Small Fermi Energy Research Articles

Lifshitz transitions and zero point lattice fluctuations in sulfur hydride showing near room temperature superconductivity

AbstractEmerets’s experiments on pressurized sulfur hydride have shown that H3S metal has the highest known superconducting critical temperature Tc = 203 K. The Emerets data show pressure induced changes of the isotope coefficient between 0.25 and 0.5, in disagreement with Eliashberg theory which predicts a nearly constant isotope coefficient.We assign the pressure dependent isotope coefficient to Lifshitz transitions induced by pressure and zero point lattice fluctuations. It is known that pressure could induce changes of the topology of the Fermi surface, called Lifshitz transitions, but were neglected in previous papers on the H3S superconductivity issue. Here we propose thatH3S is a multi-gap superconductor with a first condensate in the BCS regime (located in the large Fermi surface with high Fermi energy) which coexists with second condensates in the BCS-BEC crossover regime (located on the Fermi surface spots with small Fermi energy) near the and Mpoints.We discuss the Bianconi-Perali-Valletta (BPV) superconductivity theory to understand superconductivity in H3S since the BPV theory includes the corrections of the chemical potential due to pairing and the configuration interaction between different condensates, neglected by the Eliashberg theory. These two terms in the BPV theory give the shape resonance in superconducting gaps, similar to Feshbach resonance in ultracold fermionic gases, which is known to amplify the critical temperature. Therefore this work provides some key tools useful in the search for new room temperature superconductors.

Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction inYbRh2Si2

The heavy-fermion metal YbRh2Si2 displays a field-driven quantum phase transition where signatures of a Fermi-surface reconstruction have been identified, often interpreted as breakdown of the Kondo effect. We argue that instead many properties of the material can be consistently described assuming a Zeeman-driven Lifshitz transition of narrow heavy-fermion bands. Using a suitable quasiparticle model, we find a smeared jump in the Hall constant and lines of maxima in susceptibility and specific heat, very similar to experimental data. An intermediate non-Fermi liquid regime emerges due to the small effective Fermi energy near the transition. Further experiments to discriminate the different scenarios are proposed.

Small Fermi energy, strong electron–phonon effects and anharmonicity in MgB2

The investigation of the electron–phonon properties in MgB2 has attracted a huge interest after the discovery of superconductivity with Tc=39K in this compound. Although superconductivity is often described in terms of the conventional Eliashberg theory, properly generalized in the multiband/multigap scenario, important features distinguish MgB2 from other conventional strong-coupling superconductors. Most important it is the fact that a large part of the total electron–phonon strength seems to be concentrated here in only one phonon mode, the boron–boron E2g stretching mode. Another interesting property is the small Fermi energy of the σ bands, which are strongly coupled with the E2g mode. In this contribution, we discuss how the coexistence of both these features give rise to an unconventional phenomenology of the electron–phonon properties.

Nonadiabatic breakdown and pairing in high-Tc compounds

The electron-phonon interaction plays a fundamental role in the superconducting and normal-state properties of all the high-Tc materials, from cuprates to fullerenes. Another common element of these compounds is in addition the extremely small Fermi energy EF, which is comparable with the range ωph of the phonon frequencies. In such a situation the adiabatic principle ωph∕EF⪡1, on which the standard theory of the electron-phonon interaction and of the superconductivity relies, breaks down. In this contribution we discuss the physical consequences of the breakdown of the adiabatic assumption, with special interest on the superconducting properties. We review the microscopic derivation of the nonadiabatic theory of the electron-phonon coupling which explicitly takes into account higher-order electron-phonon scattering not included in the conventional picture. Within this context we discuss also the role of the repulsive electron-electron correlation and the specific phenomenology of cuprates and fullerides.

Anomalous quasiparticle transport in the superconducting state ofCeCoIn5

We report on a study of thermal Hall conductivity ${\ensuremath{\kappa}}_{xy}$ in the superconducting state of ${\mathrm{CeCoIn}}_{5}$. The scaling relation and the density of states of the delocalized quasiparticles, both obtained from ${\ensuremath{\kappa}}_{xy}$, are consistent with $d$-wave superconducting symmetry. The onset of superconductivity is accompanied by a steep increase in the thermal Hall angle, pointing to a striking enhancement in the quasiparticle mean free path. This enhancement is drastically suppressed in a very weak magnetic field. These results highlight that ${\mathrm{CeCoIn}}_{5}$ is unique among superconductors. A small Fermi energy, a large superconducting gap, a short coherence length, and a long mean free path all indicate that ${\mathrm{CeCoIn}}_{5}$ is clearly in the superclean regime $({\ensuremath{\epsilon}}_{F}∕\ensuremath{\Delta}⪡\ensuremath{\ell}∕\ensuremath{\xi})$, in which a peculiar vortex state is expected.

Nonadiabatic phenomenology in small Fermi energy superconductors

Abstract High- T c and unconventional superconductivity appears in a number of different materials with different physical properties. A common characteristics shared by almost all these compounds is that they are ‘bad metal’ in the sense that their effective charge carrier density is quite small, leading to a small Fermi energy E F . In such a situation the dynamics of the electronic and lattice degrees of freedom becomes comparable ( ω ph ∼ E F ) driving these systems towards a breakdown of the Born-Oppenheimer adiabatic principle ( ω ph ≪ E F ) ruled by the comparison between the phonon frequency scale ω ph and E F . The standard concept of Fermi liquid picture applied to the electron–phonon interaction needs thus to be deeply revised. We discuss the interesting implications of the onset of nonadiabatic effects on many properties of systems with small Fermi energy.

Abnormal positive magnetoresistance in a weak magnetic field in Ge:As on the metallic side close to the metal–insulator transition

We observed abnormal positive magnetoresistance (apm) in Ge at relatively small magnetic fields and low temperature (down to 30 mK) which was very different from the positive magnetoresistance connected with the shrinkage effect and also different to the negative magnetoresistance which was obtained in bulk GaAs for control purposes. Experiments were performed on isotropic-engineered bulk Ge with high homogeneous impurity distribution obtained by neutron-transmutation doping on the metallic side of metal–insulator transition (MIT) very close to N c. The apm was saturated in magnetic fields in a range of 0.4–0.6 T. We consider that the resistivity of our system is influenced by electron–phonon interactions which form superconducting fluctuations (Maki–Thomson correction to the conductivity) similar to Bose–Einstein condensation for barely free electrons with small Fermi energy. In a small magnetic field, these fluctuations are suppressed, resulting in an apm.

Small Fermi energy, zero-point fluctuations, and nonadiabaticity inMgB2

Small Fermi energy effects are induced in MgB$_2$ by the low hole doping in the $\sigma$ bands which are characterized by a Fermi energy $E_{\rm F}^\sigma \sim 0.5$ eV. We show that, due to the particularly strong deformation potential relative to the $E_{2g}$ phonon mode, lattice fluctuations are reflected in strong fluctuations in the electronic band structure. Quantum fluctuations associated to the zero-point lattice motion are responsible for an uncertainty of the Fermi energy of the order of the Fermi energy itself, leading to the breakdown of the adiabatic principle underlying the Born-Oppenheimer approximation in MgB$_2$ even if $\omega_{\rm ph}/E_{\rm F} \sim 0.1-0.2$, where $\omega_{\rm ph}$ are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.

Nonadiabatic electron–phonon effects in low carrier density superconductors

AbstractDifferent families of unconventional superconductors present a low charge carrier density as a common trait, suggesting that the low charge density can be at the basis of a unifying picture for different superconductors. In the past years we have suggested that the electron–phonon interaction can be responsible for a high‐Tc superconducting pairing in a nonadiabatic regime, where nonadiabatic effects are triggered on by the small electronic Fermi energy associated with the low charge density character. A coherent picture of such a framework requires however reconciling the low charge density and the small Fermi energy with a finite metallic character (sizable density of states and large Fermi surfaces). In this paper we investigate the peculiar conditions which are needed to be encountered in order to fulfill these requirements. We discuss the specific case of fullerenes, cuprates and MgB2 alloys by analyzing their specific structural and electronic properties The comparison between these materials and simple instructive models permits to underline the different routes to reconcile these characteristics in different compounds. In cuprates and fullerenes the interplay between small Fermi energies and large Fermi surface is strictly connected with strong electronic correlation effects. A comprehensive understanding of these issues can be useful to the future search for new nonadiabatic high‐Tc materials. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Small Fermi energy effects in MgB 2 and related compounds

Superconductivity at T c≃40 K in MgB 2 is thought to origin from the strong electron–phonon (el–ph) coupling of the σ-bands, whereas the residual interband scattering gives rise to the multigap phenomenology. The extremely low charge density of the σ-bands is reflected in the small Fermi energy E F σ , a fraction of eV, a common feature which is shared also by cuprates and fullerides. In our contribution we discuss the anomalous effects arising from the small Fermi energy phenomenology, when E F σ becomes comparable with the other energy scales of the systems. In particular we analyze the nonadiabatic effects arising from the finite adiabatic ratio ω ph/ E F σ ; the anharmonic character of the E 2 g phonon mode, which is shown to be related to the smallness of the Fermi energy with respect to the electron–phonon coupling g E 2 g : E F σ ∼ g E 2 g ; the anomalous effects of disorder when impurity scattering rate γ imp is compared with E F σ . We discuss also the possibility of an enhancement of the nonadiabatic character due to zero point quantum fluctuations.

Electron-phonon renormalization in small Fermi energy systems

The puzzling features of recent photoemission data in cuprates have been object of several analysis in order to identity the nature of the underlying electron-boson interaction. In this paper we point out that many basilar assumptions of the conventional analysis as expected to fail in small Fermi energy systems when, as the cuprates, the Fermi energy $E_{\rm F}$ is comparable with the boson energy scale. We discuss in details the novel features appearing in the self-energy of small Fermi energy systems and the possible implications on the ARPES data in cuprates.

NONADIABATIC EFFECTS AND THE ROLE OF SMALL FERMI ENERGY IN MgB2

There is nowadays a general agreement on a key role of the σ bands in the superconducting properties of MgB 2. We show that peculiar characteristics of the σ bands give rise to nonadiabatic and anharmonic effects which break the conventional Migdal-Eliashberg framework. Both these features are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the σ bands. In this context we discuss how the nonadiabatic theory leads to a coherent interpretation of the superconducting properties of MgB 2 without invoking very large couplings and it naturally explains the role of the disorder on T c . It also leads to various specific predictions for the properties of MgB 2 and for the material optimization of these type of compounds. Anharmonicity is also investigated by means of LDA calculations. We find that the anharmonic character of the E2g phonon is essentially driven by the small Fermi energy of the σ holes. We present a simple analytic model which allows us to understand in microscopic terms the role of the small Fermi energy and of the electronic structure. The relation between anharmonicity and nonadiabaticity is pointed out and discussed in relation to various materials.

The origin of phonon anharmonicity in MgB2 and related compounds

The recent discovery of a superconducting transition at 39 K in MgB2—made of alternating Mg and graphene-like B planes—has raised great interest, for both its technological and theoretical implications. It was clear since the very beginning that the properties of this material are related to an anomalous coupling between the charge carriers in the σ bands—due to in-plane bonds between Boron atoms—and the phonon mode (E2g) which involves in-plane vibrations of the B ions. Theoretical studies have thus been focused on the search for possible anomalies in the e–ph coupling: one of the first results was the discovery that the E2g phonon is highly anharmonic, but the connection between anharmonicity and Tc in this material is still a controversial point. We first present a detailed first-principles study of the E2g phonon anharmonicity in MgB2 and analogous compounds which are not superconducting, AlB2 and graphite, and in a hypothetical hole-doped graphite (C2+2); we then introduce an analytical model which allows us to relate the onset of anharmonicity with the small Fermi energy of the carriers in σ bands. Our study suggests a possible relation between anharmonicity and non-adiabaticity; non-adiabatic effects, which can lead to a sensible increase of Tc with respect to values predicted by conventional theory, become in fact relevant when phonon frequencies are comparable to electronic energy scales.

Spin susceptibility in small Fermi energy systems: effects of nonmagnetic impurities

In small Fermi energy metals, disorder can deeply modify superconducting state properties leading to a strong suppression of the critical temperature $T_c$. In this paper, we show that also normal state properties can be seriously influenced by disorder when the Fermi energy $E_{\rm F}$ is sufficiently small. We calculate the normal state spin susceptibility $\chi$ for a narrow band electron-phonon coupled metal as a function of the non-magnetic impurity scattering rate $\gamma_{\rm imp}$. We find that as soon as $\gamma_{\rm imp}$ is comparable to $E_{\rm F}$, $\chi$ is strongly reduced with respect to its value in the clean limit. The effects of the electron-phonon interaction including the nonadiabatic corrections are discussed. Our results strongly suggest that the recent finding on irradiated MgB$_2$ samples can be naturally explained in terms of small $E_{\rm F}$ values associated with the $\sigma$-bands of the boron plane, sustaining therefore the hypothesis that MgB$_2$ is a nonadiabatic metal.

Small Fermi energy and phonon anharmonicity inMgB2and related compounds

The remarkable anharmonicity of the E_{2g} phonon in MgB_2 has been suggested in literature to play a primary role in its superconducting pairing. We investigate, by means of LDA calculations, the microscopic origin of such an anharmonicity in MgB_2, AlB_2, and in hole-doped graphite. We find that the anharmonic character of the E_{2g} phonon is essentially driven by the small Fermi energy of the sigma holes. We present a simple analytic model which allows us to understand in microscopic terms the role of the small Fermi energy and of the electronic structure. The relation between anharmonicity and nonadiabaticity is pointed out and discussed in relation to various materials.

Magnetic and thermal properties of nanoscale heavy-fermion particles

The heavy-fermion state in some rare-earth and actinide compounds arises from a hybridization of extended conduction states with strongly correlated localized f states. The properties of the heavy fermions are those of a Fermi liquid with small Fermi energy of the order of ${T}_{K}.$ In nanosized particles, however, the conduction states have discrete energy levels and the energy spacing leads to an additional energy scale that competes with the Kondo temperature. A small heavy-fermion particle is considered, described by the Anderson model in the $U\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, so that only two electronic configurations---namely, ${f}^{0}$ and ${f}^{1}$---are allowed. A mean-field approximation with one slave boson per f site is used to study the susceptibility, the entropy, and the specific heat at low temperatures. All quantities increase rapidly with T as a consequence of exponential activations due to the discreteness of the energy spectrum until the heavy-electron state is formed. The possibility of ferromagnetic order is investigated using the formulation of Kotliar and Ruckenstein in terms of three auxiliary bosons per site. The mean-field approximation yields several possible magnetic phases for the ground state as a function of the f-level position. In the strongly mixed-valent regime the transition from the paramagnetic to the ferromagnetic phase is signaled as a function of temperature by a diverging susceptibility. It is concluded that the thermal and magnetic properties of very small heavy-fermion particles are quite different from those of bulk heavy-fermion material.

Kondo effect in a nanosized particle

A magnetic impurity embedded into a metal is spin compensated into a spin singlet via the Kondo effect. The low-temperature thermodynamic properties are Fermi-liquid-like, with a small Fermi energy of the order of the Kondo temperature. In nanoscale particles, however, the conduction states have discrete energy levels and the energy spacing leads to an additional energy scale that competes with ${T}_{K}.$ We consider a small metallic sphere with a spin-$\frac{1}{2}$ impurity at its center, interacting with the metallic states via a contact Kondo exchange potential. Hence only s states couple to the impurity. For equally spaced energy levels in the host, the problem is reduced to the Bethe ansatz solution of the Kondo model in a finite box. All energy levels are obtained as a function of the Kondo coupling for three and five s states interacting with the impurity. The specific heat and the susceptibility are exponentially activated at low T due to the discreteness of the energy spectrum, until a Kondo-like Fermi-liquid state is formed at intermediate temperatures. For larger systems we obtain the equations governing the ground state and lowest nonmagnetic and magnetic excitations, which determine the leading low-T activation energies. The model also represents a quantum dot in the Coulomb blockade regime as a side branch to a short quantum wire.

Nonadiabatic channels in the superconducting pairing of fullerides

We show the intrinsic inconsistency of the conventional phonon mediated theory of superconductivity in relation to the observed properties of Rb3C60. The recent, highly accurate measurement of the carbon isotope coefficient alpha(C) = 0.21, together with the high value of T(c) (30 K) and the very small Fermi energy E(F) (0.25 eV), unavoidably implies the opening of nonadiabatic channels in the superconducting pairing. We estimate these effects and show that they are actually the key elements for the high value of T(c) in these materials compared to the very low values of graphite intercalation compounds.

In-plane resistivity and an explanation for the characteristicT*in high-Tccuprates

We offer an explanation for the observed crossover temperature ${T}^{*}$ in in-plane resistivity ${\ensuremath{\rho}}_{\mathrm{ab}}$ of biplanar high-${T}_{c}$ cuprates. The key to our picture is the existence of nondegenerate and degenerate carriers possessing different quasiparticle relaxation rates. In the underdoped regime the change of slope $d{\ensuremath{\rho}}_{\mathrm{ab}}/dT$ at ${T}^{*}$ results from the thermal activation of nondegenerate carriers. In the overdoped regime, the nondegenerate carriers tend to become degenerate and a second small Fermi energy emerges, resulting in a change to ${T}^{2}$ behavior in ${\ensuremath{\rho}}_{\mathrm{ab}}$ at low T. We compare our results with data on several compounds. We also find an approximate scaling in conductivity.

Spin-polarized quantum transport and magnetic field-dependent carrier density in magnetic two-dimensional electron gases

Low-temperature magneto-transport and magneto-photoluminescence measurements are reported in magnetic two-dimensional electron gas samples formed by modulation doping shallow (Zn,Cd,Mn)Se single quantum wells. The small Fermi energy (∼1–2 meV) and large exchange-induced spin splitting (∼10 meV) results in a completely spin-polarized electron gas at filling factors as high as ν=12. Further, the spin splitting significantly perturbs the confinement potential, resulting in a magnetic field-dependent carrier density.