Surface dynamics of Mo(1 1 0)–H and Mo(1 1 0)–Li

We compare the surface dynamics of the adsorbate systems Mo(1 1 0)–H and Mo(1 1 0)–Li. In both cases electron energy loss spectroscopy measurements revealed strong substrate surface phonon anomalies. Whereas the phonon anomaly of the hydrogen-covered surface was unequivocally assigned to be of the Kohn type, the anomalous behavior of the surface phonons of the lithium-covered surface remained obscure. In this paper we develop an experimental criterion based on the dispersion of adsorbate phonons, which allows to decide whether the observed substrate surface phonon anomaly is of the Kohn type or not. Employing this criterion we now definitely rule out that the anomaly on Mo(1 1 0)–Li is due to the Kohn effect.     

Electron-phonon coupling on the surface of the topological insulator Bi2Se3 determined from surface-phonon dispersion measurements

In this Letter, we report measurements of the coupling between Dirac fermion quasiparticles (DFQs) and phonons on the (001) surface of the strong topological insulator Bi2Se3. While most contemporary investigations of this coupling have involved examining the temperature dependence of the DFQ self-energy via angle-resolved photoemission spectroscopy measurements, we employ inelastic helium-atom scattering to explore, for the first time, this coupling from the phonon perspective. Using a Hilbert transform, we are able to obtain the imaginary part of the phonon self-energy associated with a dispersive surface-phonon branch identified in our previous work [Phys. Rev. Lett. 107, 186102 (2011)] as having strong interactions with the DFQs. From this imaginary part of the self-energy we obtain a branch-specific electron-phonon coupling constant of 0.43, which is stronger than the values reported from the angle-resolved photoemission spectroscopy measurements.     

Dynamical mean field study of the Dirac liquid

Renormalization is one of the basic notions of condensed matter physics. Based on the concept of renormalization, the Landau’s Fermi liquid theory has been able to explain, why despite the presence of Coulomb interactions, the free electron theory works so well for simple metals with extended Fermi surface (FS). The recent synthesis of graphene has provided the condensed matter physicists with a low energy laboratory of Dirac fermions where instead of a FS, one has two Fermi points. Many exciting phenomena in graphene can be successfully interpreted in terms of free Dirac electrons. In this paper, employing dynamical mean field theory (DMFT), we show that an interacting Dirac sea is essentially an effective free Dirac theory. This observation suggests the notion of Dirac liquid as a fixed point of interacting 2 + 1 dimensional Dirac fermions. We find one more fixed point at strong interactions describing a Mott insulating state, and address the nature of semi-metal to insulator (SMIT) transition in this system.     

Observation of anomalous phonon softening in bilayer graphene

The interaction of electron-hole pairs with lattice vibrations exhibits a wealth of intriguing physical phenomena such as the renowned Kohn anomaly. Here we report the observation in bilayer graphene of an unusual phonon softening that provides the first experimental proof for another type of phonon anomaly. Similar to the Kohn anomaly, which is a logarithmic singularity in the phonon group velocity [W. Kohn, Phys. Rev. Lett. 2, 393 (1959)], the observed phonon anomaly exhibits a logarithmic singularity in the optical-phonon energy. Arising from a resonant electron-phonon coupling effect, the anomaly was also expected, albeit not observed, in monolayer graphene. We propose an explanation for why it is easier to observe in bilayer samples.     

Electric field effect tuning of electron-phonon coupling in graphene

Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long-wavelength optical phonons of graphene. The EFE in this two-dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and linewidth demonstrate optically the particle-hole symmetry about the charge-neutral Dirac point. The linear dependence of the phonon frequency on the EFE-modulated Fermi energy is explained as the electron-phonon coupling of massless Dirac fermions.     

Superconductivity and lattice instability in compressed lithium from Fermi surface hot spots

The highest superconducting temperature Tc observed in any elemental metal (Li with Tc approximately 18-20 K at pressure 35-48 GPa) is shown to arise from increasingly strong electron-phonon coupling concentrated along intersections of Kohn anomaly surfaces with the evolving Fermi surface. First-principles linear response calculations of the phonon spectrum and spectral function alpha2F(omega) reveal very strong Q- and phonon-polarization dependence of coupling strength, resulting in values of in the observed range. The sharp momentum dependence of the coupling even for the simple Li Fermi surface indicates more generally that a fine Q mesh is required for precise evaluation of lamda.     

Observation of magnetophonon resonance of Dirac fermions in graphite

Coherent coupling of Dirac fermion magnetoexcitons with an optical phonon is observed in graphite as marked magnetic-field dependent splittings and anticrossing behavior of the two coupled modes. The sharp magnetophonon resonance occurs in regions of the graphite sample with properties of superior single-layer graphene having enhanced lifetimes of Dirac fermions. The greatly reduced carrier broadening to values below the graphene electron-phonon coupling constant explains the appearance of sharp resonances that reveal a fundamental interaction of Dirac fermions.     

Energy anomaly and polarizability of carbon nanotubes

The energy of Fermi sea perturbed by an external potential is analyzed with the help of an energy anomaly. Using an example of massive Dirac fermions on a circle, we illustrate how the anomaly accounts for the contribution of the deep-lying states. The energy anomaly is a universal function of the applied field and is related to known field-theoretic anomalies. Applied to the transverse polarizability of carbon nanotubes, the anomaly reveals universality and scale invariance of the response dominated by electrons. The electron band transformation in a strong field-effect regime is predicted.     

Temperature relaxation and energy loss of hot carriers in graphene

The temperature relaxation and energy loss of hot Dirac fermions are investigated theoretically in graphene with carrier–optical phonon scattering. The time evolutions of temperature and energy loss for hot Dirac fermions in graphene are calculated self-consistently. It shows that the carrier–optical phonon coupling results in the energy relaxation of hot carriers excited by an electric field, and the relaxation time for temperature is about 0.5–1 ps and the corresponding energy loss is about 10–25 nW per carrier for typically doped graphene samples with a carrier density range of 1–5×10¹² cm^?2. Moreover, we analyze the dependence of temperature and energy relaxation on initial hot carrier temperature, lattice temperature and carrier density in detail.     

Index of a family of lattice Dirac operators and its relation to the non-Abelian anomaly on the lattice

In the continuum, a topological obstruction to the vanishing of the non-Abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac operators in 2n dimensions. In this paper an analogous result is derived for chiral fermions on the lattice in the overlap formulation. This involves deriving an index theorem for a family of lattice Dirac operators satisfying the Ginsparg-Wilson relation. The index density is proportional to Lüscher's topological field in 2n+2 dimensions.     

Reflectivity of a one-dimensional electron-phonon system

The effect of the giant Kohn anomaly in a one dimensional system on the optical reflectivity is calculated, for parameters believed to be characteristic for TTFTCNQ. It is found that the Kohn anomaly in the optical phonon branch due to stretching vibrations of the CN groups, whose unperturbed frequency is 2100–2200 cm^?1, produces a minimum in the reflectivity at 1600 cm^?, approximately. This minimum coincides with the minimum w found experimentally by Bright, Garito and Heeger. By this mechanism, phonons with a wavevector of order 2k_F affect the reflectivity of photons with q ≈ 0.     

Mixing renormalization in Majorana neutrino theories

The renormalization of general theories with inter-family mixing of Dirac and/or Majorana fermions is studied at the one-loop electroweak order. The phenomenological significance of the mixing-matrix renormalization is discussed, within the context of models based on the SU(2)_L⊗U(1)_Y gauge group. The effect of radiative neutrino masses present in these models is naturally taken into account in this formulation. As an example, charged-lepton universality in pion decays is investigated in the heavy-neutrino limit. Non-decoupling heavy-neutrino effects induced by mixing renormalization are found to considerably affect the predictions in these new-physics scenarios.     

Chirality-induced dynamic kohn anomalies in graphene

We develop a theory for the renormalization of the phonon energy dispersion in graphene due to the combined effects of both Coulomb and electron-phonon (e-ph) interactions. We obtain the renormalized phonon energy spectrum by an exact analytic derivation of the phonon self-energy, finding three distinct Kohn anomalies (KAs) at the phonon wave vector q=omega/v, 2k_{F}+/-omega/v for LO phonons and one at q=omega/v for TO phonons. The presence of these new KAs in graphene, in contrast to the usual KA q=2k_{F} in ordinary metals, originates from the dynamical screening of e-ph interaction (with a concomitant breakdown of the Born-Oppenheimer approximation) and the peculiar chirality of the graphene e-ph coupling.     

Temperature and layer number dependence of the G and 2D phonon energy and damping in graphene

We have studied the temperature and size dependence of the G and 2D phonon modes in graphene. It is shown that in a graphene monolayer the phonon energy decreases whereas the phonon damping increases with increasing temperature. The electron-phonon interaction leads to hardening whereas the fourth-order anharmonic phonon-phonon processes lead to softening of the phonon energy with increasing temperature. We have shown that the electron-phonon interaction plays an important role also by the dispersion dependence of the phonon G mode, by the observation of the Kohn anomaly. The G mode frequency decreases and damping increases, whereas the 2D phonon frequency and damping increase with increasing layer number. The temperature and size effects of the 2D mode are much stronger than those of the G mode.     

Orthogonality between scales in a renormalization group for fermions

Having in mind the development of a technical tool to treat fermionic systems, we propose a Kadanoff-Wilson block renormalization transformation employing unusual averages (an inevitable artifact due to the specificity of lattice fermions and to the desired transformation properties). The free propagator is decomposed into operators associated to different momentum scales and with orthogonal relations, and the effective actions generated from the Dirac operator by the transformations present uniform exponential decay. We argue to show the usefulness of the formalism to study correlation functions of interacting fermions.     

Electronic structure,Dirac points and Fermi arc surface states in three-dimensional Dirac semimetal Na_3Bi from angle-resolved photoemission spectroscopy

The three-dimensional(3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A_3Bi(A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission(ARPES) measurements on the two cleaved surfaces,(001) and(100), of Na_3Bi. On the(001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k_x–k_y plane and by varying the photon energy to get access to different out-of-plane k_zs. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the(100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the(100) plane. We directly observe two isolated 3D Dirac nodes on the(100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ~150 me V before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na_3Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the3 D Dirac cones, on the possible formation of surface reconstruction of the(001) surface, and on the issue of basic Brillouin zone selection for the(100) surface.     

Phonon spectrum and Kohn anomaly in platinum

The phonon frequencies of platinum are calculated using a model potential approach. The results are in fair agreement with the experimental data but do not show any Kohn anomaly or any kink, as revealed experimentally. The magnitude of the anomaly has been theoretically estimated and comes out to be very small.     

Backscattering of Dirac fermions in HgTe quantum wells with a finite gap

The density-dependent mobility of n-type HgTe quantum wells with inverted band ordering has been studied both experimentally and theoretically. While semiconductor heterostructures with a parabolic dispersion exhibit an increase in mobility with carrier density, high-quality HgTe quantum wells exhibit a distinct mobility maximum. We show that this mobility anomaly is due to backscattering of Dirac fermions from random fluctuations of the band gap (Dirac mass). Our findings open new avenues for the study of Dirac fermion transport with finite and random mass, which so far has been hard to access.     

Observation of π Berry phase in quantum oscillations of three‐dimensional Fermi surface in topological insulator Bi2Se3

We report the quantum transport studies on Bi₂Se₃ single crystal with bulk carrier concentration of ～10¹⁹ cm^–3. The Bi₂Se₃ crystal exhibits metallic character, and at low temperatures, the field dependence of resistivity shows clear Shubnikov–de Haas (SdH) oscillations above 6 T. The analysis of these oscillations through Lifshitz–Kosevich theory reveals a non‐trivial π Berry phase coming from three‐dimensional (3D) Fermi surface, which is a strong signature of Dirac fermions with three‐dimensional dispersion. The large Dingle temperature and non zero slope of Williamson–Hall plot suggest the presence of enhanced local strain field in our system which possibly transforms the regions of topological insulator to 3D Dirac fermion metal state. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Peierls-Fröhlich instability and Kohn anomaly

A mathematical basis is given to the Peierls-Fröhlich instability and the Kohn anomaly. The techniques and ideas are based on the recently developed mathematical theory of quantum fluctuations and response theory. We prove that there exists a unique resonant one-mode interaction between electrons and phonons which is responsible for the Peierls-Fröhlich instability and the phase transition in the Mattis-Langer model. We prove also that the softening of this phonon mode at the critical temperature (Kohn anomaly) is a consequence of the critical slowing down of the dynamics of the lattice distortion fluctuations. It is the result of the linear dependence of two fluctuation operators corresponding to the frozen charge density wave and the distortion order parameter.