Finite Effective Mass Research Articles

Aharonov-Bohm effect mediated by massive photons

Virtual photons play an essential role in the locally realistic description of the Aharonov-Bohm interference. We show that the effect of virtual photons in the interferometer is manifested by a change in their spectrum. In particular, when a vacuum is confined between two ideal conducting plates, the photons obey the two-dimensional Proca equation, the wave equation with finite effective mass. This results in a short-range interaction between a test charge and a magnetic flux, and hence the Aharonov-Bohm effect is reduced exponentially at a large distance between the two bodies. On the other hand, a semiclassical description is also possible, and this raises the interesting question of how to prove the physical reality of virtual photons.

Special theory of relativity for a graded index fibre

The speed of light (c) in a vacuum is independent of the choice of frames to describe the propagation, according to the theory of relativity. We consider how light is characterised in a material, where the speed of light is different from that in a vacuum due to the finite dielectric constant. The phase velocity in a material is smaller thanc, such that the speed of a moving frame can be larger than the phase velocity, such that the frame can move faster than the speed of light in a material. Consequently, an unusual Doppler effect is expected, and the wavelength in the moving frame changes from the red-shift to the blue-shift upon increasing the speed of the frame. The corresponding energy of the light also changes sign from positive to negative, while momentum is always positive, leading to the changes of signs for the phase velocity and the helicity. In a graded index fibre, where the exact solution is available, even more complicated phenomena are expected, due to the finite effective mass of photons. Upon the increase of the energy gap, generated by optical confinements and optical orbital angular momentum, the effective mass of photons increases. If the gap is large enough, momentum starts to change the sign upon increasing the frame velocity, while the energy of photons is always positive. In this case, the phase velocity diverges if momentum is in agreement with the fame velocity. Contrary to the unusual behaviours of the phase velocity, the group velocity is always belowc. This thought experiment might be useful for considering insight into the polarisation state of light.

Quasi-one-dimensional graphene structure: Study of finite bandgap and effective mass with width

Quasi-one-dimensional graphene structure: Study of finite bandgap and effective mass with width

Two-body problem in a multiband lattice and the role of quantum geometry

We consider the two-body problem in a periodic potential, and study the bound-state dispersion of a spin-$\uparrow$ fermion that is interacting with a spin-$\downarrow$ fermion through a short-range attractive interaction. Based on a variational approach, we obtain the exact solution of the dispersion in the form of a set of self-consistency equations, and apply it to tight-binding Hamiltonians with onsite interactions. We pay special attention to the bipartite lattices with a two-point basis that exhibit time-reversal symmetry, and show that the lowest-energy bound states disperse quadratically with momentum, whose effective-mass tensor is partially controlled by the quantum metric tensor of the underlying Bloch states. In particular, we apply our theory to the Mielke checkerboard lattice, and study the special role played by the interband processes in producing a finite effective mass for the bound states in a non-isolated flat band.

Subcycle observation of lightwave-driven Dirac currents in a topological surface band.

Harnessing the carrier wave of light as an alternating-current bias may enable electronics at optical clock rates1. Lightwave-driven currents have been assumed to be essential for high-harmonic generation in solids2-6, charge transport in nanostructures7,8, attosecond-streaking experiments9-16 and atomic-resolution ultrafast microscopy17,18. However, in conventional semiconductors and dielectrics, the finite effective mass and ultrafast scattering of electrons limit their ballistic excursion and velocity. The Dirac-like, quasi-relativistic band structure of topological insulators19-29 may allow these constraints to be lifted and may thus open a new era of lightwave electronics. To understand the associated, complex motion of electrons, comprehensive experimental access to carrier-wave-driven currents is crucial. Here we report angle-resolved photoemission spectroscopy with subcycle time resolution that enables us to observe directly how the carrier wave of a terahertz light pulse accelerates Dirac fermions in the band structure of the topological surface state of Bi2Te3. While terahertz streaking of photoemitted electrons traces the electromagnetic field at the surface, the acceleration of Dirac states leads to a strong redistribution of electrons in momentum space. The inertia-free surface currents are protected by spin-momentum locking and reach peak densities as large as two amps per centimetre, with ballistic mean free paths of several hundreds of nanometres, opening up a realistic parameter space for all-coherent lightwave-driven electronic devices. Furthermore, our subcycle-resolution analysis of the band structure may greatly improve our understanding of electron dynamics and strong-field interaction in solids.

Spin-orbit interaction effects on the electronic structure of coaxial quantum well wires

The finite element method and effective mass approximation are used to investigate the simultaneous effects of SOI, electric and magnetic fields and quantum geometry on the energy and wave function of a cylindrical quantum well wire. Calculations are performed for a typical GaAs/AlxGa1−xAs cylindrical quantum well wire. It is found that SOI, external fields and layers thickness have considerable effects on the energy eigenvalues and functions of the system. Moreover it is shown that the tunneling effect and energy level anti-crossing depend on the SOI and external factors. We have proposed the SOI strength as an agent to control the tunneling effect in typical nanostructures.

Edwards polaron formation : From one to three dimensions

Employing a self-consistent (optimized) variational diagonalization scheme, we investigate the formation of polaronic quasiparticles in a spinless fermion-boson transport model that couples the movement of charge carriers to fluctuations and correlations of a background medium. The background is parameterized by bosonic degrees of freedom. The variational fermion-boson Hilbert space is constructed to achieve high accuracy in one to three spatial dimensions with modest computational requirements. To characterize the ground-state properties of the Edwards model in the single-particle sector, we present exact numerical results for the polaron band dispersion, quasiparticle weight, Drude weight, mass enhancement, and the particle-boson correlations in a wide parameter regime. In the Edwards model, transport will be quasifree, diffusive or boson-assisted in the weakly fermion-boson coupled, fluctuation-dominated or strongly correlated regimes, respectively. Thereby correlated transport is not only assisted but also limited by the bosonic excitations. As a result, the Drude weight remains finite even in the limit of very small boson frequencies. For a strongly correlated background, closed loops are important, in any dimension, to generate a finite effective particle mass even when the free fermion has an infinite mass.

Chemical potential and compressibility of quantum Hall bilayer excitons

This paper considers a system of two parallel quantum Hall layers with total filling factor $0$ or $1$. When the distance between the layers is small enough, electrons and holes in opposite layers form inter-layer excitons, which have a finite effective mass and interact via a dipole-dipole potential. Results are presented for the chemical potential $\mu$ of the resulting bosonic system as a function of the exciton concentration $n$ and the interlayer separation $d$. Both $\mu$ and the interlayer capacitance have an unusual nonmonotonic dependence on $d$, owing to the interplay between an increasing dipole moment and an increasing effective mass with increasing $d$. A phase transition between superfluid and Wigner crystal phases is shown to occur at $d \propto n^{-1/10}$. Results are derived first via simple intuitive arguments, and then verified with more careful analytic derivations and numeric calculations.

Surface states in a 3D topological insulator: The role of hexagonal warping and curvature

We explore a combined effect of hexagonal warping and a finite effective mass on both the tunneling density of electronic surface states and the structure of Landau levels of 3D topological insulators. We find the increasing warping to transform the square-root van Hove singularity into a logarithmic one. For moderate warping, an additional logarithmic singularity and a jump in the tunneling density of surface states appear. By combining the perturbation theory and the WKB approximation, we calculate the Landau levels in the presence of hexagonal warping. We predict that due to the degeneracy removal, the evolution of Landau levels in the magnetic field is drastically modified.

Effective mass of photon in liquid water environment of life and soft maters

It is well known that from four fundamental forces, only electro-magnetic force plays clear and important role in our life reality. The spin one exchange boson caring the electromagnetic interaction is photon. The condition of zero-mass of photon leads to the Coulomb law with long-range interaction behavior. We consider analogy Anderson-Higgs mechanism, in some liquid water environments at a certain temperature, photon can have a finite effective mass, consequence to a Yukawa type potential. This screening potential could leads to sort-range behavior of electro-magnetic effective interaction. We use this mechanism to develop physics models to explain some phenomena in life and soft systems.

A scenario for critical scalar field collapse in AdS3

We present a family of exact solutions, depending on two parameters α and b (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant Λ. For b = 0 these solutions reduce to the static Bañados–Teitelboim–Zanelli (BTZ) family of vacuum solutions, with mass . For , the solutions become dynamical and develop a strong spacelike central singularity. The solutions are black-hole like, with a global structure topologically similar to that of the BTZ black holes, and a finite effective mass. We show that the near-singularity behavior of the solutions with agrees qualitatively with that observed in numerical simulations of sub-critical collapse, including the independence of the near-critical regime on the angle deficit of the spacetime. We analyze in the approximation the linear perturbations of the self-similar threshold solution, , and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.

Dielectric response of II–VI semiconductor core–shell ensembles: Study of the lossless optical condition

We theoretically investigate optical properties of II–VI core–shell distribution mixtures made of two type-I sized-nanoshells as a plausible negative dielectric function material. The nonlocal optical response of the semiconductor QD is described by using a resonant excitonic dielectric function, while the shell response is modeled with Demangeot formula. Achieving the zero-loss at an optical frequency ω, i.e., ϵeff=ϵeff′+iϵeff″ with ϵeff′<0 and ϵeff″=0, is of fundamental importance in nanophotonics. Resonant states in semiconductors provide a source for negative dielectric function provided that the dipole strength and the oscillator density are adequate to offset the background. Furthermore, the semiconductor offers the prospect of pumping, either optically or electrically, to achieve a gain mechanism that can offset the loss. We analyse optimal conditions that must be satisfied to achieve semiconductor-based negative index materials. By comparing with II–VI semiconductor quantum dots (QDs) previously reported in the literature, the inclusion of phonon and shell contributions in the ϵeff along with the finite barrier Effective Mass Approximation (EMA) approach, we found similar qualitative behaviours for the ϵeff. The lossless optical condition along with ϵeff′<0 is discussed in terms of sizes, volume fractions and embedding medium of the mixtures׳ distributions. Furthermore, we estimated optical power to maintain nanocrystals density in excited states and this value is less than that previously obtained in II–VI semiconductor QDs.

Low-energy equivalence between periodically gated graphene structures and bilayer-like gated graphene

The linear dispersion law of graphene is modified in periodically gated structures, the charge carriers acquiring a finite effective mass. We show that, in the low energy approximation, periodically gated graphene structures are equivalent, from the point of view of charge transport, to a bilayer-like gated graphene region, i.e., to a material that satisfies the same equation as bilayer graphene but with a potentially different effective mass. The hypothetic bilayer-like material becomes identical to the genuine bilayer graphene if its effective mass matches that of the latter. The effective mass, potential energy, and width of bilayer-like graphene can be identified by imposing the condition that the transmission coefficient through the bilayer-like region, computed using a transfer matrix approach, is identical to that through the periodically gated graphene structure.

Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state

Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires and graphene. Recently, a new method has emerged with the recognition that symmetry-protected topological (SPT) phases, which occur in systems with an energy gap to quasiparticle excitations (such as insulators or superconductors), can host robust surface states that remain gapless as long as the relevant global symmetry remains unbroken. The nature of the charge carriers in SPT surface states is intimately tied to the symmetry of the bulk, resulting in one- and two-dimensional electronic systems with novel properties. For example, time reversal symmetry endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, fixing the orientation of their spin relative to their momentum. Weakly breaking this symmetry generates a gap on the surface, resulting in charge carriers with finite effective mass and exotic spin textures. Analogous manipulations have yet to be demonstrated in two-dimensional topological insulators, where the primary example of a SPT phase is the quantum spin Hall state. Here we demonstrate experimentally that charge-neutral monolayer graphene has a quantum spin Hall state when it is subjected to a very large magnetic field angled with respect to the graphene plane. In contrast to time-reversal-symmetric systems, this state is protected by a symmetry of planar spin rotations that emerges as electron spins in a half-filled Landau level are polarized by the large magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability, which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with a tunable bandgap and an associated spin texture.

Vibrational Excitations and Low-Energy Electronic Structure of Epoxide-Decorated Graphene

We report infrared studies of adsorbed atomic oxygen (epoxide functional groups) on graphene. Two different systems are used as a platform to explore these interactions, namely, epitaxial graphene/SiC(0001) functionalized with atomic oxygen (graphene epoxide, GE) and chemically reduced graphene oxide (RGO). In the case of the model GE system, IR reflectivity measurements show that epoxide groups distort the graphene π bands around the K-point, imparting a finite effective mass and contributing to a band gap. In the case of RGO, epoxide groups are found to be present following the reduction treatment by a combination of polarized IR reflectance and transmittance measurements. Similar to the GE system, a band gap in the RGO sample is observed as well.

Binding carriers to a nonmagnetic impurity in a two-dimensional square Ising antiferromagnet

A hole in a two-dimensional Ising antiferromagnet was believed to be infinitely heavy due to the string of wrongly oriented spins it creates as it moves, which should trap it near its original location. Trugman showed that, in fact, the hole acquires a finite effective mass due to contributions from so-called Trugman loop processes, where the hole goes nearly twice around closed loops, first creating and then removing wrongly oriented spins, and ending up at a different lattice site. This generates effective second- and third-nearest-neighbor hopping terms which keep the quasiparticle on the sublattice it was created on. Here, we investigate the trapping of the quasiparticle near a single attractive nonmagnetic impurity placed at one lattice site. We consider the two cases with the quasiparticle and impurity being on the same versus on different sublattices. The main result is that even though the quasiparticle can not see the bare disorder in the latter case, the coupling to magnons generates an effective renormalized disorder on its own sublattice which is strong enough to lead to bound states, which however have a very different spectrum than when the quasiparticle and impurity are on the same sublattice.

Note on Hartman effect in gapped graphene

In this manuscript the effect of an opening gap on the dwell time corresponding to the electronic tunneling in graphene is explored. It is shown that tunneling time of quasiparticles in passing through junctions of gapped graphene as well as pure flakes is not independent of the barrier thickness and therefore Hartman effect is not observed due to tunneling of relativistic electrons with a finite effective mass in graphene. The numerical results also reveal that the traversal time in gapped graphene is equal to the traversal time in absence of the barrier for a broad range of incident energy. It is also found that the origin of the problem of Hartman effect could be explained in terms of an average-constant behavior of the probability density of the electronic wave under the barrier.

Spectroscopic characterization of gapped graphene in the presence of circularly polarized light

We present a description of the energy loss of a charged particle moving parallel to a graphene layer and graphene double layers. Specifically, we compare the stopping power of the plasma oscillations for these two configurations in the absence as well as the presence of circularly polarized light whose frequency and intensity can be varied to yield an energy gap of several hundred meV between the valence and conduction bands. The dressed states of the Dirac electrons by the photons yield collective plasma excitations whose characteristics are qualitatively and quantitatively different from those produced by Dirac fermions in gapless graphene, due in part to the finite effective mass of the dressed electrons. For example, the range of wave numbers for undamped self-sustaining plasmons is increased as the gap is increased, thereby increasing the stopping power of graphene for some range of charged particle velocity when graphene is radiated by circularly polarized light.

Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions

HgTe quantum wells and surfaces of three-dimensional topological insulators support Dirac fermions with a single-valley band dispersion. In the presence of disorder they experience weak antilocalization, which has been observed in recent transport experiments. In this work we conduct a comparative theoretical study of the weak antilocalization in HgTe quantum wells and topological surface states. The difference between these two single-valley systems comes from a finite band gap (effective Dirac mass) in HgTe quantum wells in contrast to gapless (massless) surface states in topological insulators. The finite effective Dirac mass implies a broken internal symmetry, leading to suppression of the weak antilocalization in HgTe quantum wells at times larger than certain t_M, inversely proportional to the Dirac mass. This corresponds to the opening of a relaxation gap 1/t_M in the Cooperon diffusion mode which we obtain from the Bethe-Salpeter equation including relevant spin degrees of freedom. We demonstrate that the relaxation gap exhibits an interesting nonmonotonic dependence on both carrier density and band gap, vanishing at a certain combination of these parameters. The weak-antilocalization conductivity reflects this nonmonotonic behavior which is unique to HgTe QWs and absent for topological surface states. On the other hand, the topological surface states exhibit specific weak-antilocalization magnetoconductivity in a parallel magnetic field due to their exponential decay in the bulk.

Enhancement of phonon-drag thermopower in bilayer graphene

Phonon-drag thermopower ${S}^{\text{g}}$ is theoretically studied in a bilayer graphene (BLG). Two-dimensional (2D) electrons with chiral property, finite effective mass, and parabolic dispersion are assumed to interact with the 2D acoustic phonons having a linear dispersion via deformation-potential coupling. A comparison is made with the very recent experimental results of Nam et al. [arXiv:1005.4739 (unpublished)] for $30\ensuremath{\le}T\ensuremath{\le}70\text{ }\text{K}$. Numerically ${S}^{\text{g}}$ is studied as a function of temperature $T$, electron concentration ${n}_{\text{s}}$, and phonon mean-free path. ${T}^{3}$ behavior of ${S}^{\text{g}}$ at very low $T$ changes gradually to sublinear at higher $T$ and the effect of chiral property of the electrons is seen explicitly. We suggest the possibility of significant enhancement of ${S}^{\text{g}}$ at lower carrier concentrations by increasing the linear dimension of the sample and reducing its edge roughness. We find that ${S}^{\text{g}}$ in BLG is enhanced by a factor of 7 compared with the magnitude of ${S}^{\text{g}}$ in monolayer graphene, for ${n}_{\text{s}}=0.5\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }{\text{cm}}^{\ensuremath{-}2}$ in the Bloch-Gr\uneisen (BG) regime. In BG regime ${S}^{\text{g}}\ensuremath{\sim}{T}^{3}$, a manifestation of 2D phonons with linear dispersion and ${S}^{\text{g}}\ensuremath{\sim}{n}_{\text{s}}^{\ensuremath{-}3/2}$, a characteristic of 2D electrons with parabolic dispersion. A comparison is also made with the results in conventional and ideal 2D systems. ${S}^{\text{g}}$ is found to be very significant in comparison with the diffusion thermopower ${S}^{\text{d}}$ and the latter is shown to be $\ensuremath{\sim}T$, ${n}_{\text{s}}^{\ensuremath{-}1}$ at low $T$ and high ${n}_{\text{s}}$. Herring's law, ${S}^{\text{g}}{\ensuremath{\mu}}_{\text{p}}\ensuremath{\sim}{T}^{\ensuremath{-}1}$, relating phonon-limited mobility ${\ensuremath{\mu}}_{\text{p}}$ to ${S}^{\text{g}}$, is found to be valid in BLG.