Two-dimensional Dirac Fermions Research Articles

Pseudo entropy under joining local quenches

We compute the pseudo entropy in two-dimensional holographic and free Dirac fermion CFTs for excited states under joining local quenches. Our analysis reveals two of its characteristic properties that are missing in the conventional entanglement entropy. One is that, under time evolution, the pseudo entropy exhibits a dip behavior as the excitations propagate from the joined point to the boundaries of the subsystem. The other is that the excess of pseudo entropy over entanglement entropy can be positive in holographic CFTs, whereas it is always non-positive in free Dirac fermion CFTs. We argue that the entropy excess can serve as a measure of multi-partite entanglement. Its positivity implies that the vacuum state in holographic CFTs possesses multi-partite entanglement, in contrast to free Dirac fermion CFTs.

Gate tunable terahertz cyclotron emission from two-dimensional Dirac fermions

Two-dimensional Dirac fermions in HgTe quantum wells close to the topological phase transition can generate significant cyclotron emission that is magnetic field tunable in the terahertz frequency range. Due to their relativistic-like dynamics, their cyclotron mass is strongly dependent on their electron concentration in the quantum well, providing a second tunability lever and paving the way for a gate-tunable, permanent-magnet Landau laser. In this work, we demonstrate the proof-of-concept of such a back-gate tunable THz cyclotron emitter at a fixed magnetic field. The emission frequency detected at 1.5 T is centered at 2.2 THz and can already be electrically tuned over 250 GHz. With an optimized gate and a realistic permanent magnet of 1.0 T, we estimate that the cyclotron emission could be continuously and rapidly tunable by the gate bias between 1 and 3 THz, that is to say on the less covered part of the THz gap.

TMM computed Graphene optical properties: Comparison to experimental data

Graphene is a revolutionary two-dimensional substance whose unusual features have piqued the interest of scientists and technologists alike. Owing to the structure and behavior of the electrons in the material, it exhibits fascinating optical properties. In this study, the transmittance, reflectance, and absorbance were investigated using a Python-based version of the Transfer Matrix Method. The computations are carried out using experimental refractive indices. The derived results agree quite well with the existing experimental results, even better than the two-dimensional Dirac fermions model. Specifically, in the UV spectrum, the observed transmittance behavior was successfully mirrored in the case of the CVD monolayer graphene. Our results also suggest that transmittance can be used as an efficient probe for determining the thickness of graphene membranes. However, the transmittance did not vary linearly with the number of layers, as the thickness increased. Although it was demonstrated that it could be modeled perfectly by linear regression for the first five layers and less conveniently for the first ten layers, the entire shape is modeled by a second-order polynomial function. The dependence of the optical properties of graphene on the angle of incidence, wavelength, and polarization has been investigated extensively.

Random magnetic field and the Dirac Fermi surface

We study a single two-dimensional Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated to each point on the Fermi surface) coupled by a random vector potential. This low-energy theory exhibits an exactly solvable random fixed line, along which we directly compute various disorder-averaged observables without the need for the usual replica, supersymmetry, or Keldysh techniques. We find the longitudinal dc conductivity in the collisionless $\ensuremath{\hbar}\ensuremath{\omega}/{k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit to be nonuniversal and to vary continuously along the fixed line.

Long-range adsorbate interactions mediated by two-dimensional Dirac fermions

We provide here an analytical formalism to describe the indirect interaction between adsorbed atom or molecule pairs mediated by two-dimensional (2D) Dirac fermions. We show that in contrast to the case of traditional 2D electron gas, in the 2D Dirac system, the long-range interaction behaves as 1/r 3 decaying Friedel oscillation. This analytical formalism is fully consistent with a tight-binding numerical calculation of honeycomb lattices. Our formalism is suitable for the realistic 2D Dirac materials, such as graphene and surface states of three-dimensional topological insulators.

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 non-Abelian 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 ${\mathrm{QED}}_{3}$ 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.

Two-dimensional Dirac fermions in a mass superlattice

We study two-dimensional (2D) Dirac fermions in the presence of a periodic mass term alternating between positive and negative values along one direction. This scenario could be realized for a graphene monolayer or for the surface states of topological insulators. The low-energy physics is governed by chiral Jackiw-Rebbi modes propagating along zero-mass lines, with the energy dispersion of the Bloch states given by an anisotropic Dirac cone. By means of the transfer matrix approach, we obtain exact results for a piecewise constant mass superlattice. On top of Bloch states, two different classes of boundary and/or interface modes can exist in a finite-size geometry or in a nonuniform electrostatic potential, respectively. We compute the dispersion relation for both types of boundary and interface modes, which originate either from states close to the superlattice Brillouin zone (BZ) center or, via a Lifshitz transition, from states near the BZ boundary. In the presence of a potential step, we predict that the interface modes, the Bloch wave functions, and the electrical conductance will sensitively depend on the step position relative to the mass superlattice.

Coherent Interlayer Coupling in Quasi-Two-Dimensional Dirac Fermions in α-(BEDT-TTF)2I3

Theoretical and experimental studies have supported that the electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure is described by two-dimensional Dirac fermions. When the interlayer tunneling is coherent, the electronic structure of the system becomes three-dimensional, and we expect the peak structure to appear in the interlayer resistivity under magnetic fields. We theoretically and experimentally show that the peak appears in the interlayer resistivity at low temperatures and high magnetic fields. From the experiment, we estimate that the magnitude of the interlayer tunneling is $t_1 \sim 1$ meV. Our result opens the door to investigating the three-dimensional electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$.

Terahertz cyclotron emission from two-dimensional Dirac fermions

Since the emergence of graphene, we have seen several proposals for the realization of Landau lasers tunable over the terahertz frequency range. The hope was that the non-equidistance of the Landau levels from Dirac fermions would suppress the harmful non-radiative Auger recombination. Unfortunately, even with this non-equidistance an unfavorable non-radiative process persists in Landau-quantized graphene, and so far no cyclotron emission from Dirac fermions has been reported. One way to eliminate this last non-radiative process is to sufficiently modify the dispersion of the Landau levels by opening a small gap in the linear band structure. A proven example of such gapped graphene-like materials are HgTe quantum wells close to the topological phase transition. In this work, we experimentally demonstrate Landau emission from Dirac fermions in such HgTe quantum wells, where the emission is tunable by both the magnetic field and the carrier concentration. Consequently, these results represent an advance in the realization of terahertz Landau lasers tunable by magnetic field and gate-voltage.

Transport anisotropy and metal-insulator transition in striped Dirac fermion systems

Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transitions induced by the stripe of charge density in an interacting two-dimensional Dirac fermion system. The stripe will introduce the transport anisotropy and insulating intermediate phase into the system, accompanied by the change of band structure and a peak of density of states around Fermi energy. In the case of strong correlation, stripe exhibits competition with Coulomb repulsion through closing the energy gap and disrupting the magnetic order and finally drives the system in the Mott insulating phase back to the metallic state. Our results may provide a feasible way to modify transport properties by setting charge stripes in experiments.

Unusual Magnetotransport from two-dimensional Dirac Fermions in Pd3Bi2Se2

Pd$_{3}$Bi$_{2}$Se$_{2}$ has been proposed to be topologically non-trivial in nature. However, evidence of its non-trivial behavior is still unexplored. We report the growth and magneto-transport study of Pd$_{3}$Bi$_{2}$Se$_{2}$ thin films, revealing for the first time the contribution of two-dimensional (2D) topological surface states. We observe exceptional non-saturated linear magnetoresistance which results from Dirac fermions inhabiting the lowest Landau level in the quantum limit. The transverse magnetoresistance changes from a semi-classical weak-field $B^{2}$ dependence to a high-field $B$ dependence at a critical field $B^{\star}$. It is found that $B^{\star} \propto T^2$, which is expected from the Landau level splitting of a linear energy dispersion. In addition, the magnetoconductivity shows signatures of 2D weak anti-localization (WAL). These novel magnetotransport signatures evince the presence of 2D Dirac fermions in Pd$_{3}$Bi$_{2}$Se$_{2}$ thin films.

SO(4) multicriticality of two-dimensional Dirac fermions

We study quantum multicritical behavior in a (2+1)-dimensional Gross-Neveu-Yukawa field theory with eight-component Dirac fermions coupled to two triplets of order parameters that act as Dirac masses, and transform as $(1,0) + (0,1)$ representation under the SO(4)$\simeq$SO(3)$\times$SO(3) symmetry group. This field theory is relevant to spin-1/2 fermions on honeycomb or $\pi$-flux lattices, for example, near the transition points between an $s$-wave superconductor and a charge-density wave, on one side, and N\'eel order, on the other. Two triplets of such order parameters always allow for a common pair of two other order parameters that would complete them to the maximal set of compatible (anticommuting) orders of five. We first derive a unitary transformation in the Nambu (particle-hole) space which maps any two such triplets, possibly containing some superconducting orders, onto purely insulating order parameters. This allows one to consider a universal SO(4) Gross-Neveu-Yukawa description of the multicriticality without any Nambu doubling. We then proceed to derive the renormalization-group flow of the coupling constants at one-loop order in $4-\epsilon$ space-time dimensions, allowing also a more general set of order parameters transforming under SO($n_a$)$\times$SO($n_b$). While for $n_a=n_b > 2 $ in the bosonic sector and with fermions decoupled there is a stable fixed point of the flow, the Yukawa coupling to fermions quickly leads to its elimination by a generic fixed-point collision in the relevant range of fermion flavor numbers $N_f$. This suggests the replacement of the critical behavior by a runaway flow in the physical case $n_a=n_b=3$. The structure of the RG flow at $n_a\neq n_b$ is also discussed, and some non-perturbative arguments in favor of the stability of the decoupled critical point when $n_a=3$ and $n_b=1$ in $D=2+1$ are provided.

Magnetic phase transition in disordered interacting Dirac fermion systems via the Zeeman field

Using the determinant quantum Monte Carlo method, we investigate the antiferromagnetic phase transition that is induced by the Zeeman field in a disordered interacting two-dimensional Dirac fermion system. At a fixed interaction strength $U$, the antiferromagnetic correlation is enhanced as the magnetic field increases and, when the magnetic field is larger than a ${B}_{c}(U)$, the antiferromagnetic correlation shall be suppressed by the increased magnetic field. The impact of Zeeman field $B$, Coulomb repulsion $U$, and disorder $\mathrm{\ensuremath{\Delta}}$ is not isolated. The intensity of magnetic field effect on the antiferromagnetic correlation shall be strongly suppressed by disorder. Differently, it will be promoted by weak interaction, but, when $U$ becomes larger than ${U}_{c}=4.5$, the increased interaction will suppress the intensity of this effect and here ${U}_{c}=4.5$ coincides with the critical strength inducing the metal-Mott insulator transition in a clean system. Moreover, at a fixed magnetic field $B$, strong interaction shall suppress the antiferromagnetic phase rather than promote it.

Observation of possible nonlinear anomalous Hall effect in organic two-dimensional Dirac fermion system

We report the observation of nonlinear anomalous Hall effect (NLAHE) in the multilayered organic conductor α-(BEDT-TTF)2I3 in the charge order (CO) insulating phase just under the critical pressure for transition into two-dimensional (2D) massless Dirac fermion (DF) phase. We successfully extracted the finite nonlinear Hall voltage proportional to square current at zero magnetic field. The observed NLAHE features, current direction dependence and correlation with CO, are consistent with the previous estimation assuming 2D massive DF with a pair of tilted Dirac cones. This is the first observation of topological transport in organic conductors, and also the first example of NLAHE in the electronic phase with spontaneous symmetry breaking.

Spin waves in doped graphene: A time-dependent spin density functional approach to collective excitations in paramagnetic two-dimensional Dirac fermion gases

In spin-polarized itinerant electron systems, collective spin-wave modes arise from dynamical exchange and correlation (xc) effects. We consider here spin waves in doped paramagnetic graphene with adjustable Zeeman-type band splitting. The spin waves are described using time-dependent spin density functional response theory, treating dynamical xc effects within the Slater and Singwi-Tosi-Land-Sj\"olander approximations. We obtain spin-wave dispersions and spin stiffnesses as a function of doping and spin polarization, and we discuss the prospects for their experimental observation.

Optical evidence for non-Hermitian topological phases of two-dimensional Dirac fermions

We theoretically investigate the topological band structures of a non-Hermitian Dirac Hamiltonian in two dimensions that effectively describes a non-Hermitian Chern insulator. The optical conductivity in various phases has been calculated. Five distinct phases with different topological features are shown explicitly. We redefine the point-gapped phase for the non-Hermitian counterparts and the gapless phases with the eigenenergies coalescing into a Dirac point or bulk Fermi arc, where the exceptional points (EPs) are formed at the ends of arc, as the non-Hermitian Dirac semiconductor (NHDSC), non-Hermitian Dirac semimetal (NHDSM), and non-Hermitian Fermi arc (NHFA) phases, respectively. It has been found that the evolution of topological phases can be achieved by coordinating the relative strengths of band-dependent scattering. By extending the optical response theory into the realm of non-Hermitian quantum systems, we analyze the spectral functions and the optical conductivity tensors in the respective phases in detail. We show that the mass parameter is critical for the anomalous Hall effect in the non-Hermitian system. The influence of temperature on the real and imaginary parts of frequency dependent conductivities is also presented. Our results indicate that the non-Hermiticity modifies the electron structure, so that the bulk topology is embodied in the dynamic response. We suggest an optical approach to probe new physics accompanied by non-Hermiticity in the massive Dirac systems.

Thermoelectric Effect at Quantum Limit in Two-Dimensional Organic Dirac Fermion System with Zeeman Splitting

The thermoelectric effect in a two-dimensional (2D) massless Dirac fermion (DF) system at the quantum limit is discussed to verify the prediction of high-performance thermopower in an organic conductor \alpha-(BEDT-TTF)2I3. Because of relatively large Zeeman splitting in \alpha-(BEDT-TTF)2I3, the boundless increase of thermopower at high magnetic fields, predicted without the Zeeman effect, is hardly expected, whereas there appears to be a broad local maximum. This is characteristic of 2D DF systems with Zeeman splitting and is recognized in the previous experiment. In contrast to 3D Dirac/Weyl semimetals with robust gapless features, it might be difficult to realize high-performance thermopower in real 2D DF systems under high magnetic fields.

De Haas–van Alphen oscillations near the Lifshitz transition from two electron pockets to one in the two-dimensional Dirac fermion systems

We theoretically study the de Haas-van Alphen (dHvA) oscillations in the system with changing the topology of the Fermi surface (the Lifshitz transition) by electron dopings. We employ the two-dimensional tight binding model for $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure which has two Dirac points in the first Brillouin zone. When this system is slightly doped, there exists two closed Fermi surfaces with the same area and the dHvA oscillations become saw-tooth pattern or inversed saw-tooth pattern for both cases of fixed electron filling ($\nu$) or fixed chemical potential ($\mu$) with respect to the magnetic field, respectively. By increasing dopings, the system approaches the Lifshitz transition, where two closed Fermi surfaces are close each other. Then, we find that the pattern of the dHvA oscillations changes. A jump of the magnetization appears at the center of the fundamental period and its magnitude increases in the case of the fixed electron filling, while a jump is separated into a pair of jumps and its separation becomes large in the case of the fixed chemical potential. This is due to the lifting of double degeneracy in the Landau levels. Since this lifting is seen in the two-dimensional Dirac fermion system with two Dirac points, the obtained results in this study can be applied to not only $\alpha$-(BEDT-TTF)$_2$I$_3$ but also other materials with closely located Dirac points such as graphene under the uniaxial strain, in black phosphorus, twisted bilayer graphene, and so on.

Spin Hall and inverse spin galvanic effects in graphene with strong interfacial spin-orbit coupling: A quasi-classical Green's function approach

van der Waals heterostructures assembled from atomically thin crystals are ideal model systems to study spin-orbital coupled transport because they exhibit a strong interplay between spin, lattice and valley degrees of freedom that can be manipulated by strain, electric bias and proximity effects. The recently predicted spin-helical regime in graphene on transition metal dichalcogenides, in which spin and pseudospin degrees of freedom are locked together [M. Offidani et al. Phys. Rev. Lett. 119, 196801 (2017)], suggests their potential application in spintronics. Here, by deriving an Eilenberger equation for the quasiclassical Green's function of two-dimensional Dirac fermions in the presence of} spin-orbit coupling\textcolor{black}{{} (SOC) and scalar disorder, we obtain analytical expressions for the dc spin galvanic susceptibility and spin Hall conductivity in the spin-helical regime. Our results disclose a sign change in the spin Hall angle (SHA) when the Fermi energy relative to the Dirac point matches the Bychkov-Rashba energy scale, irrespective of the magnitude of the spin-valley interaction imprinted on the graphene layer. The behavior of the SHA is connected to a reversal of the total internal angular momentum of Bloch electrons that reflects the spin-pseudospin entanglement induced by SOC. We also show that the charge-spin conversion reaches a maximum when the Fermi level lies at the edge of the spin-minority band in agreement with previous findings. Both features are fingerprints of spin-helical Dirac fermions and suggest a direct way to estimate the strength of proximity-induced SOC from transport data. The relevance of these findings for interpreting recent spin-charge conversion measurements in nonlocal spin-valve geometry is also discussed.

Inducing a metal-insulator transition in disordered interacting Dirac fermion systems via an external magnetic field

We investigate metal-insulator transitions on an interacting two-dimensional Dirac fermion system using the determinant quantum Monte Carlo method. The interplay between Coulomb repulsion, disorder and magnetic fields, drives the otherwise semi-metallic regime to insulating phases exhibiting different characters. In particular, with the focus on the transport mechanisms, we uncover that their combination exhibits dichotomic effects. On the one hand, the critical Zeeman field $B_c$, responsible for triggering the band-insulating phase due to spin-polarization on the carriers, is largely reduced by the presence of the electronic interaction and quenched disorder. On the other hand, the insertion of a magnetic field induces a more effective localization of the fermions, facilitating the onset of Mott or Anderson insulating phases. Yet these occur at moderate values of $B$, and cannot be explained by the full spin-polarization of the electrons.