We investigate the entanglement entropy (EE) and charge fluctuations in models where the low energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, \emph{i.e.}, independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and number of Dirac cones, and either for strictly two-dimensional models or for gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides non-universal, geometry dependent results.
We present analytical and numerical results that demonstrate the presence of anomalous entanglement behavior on the Dirac Billiards. We investigate the statistical distribution of the characteristic entangled measures, focusing on the mean, on the variance and on the quantum interference terms. We show a quite distinct behavior of the Dirac Billiard compared with the non-relativist (Schrodinger) ones. Particularly, we show a very plausible Bell state and a sharp amplitude of quantum interference term on entangled electrons left from the Dirac Billiards. The results have remarkable relevance to…
Two-dimensional ($2$D) semi-Dirac systems, such as $2$D black phosphorus and arsenene, can exhibit a rich topological phase transition between insulating, semi-Dirac, and band inversion phases when subjected to an external modulation. How these phase transitions manifest within the quantum transport and shot noise signatures remain an open question thus far. Here, we show that the Fano factor converges to the universal $F\approx0.179$ at the semi-Dirac phase, and transits between the sub-Poissonian ($F\approx1/3$) and the Poissonian shot noise ($F\approx1$) limit at the band inversion and the …
We calculate conductance and noise for quantum transport at the nodal point for arbitrarily tilted and anisotropic Dirac or Weyl cones. Tilted and anisotropic dispersions are generic in absence of certain discrete symmetries, such as particle-hole and lattice point group symmetries. Whereas anisotropy affects the conductance g, but leaves the Fano factor F (the ratio of shot noise power and current) unchanged, a tilt affects both g and F. Since F is a universal number in many other situations, this finding is remarkable. We apply our general considerations to specific lattice models of straine…
We demonstrate theoretically that the characteristic feature of a 2D system undergoing $N$ consequent Lifshitz topological transitions is the occurrence of spikes of entropy per particle $s$ of a magnitude $\pm \ln 2/(J-1/2)$ with $2 \leq J \leq N$ at low temperatures. We derive a general expression for $s$ as a function of chemical potential, temperature and gap magnitude for the gapped Dirac materials. Inside the smallest gap, the dependence of $s$ on the chemical potential exhibits a dip-and-peak structure in the temperature vicinity of the Dirac point. The spikes of the entropy per particl…
We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter $Δ$, there are two distinct Dirac points with linear dispersion, these are connected by a saddle point at higher energy. As $Δ$ goes to zero, the two Dirac points merge and the resulting dispersion exhibits semi-Dirac behaviour which is quadratic in the $x$-direction ("nonrelativistic") and linear the $y$-direction ("relativistic").In the clean limit for each direction ($x,y$) the contribution of the i…
We demonstrate the emergence and dynamics of intra-particle entanglement in massless Dirac fermions. This entanglement, generated by spin-orbit coupling, arises between the spin and sublattice pseudospin of electrons in graphene. The entanglement is a complex dynamic quantity but is generally large, independent of the initial state. Its time dependence implies a dynamical violation of a Bell inequality, while its magnitude indicates that large intra-particle entanglement is a general feature of graphene on a substrate. These features are also expected to impact entanglement between pairs of pa…
We consider theoretically as a function of temperature the plasmon mode arising in three-dimensional Dirac liquids, i.e., systems with linear chiral relativistic single-particle dispersion, within the random phase approximation. We find that whereas no plasmon mode exists in the intrinsic (undoped) system at zero temperature, there is a well-defined finite-temperature plasmon with superlinear temperature dependence, rendering the plasmon dispersion widely tunable with temperature. The plasmon dispersion contains a logarithmic correction due to the ultraviolet-logarithmic renormalization of the…
The presence of both inversion ($P$) and time-reversal ($T$) symmetries in solids leads to a well-known double degeneracy of the electronic bands (Kramers degeneracy). When the degeneracy is lifted, spin textures can be directly observed in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is very difficult to observe directly. Here, we use quantum interference measurements combined with first-principle band structure calculations to provide evidence for the existence of hidden entanglement between spin …
We study the persistent current in a one dimensional Dirac ring and show that the change of spin current with respect to an applied perpendicular electric field can be used to identify the topological phases. We further study the effect of Rashba spin orbit coupling and show that the Aharonov-Casher phase appearing due to Rashba spin orbit coupling vanishes in topologically nontrivial regime and thus can identify the topological phases. This Aharonov-Casher phase causes a finite spin-valley current in presence of valley mixing perturbation and is thus useful to detect the topological phases ev…
The spin-momentum locking of topological states offers an ideal platform to explore novel magneto-electric effects. These intimately depend on the ability to manipulate the spin texture in a controlled way. Here, we combine scanning tunneling microscopy with single atoms deposition to map the evolution of topological states under the influence of different magnetic perturbations. We obtain signatures of Dirac fermion-mediated magnetic order for extremely dilute adatoms concentrations. This striking observation is found to critically depend on the single adatoms magnetic anisotropy and the posi…
We combine transport, magnetization, and torque magnetometry measurements to investigate the electronic structure of ZrTe5 and its evolution with temperature. At fields beyond the quantum limit, we observe a magnetization reversal from paramagnetic to diamagnetic response, which is characteristic of a Dirac semi-metal. We also observe a strong non-linearity in the magnetization that suggests the presence of additional low-lying carriers from other low-energy bands. Finally, we observe a striking sensitivity of the magnetic reversal to temperature that is not readily explained by simple band-st…
Polymorph of 8-Pmmn borophene exhibits anisotropic tilted Dirac cones. In this work, we explore the consequences of the tilted Dirac cones in magnetotransport properties of a periodically modulated borophene. We evaluate modulation induced diffusive conductivity by using linear response theory in low temperature regime. The application of weak modulation (electric/magnetic or both) gives rise to the magnetic field dependent non-zero oscillatory drift velocity which causes Weiss oscillation in the longitudinal conductivity at low magnetic field. The Weiss oscillation is studied in presence of a…
We study quantum phase transitions involving fractional quantum Hall states, using numerical calculations of entanglements and related quantities. We tune finite-size wavefunctions on spherical geometries, by varying the interaction potential away from the Coulomb interaction. We uncover signatures of quantum phase transitions contained in the scaling behavior of the entropy of entanglement between two parts of the sphere. In addition to the entanglement entropy, we show that signatures of quantum phase transitions also appear in other aspects of the reduced density matrix of one part of the s…
In this paper, we give a systematic theoretical study on the Landau levels (LLs) and magneto-optical conductivity Re$(σ_{αα})$ in a gapped Dirac semimetal model with mixed linear and parabolic dispersions under a magnetic field, which was recently proposed by Jiang \textit{et al.} [Phys. Rev. Lett. {\bf125}, 046403 (2020)] to explain the experimental magnetoinfrared spectroscopy in the three-dimensional ZrTe$_5$ crystal. We find that the strong magnetic field can drive the LLs become noninverted and thus the strong topological insulator phase in ZrTe$_5$ turns to be a trivial insulator. In the…
We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground state energy is computed as a function of the effective interaction parameter $α$ from the Hartree-Fock approximation and, alternatively, by employing the Müller exchange functional. For N=2, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accu…
We identify an optical signature for detecting entanglement in experimental nanostructure systems comprising coupled excitonic qubits. This signature owes its strength to non-Markovian dynamical effects in the second-order temporal coherence function of the emitted radiation. We calculate autocorrelation and cross-correlation functions for both selective and collective light excitation, and prove that the coherence properties of the emitted light do indeed carry information about the entanglement of the initial multi-qubit state. We also show that this signature can survive in the presence of …
Of the available classes of insulators which have been shown to contain topologically non-trivial properties one of the most important is class AII, which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$ This class has been the subject of significant attention as it encompasses non-trivial Z$_2$ topological insulators such as the quantum spin Hall (QSH) state and the 3D strong topological insulator. One of the defining properties of this system is the robustness of the state under the addition of disorder that preserves $T.$ In this letter, we explore the phase diagram o…
Extended defects in graphene, such as linear edges, break the translational invariance and can also have an impact on the symmetries specific to massless Dirac-like quasiparticles in this material. The paper examines the consequences of a broken Dirac fermion parity in the framework of the effective boundary conditions varying from the Berry-Mondragon mass confinement to a zigzag edge. The parity breaking reflects the structural sublattice asymmetry of zigzag-type edges and is closely related to the previously predicted time-reversal symmetric edge states. We calculate the local and global den…
Many applications for topological insulators (TIs) as well as new phenomena require devices with reduced dimensions. While much progress has been made to realize thin films of TIs with low bulk carrier density, nanostructures have not yet been reported with similar properties, despite the fact that size confinement should help reduce contributions from bulk carriers. Here we demonstrate that Bi2Se3 nanoribbons, grown by a simple catalyst-free physical-vapour deposition, have inherently low bulk carrier densities, and can be further made bulk-free by size confinement, thus revealing the high mo…
We calculate the shot noise generated by evanescent modes in graphene for several experimental setups. For two impurity-free graphene strips kept at the Dirac point by gate potentials, separated by a long highly doped region, we find that the Fano factor takes the universal value F = 1/4. For a large superlattice consisting of many strips gated to the Dirac point interspersed among doped regions, we find F = 1/(8 ln 2). These results differ from the value F = 1/3 predicted for a disordered metal, providing an unambiguous experimental signature of evanescent mode transport in graphene.
Lifshitz transition is a kind of topological phase transition in which the Fermi surface is reconstructed. It can occur in the two-dimensional (2D) tilted Dirac materials when the energy bands change between the type-I phase ($0<t<1$) and the type-II phase ($t>1$) through the type-III phase ($t=1$), where different tilts are parametrized by the values of $t$. In order to characterize the Lifshitz transition therein, we theoretically investigate the longitudinal optical conductivities (LOCs) in type-I, type-II, and type-III Dirac materials within linear response theory. In the undoped case, the…
A linear Josephson junction mediated by the surface states of a time-reversal-invariant Weyl or Dirac semimetal localizes Majorana flat bands protected by the time-reversal symmetry. We show that as a result, the Josephson current exhibits a discontinuous jump at $π$ phase difference which can serve as an experimental signature of the Majorana bands. The magnitude of the jump scales proportionally to the junction width and the momentum space distance between the Weyl nodes. It also exhibits a characteristic dependence on the junction orientation. We demonstrate that the jump is robust against …
The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitation shows a crossover from metallic behavior at short sample sizes to localized at longer length. The dependence of the crossover as function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many particle critical energy in the vicinity of the Fermi energy. Impl…
The current response to an electromagnetic field in a Weyl or Dirac semimetal becomes nonlocal due to the chiral anomaly activated by an applied static magnetic field. The nonlocality develops under the conditions of the normal skin effect and is related to the valley charge imbalance generated by the joint effect of the electric field of the impinging wave and the static magnetic field. We elucidate the signatures of this nonlocality in the transmission of electromagnetic waves. The signatures include enhancement of the transmission amplitude and its specific dependence on the wave's frequenc…
We theoretically investigate the features of Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between two magnetic impurities, mediated by the interfacial bound states inside a domain wall (DW). The latter separates the two regions with oppositely signed inversion symmetry broken terms in graphene and Weyl semimetal. The DW is modelled by a smooth quantum well which hosts a number of discrete bound states including a pair of gapless, metallic zero-energy modes with opposite chiralities. We find clear signatures of these interfacial chiral bound states in spin response (RKKY exchange i…
Using polarized optical and magneto-optical spectroscopy, we have demonstrated universal aspects of electrodynamics associated with Dirac nodal-lines. We investigated anisotropic electrodynamics of NbAs$_2$ where the spin-orbit interaction triggers energy gaps along the nodal-lines, which manifest as sharp steps in the optical conductivity spectra. We show experimentally and theoretically that shifted 2D Dirac nodal-lines feature linear scaling $σ_1 (ω)\simω$, similar to 3D nodal-points. Massive Dirac nature of the nodal-lines are confirmed by magneto-optical data, which may also be indicative…
The field of topological materials science has recently been focussing on three-dimensional Dirac semimetals, which exhibit robust Dirac phases in the bulk. However, the absence of characteristic surface states in accidental Dirac semimetals (DSM) makes it difficult to experimentally verify claims about the topological nature using commonly used surface-sensitive techniques. The chiral magnetic effect (CME), which originates from the Weyl nodes, causes an $\textbf{E}\cdot\textbf{B}$-dependent chiral charge polarization, which manifests itself as negative magnetoresistance. We exploit the exten…
We theoretically investigate the emergence of non-hermitian physics at the heterojunction of a type-II Dirac semi-metal (DSM) and a dirty superconductor (DSC). The non-hermiticity is introduced in the DSM through the self-energy term incorporated via the dirtiness of the superconducting material. This causes the spectra of the effective Hamiltonian to become complex, which gives rise to the appearance of the exceptional points (EPs). This complex self energy, apart from having a frequency dependence, also acquires spatial dependence as well, which is unique and can provide interesting effects …
The complete lattice-layer entanglement structure of Bernal stacked bilayer graphene is obtained for the quantum system described by a tight-binding Hamiltonian which includes mass and bias voltage terms. Through a suitable correspondence with the parity-spin $SU(2)\otimes SU(2)$ structure of a Dirac Hamiltonian, when it brings up tensor and pseudovector external field interactions, the lattice-layer degrees of freedom can be mapped into such a parity-spin two-qubit basis which supports the interpretation of the bilayer graphene eigenstates as entangled ones in a lattice-layer basis. The Dirac…
The half filled Landau level is expected to be approximately particle-hole symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of the compressible state observed at this filling. Recent work indicates that, when particle-hole symmetry is preserved, the composite Fermions experience a quantized $π$-Berry phase upon winding around the composite Fermi-surface, analogous to Dirac fermions at the surface of a 3D topological insulator. In contrast, the effective low energy theory of the composite fermion liquid originally proposed by HLR lacks particle-hole symmetry and has …
The existence of $1/2$ modes in the entanglement spectrum (ES) has been shown to be a powerful quantum-informative signature of boundary states of gapped topological phases of matter, e.g., topological insulators and topological superconductors, where the finite bulk gap allows us to establish a crystal-clear correspondence between $1/2$ modes and boundary states. Here we investigate the recently proposed higher-order Weyl semimetals (HOWSM), where bulk supports gapless higher-order Weyl nodes and boundary supports hinge arcs and Fermi arcs. We find that the aim of unambiguously identifying hi…
In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles with linear energy dispersion. A particularly intriguing phenomenon arises with the intrinsic charge transport behavior at the Dirac point where the charge density approaches zero. In graphene, a 2-D Dirac fermion system, it was predicted that charge transport near the Dirac point is carried by evanescent modes, resulting in unconventional pseudo-diffusive charge transport even in the absence of disorder. In the past decade, experimental observation of this phenomenon remained challenging due to th…
Clustered quantum materials provide a new platform for the experimental study of many-body entanglement. Here we address a simple model of a single-molecule nano-magnet featuring N interacting spins in a transverse field. The field can induce an entanglement transition (ET). We calculate the magnetisation, low-energy gap and neutron-scattering cross-section and find that the ET has distinct signatures, detectable at temperatures as high as 5% of the interaction strength. The signatures are stronger for smaller clusters.
In certain special circumstances, such as in the vicinity of a black hole or in a uniformly accelerating frame, vacuum fluctuations appear to give rise to a finite-temperature environment. This effect, currently without experimental confirmation, can be interpreted as a manifestation of quantum entanglement after tracing out vacuum modes in an unobserved region. In this work, we identify a class of experimentally accessible quantum systems where thermal density matrices emerge from vacuum entanglement. We show that reduced density matrices of lower-dimensional subsystems embedded in $D$-dimens…
We find that the topological phase transition in a chiral ladder is characterized by dramatic signatures in many body entanglement entropy between the legs, close to half-filling. The value of entanglement entropy for various fillings close to half-filling is identical, at the critical point, but splays out on either side, thus showing a sharp signature at the transition point. A second signature is provided by the change in entanglement entropy when a particle is added (or subtracted) from half-filling which turns out to be exactly $-\log{2}$ in the trivial phase, but zero in the topological …
We consider integer quantum Hall states and calculate bulk entanglement spectrum by formulating the correlation matrix in guiding center representation. Our analytical approach is based on the projection operator with redefining the inner product of states in Hilbert space to take care of the restriction imposed by the (rectangle-tiled) checkerboard partition. The resultant correlation matrix contains the coupling constants between states of different guiding centers parameterized by magnetic length and the period of partition. We find various band-crossings by tuning the flux $Φ$ threading ea…
