Dirac Fermion System Research Articles

Quantum phase transitions of multispecies Dirac fermions

We use the determinant Quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\pi$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac fermions. It is found that the critical interaction strength $U_c$ is decreased by reducing the velocity of the outer Dirac cone, while the inner cone velocity fixes the band width. Although $U_c$ is monotonic, at fixed inverse temperature $\beta$ the antiferromagnetic (AF) structure factor has a maximum as a function of the hopping modulation. We also study the corresponding strong coupling (Heisenberg model) limit, where the sublattice magnetization is enhanced by the alternation of the exchange couplings. The AF order is shown to be non-monotonic, and maximal at an intermediate degree of anisotropy, in qualitative agreement with the Hubbard model. These results quantify the effect of the velocities on the critical interaction strength in Dirac fermion systems and enable an additional degree of control which will be useful in studying strong correlation physics in ultracold atoms in optical lattices.

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera.

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting-henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Magnetotransport in Layered Dirac Fermion System Coupled with Magnetic Moments

We theoretically investigate the magnetotransport of Dirac fermions coupled with localized moments to understand the physical properties of the Dirac material EuMnBi$_2$. Using an interlayer hopping form, which simplifies the complicated interaction between the layers of Dirac fermions and the layers of magnetic moments in EuMnBi$_2$, the theory reproduces most of the features observed in this system. The hysteresis observed in EuMnBi$_2$ can be caused by the valley splitting that is induced by the spin-orbit coupling and the external magnetic field with the molecular field created by localized moments. Our theory suggests that the magnetotransport in EuMnBi$_2$ is due to the interplay among Dirac fermions, localized moments, and spin-orbit coupling.

Strong Plasmon-Phonon Splitting and Hybridization in 2D Materials Revealed through a Self-Energy Approach

We reveal new aspects of the interaction between plasmons and phonons in 2D materials that go beyond a mere shift and increase in plasmon width due to coupling to either intrinsic vibrational modes of the material or phonons in a supporting substrate. More precisely, we predict strong plasmon splitting due to this coupling, resulting in a characteristic avoided crossing scheme. We base our results on a computationally efficient approach consisting in including many-body interactions through the electron self-energy. We specify this formalism for a description of plasmons based upon a tight-binding electron Hamiltonian combined with the random-phase approximation. This approach is accurate provided vertex corrections can be neglected, as is is the case in conventional plasmon-supporting metals and Dirac-fermion systems. We illustrate our method by evaluating plasmonic spectra of doped graphene nanotriangles with varied size, where we predict remarkable peak splittings and other radical modifications in the spectra due to plasmons interactions with intrinsic optical phonons. Our method is equally applicable to other 2D materials and provides a simple approach for investigating coupling of plasmons to phonons, excitons, and other excitations in hybrid thin nanostructures.

ARPES studies of the inverse perovskite Ca3PbO : Experimental confirmation of a candidate 3D Dirac fermion system

We investigate the band structure of the inverse perovskite ${\mathrm{Ca}}_{3}\mathrm{PbO}$, a candidate three-dimensional (3D) Dirac fermion material, through soft x-ray angle-resolved photoemission spectroscopy. Conelike band dispersions are observed for ${\mathrm{Ca}}_{3}\mathrm{PbO}$, in close agreement with the predictions of electronic structure calculations. We further demonstrate that chemical substitution of Bi for Pb is effective in tuning the Fermi level of ${\mathrm{Ca}}_{3}\mathrm{PbO}$ while leaving its electronic structure intact. Our study confirms that the inverse perovskite family provides a promising platform for the exploration of 3D Dirac fermion systems.

Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions

We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the Pseudo Quantum Electrodynamics (PQED) and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large$-N_f$ expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the non-perturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value $\alpha_c(D N_f)$. In particular, we obtain the critical coupling constant $\alpha_c\approx 0.36$ for $D N_f=8$., where $D=2,4$ corresponds to the SU(2) and SU(4) cases, respectively, and $N_f$ is the flavor number. Our results show a decreasing of the critical coupling constant in comparison with the case of pure electromagnetic interaction, thus yielding a more favorable scenario for the occurrence of dynamical symmetry breaking. For two-dimensional materials,in application in condensed matter systems, it implies an energy gap at the Dirac points or valleys of the honeycomb lattice.

Functional integral method in quantum field theory of Dirac fermions in graphene

The purpose of this work is to elaborate the functional integral method in quantum field theory of Dirac fermions in the Dirac fermion gas of a graphene single layer at vanishing absolute temperature. The starting point to be assumed as the fundamental principle of the theory is the explicit expression of the action functional of this system. The efficient mathematical tool to be used in the study is the generating functional containing the Grassmann parameters anticommuting with the Dirac fermion field operators.The analytical expression of the generating functional of free Dirac fermion system is exactly derived and efficiently used in the study of 2n-point Green functions of free Dirac fermions. Then the celebrated Hubbard–Stratonovich transformation is applied to rewrite the functional integral of the interacting system of Dirac fermions in a new form expressing in terms of a scalar Hermitian quantum field describing the collective excitations in the interacting Dirac fermion gas and related to the graphene plasmons.

Anomalous Hall Coulomb drag of massive Dirac fermions

Dirac fermions are actively investigated, and the discovery of the quantized anomalous Hall effect of massive Dirac fermions has spurred the promise of low-energy electronics. Some materials hosting Dirac fermions are natural platforms for interlayer coherence effects such as Coulomb drag and exciton condensation. Here we determine the role played by the anomalous Hall effect in Coulomb drag in massive Dirac fermion systems. We focus on topological insulator films with out-of plane magnetizations in both the active and passive layers. The transverse response of the active layer is dominated by a topological term arising from the Berry curvature. We show that the topological mechanism does not contribute to Coulomb drag, yet the longitudinal drag force in the passive layer gives rise to a transverse drag current. This anomalous Hall drag current is independent of the active-layer magnetization, a fact that can be verified experimentally. It depends non-monotonically on the passive-layer magnetization, exhibiting a peak that becomes more pronounced at low densities. These findings should stimulate new experiments and quantitative studies of anomalous Hall drag.

Magnetooptical determination of a topological index

When a Dirac fermion system acquires an energy-gap, it is said to have either trivial (positive energy-gap) or non-trivial (negative energy-gap) topology, depending on the parity ordering of its conduction and valence bands. The non-trivial regime is identified by the presence of topological surface or edge-states dispersing in the energy gap of the bulk and is attributed a non-zero topological index. In this work, we show that such topological indices can be determined experimentally via an accurate measurement of the effective velocity of bulk massive Dirac fermions. We demonstrate this approach analytically starting from the Bernevig-Hughes-Zhang Hamiltonian to show how the topological index depends on this velocity. We then experimentally extract the topological index in Pb1-xSnxSe and Pb1-xSnxTe using infrared magnetooptical Landau level spectroscopy. This approach is argued to be universal to all material classes that can be described by a Bernevig-Hughes-Zhang-like model and that host a topological phase transition.

Effect of Interband Fluctuation on Spin Susceptibility in Molecular Dirac Fermion System α-(BEDT-TTF)2I3

The nontrivial properties of interband spin fluctuations are studied by the random phase approximation in a Hubbard model describing the molecular conductor α-(BEDT-TTF)2I3, where wave functions are based on the four sublattices named A, A′, B, and C in a two-dimensional BEDT-TTF molecular plane. It is found that the ferrimagnetic polarization observed by a recent NMR measurement emerges only if there exist cross terms among intra- and inter-band irreducible susceptibility matrix elements in the presence of the on-site Coulomb interaction U. It is also found that the nontrivial sign of the interband components of the spin susceptibility, being negative only for the B sublattice, is closely related to the characteristic phase structure of wave functions in the Dirac fermion system with multisublattices. The negative value of the spin susceptibility on the B sublattice observed in the experiment is associated with this negative interband susceptibility, which comes from the excitations in the gentle-slope r...

Scars in Dirac fermion systems: the influence of an Aharonov–Bohm flux

Time-reversal (-) symmetry is fundamental to many physical processes. Typically, -breaking for microscopic processes requires the presence of magnetic field. However, for 2D massless Dirac billiards, -symmetry is broken automatically by the mass confinement, leading to chiral quantum scars. In this paper, we investigate the mechanism of -breaking by analyzing the local current of the scarring eigenstates and their magnetic response to an Aharonov–Bohm flux. Our results unveil the complete understanding of the subtle -breaking phenomena from both the semiclassical formula of chiral scars and the microscopic current and spin reflection at the boundaries, leading to a controlling scheme to change the chirality of the relativistic quantum scars. Our findings not only have significant implications on the transport behavior and spin textures of the relativistic pseudoparticles, but also add basic knowledge to relativistic quantum chaos.

Investigation of Giant Lorenz Ratio of Dirac-Fermion Systems by Numerical Calculations

Investigation of Giant Lorenz Ratio of Dirac-Fermion Systems by Numerical Calculations

Chiral anomaly in real space from stable fractional charges at the edge of a quantum spin Hall insulator

The chiral anomaly is based on a non-conserved chiral charge and can happen in Dirac fermion systems under the influence of external electromagnetic fields. In this case, the spectral flow leads to a transfer of right- to left-moving excitations or vice versa. The corresponding transfer of chiral particles happens in momentum space. We here describe an intriguing way to introduce the chiral anomaly into real space. Our system consists of two quantum dots that are formed at the helical edge of a quantum spin Hall insulator on the basis of three magnetic impurities. Such a setup gives rise to fractional charges which we show to be sharp quantum numbers for large barrier strength. Interestingly, it is possible to map the system onto a quantum spin Hall ring in the presence of a flux pierced through the ring where the relative angle between the magnetization directions of the impurities takes the role of the flux. The chiral anomaly in this system is then directly related to the excess occupation of particles in the two quantum dots. This analogy allows us to predict an observable consequence of the chiral anomaly in real space.

Schwinger pair creation in Dirac semimetals in the presence of external magnetic and electric fields

We discuss the Schwinger pair creation process for the system of massless Dirac fermions in the presence of constant external magnetic and electric fields. The pair production rate remains finite unlike the vacuum decay rate. In the recently discovered Dirac semimetals, where the massless Dirac fermions emerge, this pair production may be observed experimentally through the transport properties. We estimate its contribution to the ordinary conductivity of the semimetals.

Capacitance spectroscopy of a system of gapless Dirac fermions in a HgTe quantum well

Information on the density of states of two-dimensional Dirac fermions in a 6.6-nm-thick HgTe quantum well that corresponds to a transition from the direct to inverted spectrum is obtained for the first time by means of capacitance measurements. It is found that the density of states of Dirac electrons is a linear function of the Fermi energy at EF > 30 meV with the corresponding velocity vDF = 8.2 × 105 m/s. At lower energies, this dependence deviates from the linear law, indicating a strong effect of disorder, which is associated with fluctuations of a built-in charge, on the density of states of the studied system near the Dirac point. At negative energies, a sharp increase in the density of states is observed, which is associated with the tail of the density of states of valleys of heavy holes. The described behavior is in agreement with the proposed model, which includes both the features of the real spectrum of Dirac fermions and the effect of the fluctuation potential.

Topological Domain Wall and Valley Hall Effect in Charge Ordered Phase of Molecular Dirac Fermion System α-(BEDT-TTF)2I3

The topological domain wall and valley Hall effect are theoretically investigated in the molecular conductor α-(BEDT-TTF)2I3. By using the mean-field theory in an extended Hubbard model, it is demonstrated under a cylinder boundary condition that a domain wall emerges in the charge ordered phase, and exhibits a topological nature near the phase transition to the massless Dirac Fermion phase. The topological nature is well characterized by the Berry curvature, which has opposite signs in two charge ordered phases divided by the domain wall, and gives rise to the valley Hall conductivity with opposite signs, enabling these phases to be distinguished. It is also found that the valley Hall conductivity in the tilted Dirac cones exhibits a characteristic double-peak structure as a function of chemical potential using the semi classical formalism.

Weak antilocalization in a three-dimensional topological insulator based on a high-mobility HgTe film

The anomalous magnetoresistance (AMR) caused by the weak antilocalization effects in a three-dimensional topological insulator based on a strained mercury telluride film is experimentally studied. It is demonstrated that the obtained results are in a good agreement with the universal theory of Zduniak, Dyakonov, and Knap. It is found that the AMR in the bulk band gap is far below that expected for the system of Dirac fermions. Such a discrepancy can assumingly be related to a nonzero effective mass of Dirac fermions. The filling of energy bands in the bulk is accompanied by a pronounced increase in the AMR. This is a signature of the weak coupling between the surface and bulk charge carriers.

Transition from a Metal to a Massless-Dirac-Fermion Phase in an Organic Conductor Investigated by13C NMR

The θ-(BEDT-TTF)2I3 system is suggested to be the second organic system of massless Dirac fermions, which emerge from the metallic phase at a pressure exceeding 5 kbar. We have performed 13C NMR measurements on a single crystal of θ-(BEDT-TTF)2I3 under variable pressure across the critical pressure, 5 kbar. The Knight shift and spin–lattice relaxation rate show that a metallic state with an NMR enhancement factor of 2.2–2.4 at ambient pressure persists up to the critical pressure of 5 kbar. Above that, a marked spectral change indicative of a first-order phase transition is found. The angular dependence of NMR spectra indicates a structural phase transition from the θ-type molecular arrangement to the α-type one, which hosts the tilted Dirac cone.

Surface states of a system of dirac fermions: A minimal model

A brief survey is given of theoretical works on surface states (SSs) in Dirac materials. Within the formalism of envelope wave functions and boundary conditions for these functions, a minimal model is formulated that analytically describes surface and edge states of various (topological and non-topological) types in several systems with Dirac fermions (DFs). The applicability conditions of this model are discussed.

Electron cooling in three-dimensional Dirac fermion systems at low temperature: Effect of screening

Hot electron cooling rate P, due to acoustic phonons, is investigated in three-dimensional Dirac fermion systems at low temperature taking account of screening of electron-acoustic phonon interaction. P is studied as a function of electron temperature Te and electron concentration ne. Screening is found to suppress P very significantly for about Te 1K in Cd3As2 . In Bloch-Gruniesen (BG) regime, for screened (unscreened) case Te dependence is P ~ Te 9 (Te ) and ne dependence gives P ~ ne -5/3(ne ). The Te dependence is characteristics of 3D phonons and ne dependence is characteristics of 3D Dirac fermions. In BG regime, screening effect is found to enhance for larger ne. Screening is found to reduce the range of validity of BG regime temperature. Plot of P /Te 4 vs Te shows a maximum at temperature Tem which shifts to higher values for larger ne. Interesting observation is that maximum of P /Te 4 is nearly same for different ne and Tem / ne 1/3 appears to be nearly constant. More importantly, we propose, the ne dependent measurements of P would provide a clearer signature to identify 3D Dirac semimetal phase. PACS number(s):71.55.Ak, 72.10.-d, 72.20.Ht,