states is counter-intuitive and holds great promise for future research in optolectronic devices.

Floquet Weyl states at one-photon resonance: An origin of nonperturbative optical responses in three-dimensional materials

Electrons driven coherently by laser light can exhibit nonperturbative geometric effects. Drastic deformation and gap openings of the electrons' Floquet bands occur at one-photon resonances since the electron and hole bands hybridize through their replicas at the lowest-order photon exchange. We study the evolution of Floquet bands in three-dimensional (3D) materials driven by circularly polarized light (CPL) using the Dirac model. We find that the light-induced gap closes at a select few points in the momentum space where Floquet Weyl points are formed. The Weyl points are protected by their monopole charge and can merge, separate, or pair annihilate depending on the anisotropy of electrons and the ellipticity of the incident light. In isotropic 3D Dirac electrons driven by CPL, the Weyl points merge to form Floquet double-Weyl points with topological charge ±2. Our results reveal a universal aspect of light-matter interactions in 3D quantum materials and open a route towards controllable versatile electromagnetic responses associated with light-induced Floquet Weyl states. Published by the American Physical Society 2024

The electronic and electromagnetic Dirac equations

Maxwell’s equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which has been widely researched since the Dirac equation was proposed. In this paper, we show that the Maxwell equations can be written in an exact form of the Dirac equation by representing the four Dirac operators with 8×8 matrices. Unlike the ordinary 4×4 Dirac equation, both spin–1/2 and spin–1 operators can be derived from the 8×8 Dirac equation, manifesting that the 8×8 Dirac equation is able to describe both electrons and photons. As a result of the restrictions that the electromagnetic wave is a transverse wave, the photon is a spin–1 particle. The four–current in the Maxwell equations and the mass in the electronic Dirac equation also force the electromagnetic field to transform differently to the electronic field. We use this 8×8 representation to find that the Zitterbewegung of the photon is actually the oscillatory part of the Poynting vector, often neglected upon time averaging.

Diamond lattice in single-component molecular crystals comprising tetrabenzoporphyrin neutral radicals.

A single-component molecular radical crystal of CoIII(tbp˙-)(CN)2, where tbp = tetrabenzoporphyrinato ligand, exhibiting a diamond lattice was fabricated as a potential candidate for a three-dimensional Dirac electron system. Band structure calculations revealed that the Fermi energy level was located at the Dirac point. A small electrical resistivity of 160 Ω cm was observed at 2 K under the application of 2.4 GPa. Furthermore, substituting CoIII by FeIII or MnIII led to the introduction of local magnetic moments into the diamond-lattice system. MIII(tbp˙-)L2 crystals will open up uncharted fields in the study of the Dirac electron systems.