Electronic Topological Transition Research Articles

Electronic topological transitions in Zn under compression

The electronic structure of hcp Zn under pressure up to 10 GPa has been calculated self-consistently by means of the scalar relativistic tight-binding linear muffin-tin orbital method. The calculations show that three electronic topological transitions (ETT's) occur in Zn when the $c/a$ axial ratio diminishes under compression. One transition occurs at $c/a\ensuremath{\simeq}1.82$ when the ``needles'' appear around the symmetry point K of the Brillouin zone. The other two transitions occur at $c/a\ensuremath{\simeq}\sqrt{3},$ when the ``butterfly'' and ``cigar'' appear simultaneously both around the L point. It has been shown that these ETT's are responsible for a number of anomalies observed in Zn at compression.

Effective surface impedance of polycrystals under anomalous skin effect conditions

The effective impedance of strongly anisotropic polycrystals has been investigated under the conditions of extremely anomalous skin effect. We were interested in finding out how the value of the effective impedance depends on the geometry of the Fermi surface of a single crystal grain. The previously obtained nonperturbative solution based on the application of the impedance (the Leontovich) boundary conditions was used to calculate the effective impedance of a polycrystalline metal. Some model Fermi surfaces were examined. In the vicinity of the electronic topological transition the singularities of the effective impedance related to the change of the topology of the Fermi surface were calculated. Our results show that though a polycrystal is an isotropic medium in average, it is not sufficient to consider it as a metal with an effective spherical Fermi surface, since this can lead to the loss of some characteristic features of extremely anomalous skin effect in polycrystals.

Absence of lattice strain anomalies at the electronic topological transition in zinc at high pressure

High pressure structural distortions of the hexagonal close packed (hcp) element zinc have been a subject of controversy. Earlier experimental results and theory showed a large anomaly in lattice strain with compression in zinc at about 10 GPa which was explained theoretically by a change in Fermi surface topology. Later hydrostatic experiments showed no such anomaly, resulting in a discrepancy between theory and experiment. We have computed the compression and lattice strain of hcp zinc over a wide range of compressions using the linearized augmented plane wave (LAPW) method paying special attention to k-point convergence. We find that the behavior of the lattice strain is strongly dependent on k-point sampling, and with large k-point sets the previously computed anomaly in lattice parameters under compression disappears, in agreement with recent experiments.

Phonon anomaly in high-pressure Zn

The equation of states and phonon dispersions of hexagonal zinc have been calculated by the plane-wave pseudopotential method within the generalized-gradient approximation. Weak discontinuities are found in the pressure-volume relation as well as the c/a-volume curve. Phonon dispersions of Zn under pressure have been obtained with a direct method and the results are consistent with the neutron scattering data. At V/V0 approximately 0.88, the calculated frequencies of the acoustic phonons near the zone center softened substantially as a result of an electronic topological transition. The theoretical result is consistent with the observed anomaly in the Lam-Mossbauer factor at low temperature.

Helical magnetic ordering in Tb completely suppressed by uniaxial tension: Evidence of electronic topological transition and support for the nesting hypothesis

Helical magnetic ordering in Tb completely suppressed by uniaxial tension: Evidence of electronic topological transition and support for the nesting hypothesis

Pressure shift of the zone-center TO mode of Zn

The pressure dependence of the transverse-optical zone-center phonon mode of Zn was measured by means of Raman spectroscopy up to 58 GPa at room temperature. The frequency increases under pressure and no anomaly is observed in the pressure range around 10 GPa where electronic topological transitions are expected to occur, and where also ab initio ‘‘frozen phonon’’ calculations predict a weak anomaly in the c/a ratio. The

Strong elastic deformation influence on scattering mechanisms in quantum wires based on semimetals

The developed methods for obtaining monocrystal quantum wires of bismuth and its alloys in a glass coating allowed the considerable enlargement of the elastic strain region in samples of this type. This circumstance made it possible to investigate the influence of electronic topological transitions on the system properties and to observe peculiarities near the critical point of the structural phase transition. The resistance, Shubnikov-de Haas oscillations, Dingle temperature, and magnetic flux quantization effect were investigated in both ohmage region of the current-voltage characteristics and in the region of phonon generation under strong elastic strain. A complex dependence of conductivity on strain, temperature, wire diameter and impurity concentration was found. It is shown that the regions of small and high deformation are characterized by predomination of different scattering mechanisms. The problem of manifestation of interference effects manifestation in the phonon generation regime under strong elastic stretch in quantum wires based on Bi is discussed.

Various ordered states in a 2D interacting electron system close to an electronic topological transition

We consider a 2D electron system on a square lattice with hopping beyond nearest neighbors. The existence of the quantum critical point associated with an electronic topological transition in the noninteracting system results in density wave (DW) and high-temperature d-wave superconducting (dSC) instabilities in the presence of an exchange interaction J. We analyse different DW ordering such as isotropic Spin DW (SDW), d-wave SDW, isotropic Charge DW (CDW) and d-wave CDW. The coexistence of dSC and SDW orders leads necessarily to the existence of a third order which is a π triplet superconducting (PTS) order. A new phase diagram with a mixed phase of SDW, dSC and PTS order is found. The theory is applied to high- T c cuprates.

Fermi-liquid theory of electronic topological transitions and screening anomalies in metals

General expressions for the contributions of the Van Hove singularity (VHS)in the electron density of states to the thermodynamic potential $\Omega are obtained in the framework of microscopic Fermi liquid theory. The renormalization of the singularities in $\Omega connected with the Lifshitz electronic topological transition (ETT) is found. Screening anomalies due to virtual transitions between VHS and the Fermi level are considered. It is shown that, in contrast with the one-particle picture of ETT, the singularities in $\Omega turns out to be two-sided for interacting electrons.

Electronic topological transition in zinc metal? A 67Zn-Mössbauer investigation

The question concerning the existence of an electronic topological transition (ETT) in Zn metal under quasi-hydrostatic pressure at ∼6.6 GPa caused a considerable controversy in the literature. We briefly review low-temperature 67Zn-Mossbauer data and scalar-relativistic augmented plane wave calculations and give a consistent interpretation in terms of an ETT. To highlight some important aspects of the controversy two theoretical and two experimental publications will be discussed in more detail. At present the existence of an ETT in Zn metal is disputed both from an experimental and from a theoretical point of view. The suggestion of a transition to a commensurate spin-density wave at ∼6.6 GPa instead of an ETT may reconcile the seemingly contradictory results of 67Zn-Mossbauer experiments at 4.2 K and of room temperature inelastic neutron scattering measurements. However, it does not explain the anomalies found in theoretical calculations performed for Zn metal in this pressure range. Considerable experimental and theoretical efforts are required to confirm - or rule out - a spin-density-wave transition.

Quantum critical point associated with the electronic topological transition in a two-dimensional electron system as a driving force for anomalies in underdoped high-Tccuprates

We study an electronic topological transition (ETT) (the transition due to change in topology of Fermi surface) that occurs in a two-dimensional electron system on a square lattice with hopping beyond nearest neighbors under a change of electronic concentration n (or of hole doping $\ensuremath{\delta}=1\ensuremath{-}n).$ We show that the ETT point $(\ensuremath{\delta}={\ensuremath{\delta}}_{c}, T=0)$ is an exotic quantum critical point (QCP) with several aspects of criticality. The first trivial one is related to singularities in thermodynamic properties. A nontrivial and never considered aspect concerns a behavior of the electron-hole response function: the ETT point is a quantum multicritical point, the end point of the critical line $(T=0, \ensuremath{\delta}>{\ensuremath{\delta}}_{c})$ of static Kohn singularities. We show that the existence of this QCP results in global anomalies of the system in the presence of interaction. (We consider the interaction corresponding to the ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}J$ model.) The anomalies take place on one side of the ETT $(\ensuremath{\delta}<{\ensuremath{\delta}}_{c}$ in the case of ${t}^{\ensuremath{'}}/t<0$ corresponding to the high-${T}_{c}$ cuprates) and have a striking similarity with the anomalies observed in the high-${T}_{c}$ cuprates in the underdoped regime. The most important consequence of the ETT (besides the appearance of superconducting instability of the d-wave symmetry) is the existence of the pseudocritical zone, ${T}^{*}(\ensuremath{\delta})\ensuremath{\propto}{\ensuremath{\delta}}_{c}\ensuremath{-}\ensuremath{\delta},$ which grows from the point $\ensuremath{\delta}={\ensuremath{\delta}}_{c}$ on the side $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}.$ Below and around this zone the metal state is anomalous. Some anomalies are considered in the present paper and compared with experiment (NMR, neutron scattering).

Electronic structure of materials under pressure

Parameter-free calculations based on the density-functional theory are used to examine high-pressure phases of solids. For the elemental semiconductors, as represented by Si, the high-pressure phases are examined in some detail, and particular attention is paid to the Si(VI)orthorhombic (Cmca) structure which was resolved only very recently. For III–V semiconductors the optimization of the structural parameters of the Cmcm and Imm2 phases is described. The structural energy differences are in several cases very small, and in some cases too small to allow a safe structure prediction on the basis of the calculations. In that context we also discuss ways to go beyond the local density approximation (LDA). We show that the predicted high-pressure phases may be significantly affected by inclusion of (generalized) gradient corrections (GGA). Elemental Zn (hcp) is further taken as an example where we find that the simple LDA leads to poor results for the equilibrium volume and axial ratio (c/a). Introducing corrections, for example by GGA, it is, however, possible to achieve an accuracy that allows a study of the structural changes of Zn (and Cd) under pressure and analysis of these changes in terms of electronic topological transitions. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 880–894, 2000

Quantum SDW liquid state originating from 2D electronic topological transition as a source for anomalies in the high-Tc cuprates

A new microscopic scenario for high T c cuprates based on the existence of an electronic topological transition (ETT) in a strongly correlated 2D electron system has been developed recently. We first briefly sketch the principal results concerning the behaviour of a 2D fermion system on a square lattice close to an ETT and the main consequences for a strongly correlated system: d-wave superconductivity and SDW (CDW) quantum liquid state above T SC . We then illustrate how this theory can explain several crucial experimental facts (observed by NMR, angle resolved photoemission spectroscopy (ARPES), tunneling spectroscopy, inelastic neutron scattering) which reveal anomalous behavior in the SC state and in the metallic state above T SC .

Hall and Nernst effects in some models of anisotropic metals

General expressions for the weak-field Hall and Nernst coefficients are found for a metal with an arbitrary electron dispersion. It is shown that, contrary to the free-electron model, the signs of the Hall conductivity, the Nernst coefficient, and thermopower in real metal may differ depending on the derivative of the electron density of states on the Fermi level. Pecularities of Hall and Nernst effects are discussed for two cases: a quasi-two-dimensional metal and a conductor at the edge of the electronic topological transition.

Absence of thec/aanomaly in Zn under high pressure with a helium-pressure medium

A high-pressure powder x-ray diffraction experiment on Zn has been carried out at room temperature with He pressure-transmitting medium in order to achieve the best hydrostatic conditions. The anomaly in the volume-dependence of the $c/a$ axial ratio, which has been observed previously, can no longer be observed. Hence the anomaly is most probably induced by the nonhydrostaticity associated with the solidification of the methanol-ethanol-water pressure-transmitting medium used in the previous studies. The present results suggest reconsideration of the calculated $c/a$ anomaly based on the electronic topological transition.

Computational condensed matter physics

In the high pressure laboratory at BARC, we are pursuing a program to study the behaviour of materials under static and dynamic pressures. Theoretical component has been an integral part for guiding and interpreting new experiments. The initial phase of such efforts was devoted to the development of equation of state models at arbitrary temperatures and matter densities. With the advent of diamond anvil cell device and the simultaneous provision for laser heating of the compressed samples for static high pressure studies, and with the improvements of the diagnostic techniques in dynamic shock methods, the focus of our studies switched over to the predictions and interpretations of phase transitions. Often these efforts have led to intense experimental studies and sometimes helped in resolving the controversies in data. We adopted the first principles electronic structure calculations for high pressure studies. Our work on the electronic topological transition in zinc led to many experimental and theoretical investigations. The results of electronic structure changes in similar metal cadmium shall be compared with existing understanding in Zn under pressure. Our studies on Nb and other compounds like intermetallics and borocarbides have revealed interesting electronic structure changes under pressure. However, the electronic structure based investigations of structural stabilities at high pressures involve tedious trial and error effort, which is avoided in theab initio molecular dynamics simulations. The current status of our efforts in the use of this technique is illustrated with the example of quasicrystal based clusters.

Some consequences of electronic topological transition in 2D system on a square lattice: Excitonic ordered states

We study the ordered "excitonic" states which develop around the quantum critical point (QCP) associated with the electronic topological transition (ETT) in a 2D electron system on a square lattice. We consider the case of hopping beyond nearest neighbors when ETT has an unusual character. We show that the amplitude of the order parameter (OP) and of the gap in the electron spectrum increase with increasing the distance from the QCP, \delta_c - \delta, where \delta = 1-n and "n" is an electron concentration. Such a behavior is different from the ordinary case when OP and the gap decrease when going away from the point which is a motor for instability. The gap opens at "hot spots" and extends untill the saddle points (SP) whatever is the doping concentration. The spectrum gets a characteristic flat shape as a result of hybrydization effect in the vicinity of two different SP's. The shape of the spectrum and the angle dependence of the gap have a striking similarity with the features observed in the normal state of the underdoped high-T$_c$ cuprates. We discuss also details about the phase diagram and the behaviour of the density of states.

New Scenario for High-TcCuprates: Electronic Topological Transition as a Motor for Anomalies in the Underdoped Regime

We have discovered a new nontrivial aspect of electronic topological transition (ETT) in a 2D free fermion system on a square lattice. The corresponding exotic quantum critical point, \delta=\delta_c, T=0, (n=1-\delta is an electron concentration) is at the origin of anomalous behaviour in the interacting system on one side of ETT, \delta<\delta_c. The most important is an appearance of the line of characteristic temperatures, T^*(\delta) \propto \delta_c-\delta. Application of the theory to high-T_c cuprates reveals a striking similarity to the observed experimentally behaviour in the underdoped regime (NMR and ARPES).

Anisotropy of thermal expansion and electronic topological transitions in Zn and Cd under pressure

Using first-principles local-density electronic structure calculations we investigate the evolution of the Fermi surface of hcp Zn and Cd under hydrostatic pressure. We find a sequence of electronic topological transitions (ETT) and a region of pressure where several of these ETT's almost coincide, which apparently leads to the experimentally observed anomalies in their lattice parameters. A change of sign of the anisotropic thermal expansion is predicted in this critical region for temperatures below the Debye temperature.

SC state anomalies in the underdoped regime of high-Tc cuprates as a result of proximity to electronic topological transition

Based on a microscopical theory developed earlier we study electronic and magnetic properties of high-T c cuprates in the superconducting (SC) state. An agreement with experiments (angle resolved photoemission spectroscopy, tunneling spectroscopy, inelastic neutron scattering) is remarkable.