Fermi Velocity Renormalization Research Articles

Renormalization of Fermi Velocity and Band Gap in a Two-Dimensional System near a Conducting Plate at Finite Temperature

In a recent work, it was demonstrated within the framework of Pseudo Quantum Electro-dynamics (PQED) at zero temperature that the logarithmic renormalization of the Fermi velocity in a graphene sheet is inhibited by the presence of a single parallel conducting plate. In the present study, aiming for a more general and realistic approach, we explore the renormalization of the Fermi velocity and mass (band gap) in a two-dimensional system influenced by a conducting plate at finite temperature, also in the context of PQED. Our findings refine previous results in the literature and provide valuable insights for future investigations on the effects of external conditions within PQED.

Landau-phonon polaritons in Dirac heterostructures.

Polaritons are light-matter quasiparticles that govern the optical response of quantum materials at the nanoscale, enabling on-chip communication and local sensing. Here, we report Landau-phonon polaritons (LPPs) in magnetized charge-neutral graphene encapsulated in hexagonal boron nitride (hBN). These quasiparticles emerge from the interaction of Dirac magnetoexciton modes in graphene with the hyperbolic phonon polariton modes in hBN. Using infrared magneto-nanoscopy, we reveal the ability to completely halt the LPP propagation in real space at quantized magnetic fields, defying the conventional optical selection rules. The LPP-based nanoscopy also tells apart two fundamental many-body phenomena: the Fermi velocity renormalization and field-dependent magnetoexciton binding energies. Our results highlight the potential of magnetically tuned Dirac heterostructures for precise nanoscale control and sensing of light-matter interaction.

Nanometric Moiré Stripes on the Surface of Bi2Se3 Topological Insulator.

Mismatch between adjacent atomic layers in low-dimensional materials, generating moiré patterns, has recently emerged as a suitable method to tune electronic properties by inducing strong electron correlations and generating novel phenomena. Beyond graphene, van der Waals structures such as three-dimensional (3D) topological insulators (TIs) appear as ideal candidates for the study of these phenomena due to the weak coupling between layers. Here we discover and investigate the origin of 1D moiré stripes on the surface of Bi2Se3 TI thin films and nanobelts. Scanning tunneling microscopy and high-resolution transmission electron microscopy reveal a unidirectional strained top layer, in the range 14–25%, with respect to the relaxed bulk structure, which cannot be ascribed to the mismatch with the substrate lattice but rather to strain induced by a specific growth mechanism. The 1D stripes are characterized by a spatial modulation of the local density of states, which is strongly enhanced compared to the bulk system. Density functional theory calculations confirm the experimental findings, showing that the TI surface Dirac cone is preserved in the 1D moiré stripes, as expected from the topology, though with a heavily renormalized Fermi velocity that also changes between the top and valley of the stripes. The strongly enhanced density of surface states in the TI 1D moiré superstructure can be instrumental in promoting strong correlations in the topological surface states, which can be responsible for surface magnetism and topological superconductivity.

Angle-tunable two-photon absorption in twisted graphene systems

We theoretically study the two-photon absorption of twisted bilayer, trilayer and double bilayer graphene with Bernal stacking and demonstrate the layer and twist angle dependent two-photon absorption properties based on both the density functional theory calculations and our developed continuum model for small angle range. The expressions of two-photon absorption for above mentioned three twisted graphene layers around Dirac points are obtained. For small rotation angles which are less than 15 ° , the rotation angle well tunes the two-photon absorption coefficient in terms of the angle-dependent renormalized Fermi velocity. • Energy bands of twisted graphene systems around K point were investigated using DFT calculation. • Two-photon absorption spectra in twisted graphene systems were simulated on the basis of the second-order perturbation theory. • Twist angle effectively tuned the two-photon absorption coefficient within the small angle range ( θ < 15 ° ).

Optical coherent injection of carrier and current in twisted bilayer graphene

We theoretically investigate optical injection processes, including one- and two-photon carrier injection and two-color coherent current injection, in twisted bilayer graphene with moderate angles. The electronic states are described by a continuum model, and the spectra of injection coefficients are numerically calculated for different chemical potentials and twist angles, where the transitions between different bands are understood by the electron energy resolved injection coefficients. The comparison with the injection in monolayer graphene shows the significance of the interlayer coupling in the injection processes. For undoped twisted bilayer graphene, all spectra of injection coefficients can be divided into three energy regimes, which vary with the twist angle. For very low photon energies in the linear dispersion regime, the injection is similar to graphene with a renormalized Fermi velocity determined by the twist angle; for very high photon energies where the interlayer coupling is negligible, the injection is the same as that of graphene; and in the middle regime around the transition energy of the Van Hove singularity, the injection shows fruitful fine structures. Furthermore, the two-photon carrier injection diverges for the photon energy in the middle regime due to the existence of double resonant transitions.

Influence of the four-fermion interactions in a (2+1)D massive electron system

The description of the electromagnetic interaction in two-dimensional Dirac materials, such as graphene and transition-metal dichalcogenides, in which electrons move in the plane and interact via virtual photons in 3d, leads naturally to the emergence of a projected non-local theory, called pseudo-quantum electrodynamics (PQED), as an effective model suitable for describing electromagnetic interaction in these systems. In this work, we investigate the role of a complete set of four-fermion interactions in the renormalization group functions when we coupled it with the anisotropic version of massive PQED, where we take into account the fact that the Fermi velocity is not equal to the light velocity. We calculate the electron self-energy in the dominant order in the $1/N$ expansion in the regime where $m ^ 2 \ll p ^ 2$. We show that the Fermi velocity renormalization is insensitive to the presence of quartic fermionic interactions, whereas the renormalized mass may have two different asymptotic behaviors at the high-density limit, which means a high-energy scale.

Correlated Magnetic Weyl Semimetal State in Strained Pr2 Ir2 O7.

Correlated topological phases (CTPs) with interplay between topology and electronic correlations have attracted tremendous interest in condensed matter physics. Therein, correlated Weyl semimetals (WSMs) are rare in nature and, thus, have so far been less investigated experimentally. In particular, the experimental realization of the interacting WSM state with logarithmic Fermi velocity renormalization has not been achieved yet. Here, experimental evidence of a correlated magnetic WSM state with logarithmic renormalization in strained pyrochlore iridate Pr2 Ir2 O7 (PIO) which is a paramagnetic Luttinger semimetal in bulk, is reported. Benefitting from epitaxial strain, "bulk-absent" all-in-all-out antiferromagnetic ordering can be stabilized in PIO film, which breaks time-reversal symmetry and leads to a magnetic WSM state. With further analysis of the experimental data and renormalization group calculations, an interacting Weyl liquid state with logarithmically renormalized Fermi velocity, similar to that in graphene, is found, dressed by long-range Coulomb interactions. This work highlights the interplay of strain, magnetism, and topology with electronic correlations, and paves the way for strain-engineering of CTPs in pyrochlore iridates.

Dirac fermions in graphene using the position-dependent translation operator formalism

Within the position-dependent translation operator formalism for quantum systems, we obtain analytical expressions for the eigenstates and the Landau level spectrum of Dirac fermions in graphene in the presence of a perpendicularly applied magnetic field and, as a consequence of the formalism, with a generalized form of the momentum operator. Moreover, we explore the behavior of wave packet dynamics in such a system by considering different initial pseudospin polarizations and metric parameters. Our findings show that the Landau levels, the wave packet trajectories, and velocities are significantly affected by the choice of the metric in the non-Euclidean space of the deformed momentum operator, exhibiting a tunable energy level spacing. In the dynamics analysis, one observes an enhancement of the oscillation amplitude of the average positions for all investigated pseudospin polarizations due to the nonsymmetric evolution of the wave packet induced by the different metrics in the system. The present formalism is shown to be a theoretical platform to describe the effects of two scenarios due to (i) a lattice deformation in graphene, giving rise to a natural Fermi velocity renormalization, or even (ii) a nonuniform mass term, induced by a specific substrate, that varies on a length scale much greater than the magnetic field length.

Pseudo quantum electrodynamics and Chern-Simons theory coupled to two-dimensional electrons

We study a nonlocal theory that combines both the Pseudo quantum electrodynamics (PQED) and Chern-Simons actions among two-dimensional electrons. In the static limit, we conclude that the competition of these two interactions yields a Coulomb potential with a screened electric charge given by $e^2/(1+\theta^2)$, where $\theta$ is the dimensionless Chern-Simons parameter. This could be useful for describing the substrate interaction with two-dimensional materials and the doping dependence of the dielectric constant in graphene. In the dynamical limit, we calculate the effective current-current action of the model considering Dirac electrons. We show that this resembles the electromagnetic and statistical interactions, but with two different overall constants, given by $e^2/(1+\theta^2)$ and $e^2\theta/(1+\theta^2)$. Therefore, the $\theta$-parameter does not provide a topological mass for the Gauge field in PQED, which is a relevant difference in comparison with quantum electrodynamics. Thereafter, we apply the one-loop perturbation theory in our model. Within this approach, we calculate the electron self-energy, the electron renormalized mass, the corrected gauge-field propagator, and the renormalized Fermi velocity for both high- and low-speed limits, using the renormalization group. In particular, we obtain a maximum value of the renormalized mass for $\theta\approx 0.36$. This behavior is an important signature of the model and relations with doping control of band gap size are also discussed in the conclusions.

Fermi velocity renormalization in graphene probed by terahertz time-domain spectroscopy

We demonstrate terahertz time-domain spectroscopy (THz-TDS) to be an accurate, rapid and scalable method to probe the interaction-induced Fermi velocity renormalization of charge carriers in graphene. This allows the quantitative extraction of all electrical parameters (DC conductivity σDC, carrier density n, and carrier mobility µ) of large-scale graphene films placed on arbitrary substrates via THz-TDS. Particularly relevant are substrates with low relative permittivity (< 5) such as polymeric films, where notable renormalization effects are observed even at relatively large carrier densities (>1012 cm−2, Fermi level > 0.1 eV). From an application point of view, the ability to rapidly and non-destructively quantify and map the electrical (σDC, n, µ) and electronic () properties of large-scale graphene on generic substrates is key to utilize this material in applications such as metrology, flexible electronics as well as to monitor graphene transfers using polymers as handling layers.

Electronic correlations in nodal-line semimetals

Dirac fermions with highly dispersive linear bands1–3 are usually considered weakly correlated due to the relatively large bandwidths (W) compared to Coulomb interactions (U). With the discovery of nodal-line semimetals, the notion of the Dirac point has been extended to lines and loops in momentum space. The anisotropy associated with nodal-line structure gives rise to greatly reduced kinetic energy along the line. However, experimental evidence for the anticipated enhanced correlations in nodal-line semimetals is sparse. Here, we report on prominent correlation effects in a nodal-line semimetal compound, ZrSiSe, through a combination of optical spectroscopy and density functional theory calculations. We observed two fundamental spectroscopic hallmarks of electronic correlations: strong reduction (1/3) of the free-carrier Drude weight and also the Fermi velocity compared to predictions of density functional band theory. The renormalization of Fermi velocity can be further controlled with an external magnetic field. ZrSiSe therefore offers the rare opportunity to investigate correlation-driven physics in a Dirac system. What happens to topological materials when their electrons are strongly interacting is an open question. Shao and others demonstrate that ZrSiSe is a material that can address this as it has a topological band structure and non-trivial correlations.

Possible Fröhlich surface polaron formation in graphene on a polar substrate

Abstract We theoretically study the formation of Frohlich polaron in monolayer graphene on a substrate made of polar materials. In this calculation, the Rayleigh-Schrodinger perturbation theory is used to obtain analytical expression of polaron energy. The decrease (increase) in the electron (hole) energy due to interaction with surface optical phonons indicates that the formation of a surface polaron is preferred. The charge carrier-phonon interaction in monolayer graphene on a polar substrate does not lead to the formation of a gap between the valence and the conduction bands, as there exist the same energy shifts for both electron and hole at k = 0 . The expression for the renormalized Fermi velocity due to carrier-phonon coupling for small values of k is obtained. Our results show that the influence of the screening effect on polaron energies is significant for k ≤ k F .

Triangular Potential Effects on the Fermi Velocity Renormalization in 8-Pmmn Borophene

A novel mechanism has been reported for the intrinsic electronic properties of the 8-Pmmn Borophene to investigate the electronic energy spectrum and spectrum parameters of the structure. To examine the structure, we extract the energy spectrum of the Hamiltonian for the monolayer borophene by using analytical method. Additionally, for the intrinsic properties, first we obtained the bare Fermi velocity which findings of the study are consistent with experimental results . After obtained the bare state Fermi velocity 8-Pmmn borophene , dressed with triangular potential and renormalized Fermi velocity has been obtained. Corresponding renormalized Fermi velocity reshaped with the triangular potential which has non-negligible contribution to the intrinsic properties of borophene. This finding has important implications for developing electronic devices which made from the boron due to increasing the controllability of the structure.

Many-body filling factor dependent renormalization of Fermi velocity in graphene in strong magnetic field

We present the theory of many-body corrections to cyclotron transition energies in graphene in strong magnetic field due to Coulomb interaction, considered in terms of the renormalized Fermi velocity. A particular emphasis is made on the recent experiments where detailed dependencies of this velocity on the Landau level filling factor for individual transitions were measured. Taking into account the many-body exchange, excitonic corrections and interaction screening in the static random-phase approximation, we successfully explained the main features of the experimental data, in particular that the Fermi velocities have plateaus when the 0th Landau level is partially filled and rapidly decrease at higher carrier densities due to enhancement of the screening. We also explained the features of the nonmonotonous filling-factor dependence of the Fermi velocity observed in the earlier cyclotron resonance experiment with disordered graphene by taking into account the disorder-induced Landau level broadening.

Impacts of in-plane strain on commensurate graphene/hexagonal boron nitride superlattices

Due to atomically thin structure, graphene/hexagonal boron nitride (G/hBN) heterostructures are intensively sensitive to the external mechanical forces and deformations being applied to their lattice structure. In particular, strain can lead to the modification of the electronic properties of G/hBN. Furthermore, moiré structures driven by misalignment of graphene and hBN layers introduce new features to the electronic behavior of G/hBN. Utilizing ab initio calculation, we study the strain-induced modification of the electronic properties of diverse stacking faults of G/hBN when applying in-plane strain on both layers, simultaneously. We observe that the interplay of few percent magnitude in-plane strain and moiré pattern in the experimentally applicable systems leads to considerable valley drifts, band gap modulation and enhancement of the substrate-induced Fermi velocity renormalization. Furthermore, we find that regardless of the strain alignment, the zigzag direction becomes more efficient for electronic transport, when applying in-plane non-equibiaxial strains.

Field theoretic renormalization study of interaction corrections to the universal ac conductivity of graphene

The two-loop interaction correction coefficient to the universal ac conductivity of disorder-free intrinsic graphene is computed with the help of a field theoretic renormalization study using the Bogoliubov-Parasiuk-Hepp-Zimmermann prescription. Non-standard Ward identities imply that divergent subgraphs (related to Fermi velocity renormalization) contribute to the renormalized optical conductivity. Proceeding either via densitydensity or via current-current correlation functions, a single well-defined value is obtained: mathcal{C}=left.left(19-6pi right)/12right)=0.01 in agreement with the result first obtained by Mishchenko and which is compatible with experimental uncertainties.

Chemical-potential flow equations for graphene with Coulomb interactions

We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results confirm that the charge carrier density dependence of the Fermi velocity is negligible, validating the comparison of the fRG calculation at zero density of Bauer et al., Phys. Rev. B 92, 121409 (2015) with the experiment of Elias et al., Nat. Phys. 7, 701 (2011).

Cavity effects on the Fermi velocity renormalization in a graphene sheet

Recently, in the literature, it was shown that the logarithmic renormalization of the Fermi velocity in a plane graphene sheet (which, in turn, is related to the Coulombian static potential associated to electrons in the sheet) is inhibited by the presence of a single parallel conducting plate. In the present paper, we investigate the situation of a suspended graphene sheet in a cavity formed by two conducting plates parallel to the sheet. The effect of a cavity on the interaction between electrons in the graphene is not merely the addition of the effects of each plate individually. From this, one can expect that the inhibition of the renormalization of the Fermi velocity generated by a cavity is not a mere addition of the inhibition induced by each single plate. In other words, the simple addition of the result for the inhibition of the renormalization of the Fermi velocity found in the literature for a single plate could not be used to predict the exact behavior of the inhibition for the graphene between two plates. Here, we show that, in fact, this is what happens and calculate how the presence of a cavity formed by two conducting plates parallel to the suspended graphene sheet amplifies, in a non-additive manner, the inhibition of the logarithmic renormalization of the Fermi velocity. In the limits of a single plate and no plates, our formulas recover those found in the literature.

Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction

Renormalization of Landau level energies in graphene in strong magnetic field due to Coulomb interaction is studied theoretically, and calculations are compared with two experiments on carrier-density dependent scanning tunneling spectroscopy. An approximate preservation of the square-root dependence of the energies of Landau levels on their numbers and magnetic field in the presence of the interaction is examined. Many-body calculations of the renormalized Fermi velocity with the statically screened interaction taken in the random-phase approximation show good agreement with both experiments. The crucial role of the screening in achieving quantitative agreement is found. The main contribution to the observed rapid logarithmic growth of the renormalized Fermi velocity on approach to the charge neutrality point turned out to be caused not by mere exchange interaction effects, but by weakening of the screening at decreasing carrier density. The importance of a self-consistent treatment of the screening is also demonstrated.

Real-Space Imaging of the Tailored Plasmons in Twisted Bilayer Graphene.

We report a systematic plasmonic study of twisted bilayer graphene (TBLG)-two graphene layers stacked with a twist angle. Through real-space nanoimaging of TBLG single crystals with a wide distribution of twist angles, we find that TBLG supports confined infrared plasmons that are sensitively dependent on the twist angle. At small twist angles, TBLG has a plasmon wavelength comparable to that of single-layer graphene. At larger twist angles, the plasmon wavelength of TBLG increases significantly with apparently lower damping. Further analysis and modeling indicate that the observed twist-angle dependence of TBLG plasmons in the Dirac linear regime is mainly due to the Fermi-velocity renormalization, a direct consequence of interlayer electronic coupling. Our work unveils the tailored plasmonic characteristics of TBLG and deepens our understanding of the intriguing nano-optical physics in novel van der Waals coupled two-dimensional materials.