Small Fermi Energy Research Articles

Strongly suppressed diffuse scattering in periodic graphene metamaterials.

As an emerging two-dimensional material, graphene offers an alternative material platform for exploring new metamaterial phenomena and device functionalities. In this work, we examine diffuse scattering properties in graphene metamaterials. We take periodic graphene nanoribbons as a representative example and show that diffuse reflection in graphene metamaterials as dominated by diffraction orders is restricted to wavelengths less than that of first-order Rayleigh anomaly, and is enhanced by plasmonic resonances in graphene nanoribbons, as similar to metamaterials made of noble metals. However, the overall magnitude of diffuse reflection in graphene metamaterial is less than 10-2 due to the large period to nanoribbon size ratio and ultra-thin thickness of the graphene sheet, which suppress the grating effect from the structural periodicity. Our numerical results indicate that, in contrast to the cases of metallic metamaterials, diffuse scattering plays a negligible role in spectral characterization of graphene metamaterials in cases with large resonance wavelength to graphene feature size ratio, which corresponds to typical chemical vapor deposition (CVD)-grown graphene with relatively small Fermi energy. These results shed light on fundamental properties of graphene nanostructures and are helpful in designing graphene metamaterials for applications in infrared sensing, camouflaging, and photodetection, etc.

Polarons in spinless metals—a variational solution

We propose a simple variational solution for calculating one-particle spectral functions in lattice models of spinless metals with strong electron-phonon coupling. It is based on a generalization of the Momentum Average variational approximation for single polarons, combined with the assumption that the other fermions in the system are locked into an inert Fermi sea. We expect the method to be accurate for fermion addition spectral functions in metals with a small Fermi energy (nearly empty band), and for fermion removal spectral functions in metals with a large Fermi energy (nearly full band), provided that the characteristic phonon frequency is not too small. Both these regions are far from the region where the Migdal theorem holds, thus our results offer new insights into polaronic behavior in a largely unexplored part of the parameter space. Here, we show results for the Holstein coupling in one-dimension and present ways to gauge their accuracy, but ultimately this will need to be verified against numerical calculations. This variational method can be extended straightforwardly to higher dimensions and other forms of electron-phonon coupling.

Electron–phonon coupling in lightly [formula omitted]-doped 1T monolayers of PdSTe and PdSeTe: A rigid band approximation approach

In this paper, we present a preliminary study to determine the electron–phonon (el–ph) coupling in Janus 1T monolayered PdSTe and PdSeTe within the rigid band approximation (RBA). Under the assumption that both electronic band structures and phonon dispersions remain intact, or suffer slight changes at most, the Fermi energy is manually shifted towards the conduction bands. Without spin–orbit coupling (SOC), these structures are predicted to be semiconductors with electronic bandgaps of 0.33 eV for PdSTe and 0.34 eV for PdSeTe and with an insignificant electron–phonon coupling. We find that minimal small Fermi energy shifts of the order of 35 meV and 65 meV applied to 1T PdSTe and PdSeTe respectively, are sufficient to produce non-zero values of λ in both systems. These shifts could physically correspond to small electron doping of the materials, not exceeding 4%. Our calculations give that λ=1.77 and λ=0.5 for PdSTe and PdSeTe respectively. The corresponding lowest superconducting temperatures (Tc) register 0.28 K for PdSeTe and 28.19 K for PdSTe. We also demonstrate that the longitudinal optical and acoustical phonon modes may play a key role in the process of superconductivity of the doped materials. The above temperature of PdSTe is larger than those for 2D borophene, stanene, phosophorene and arsenene indicating that, in principle if the right dopant is found, lightly n-doped PdSTe could be promising in the area of 2D superconductors.

Phonon-mediated superconductivity in bismuthates by nonadiabatic pairing

In the present paper, the impact of small Fermi energy on the selected parameters of the superconducting state in Ba$_{1-x}$K$_{x}$BiO$_{3}$ (BKBO) is studied at $x \in (0.3, 0.4, 0.5)$. This is done by employing the adiabatic and non-adiabatic Eliashberg equations in context of the available experimental data. It is found that the retardation, strong-coupling and the non-adiabatic effects notably influence superconducting phase in BKBO. In particular, the electron-electron interaction, approximated here by the Coulomb pseudopotential, is argued to be reduced by the non-adiabatic effects that supplement retardation and allow for the phonon-mediated superconductivity. These findings are reinforced by further analysis of the isotope effect showing reduction of the isotope coefficient with respect to the canonical Bardeen-Cooper-Schrieffer (BCS) level, as caused by the interplay of all effects mentioned above. Although physics behind the isotope effect appears to be complex, its resulting behavior comply with the scenario for the conventional superconductors. In summary, obtained results confirm recent theoretical and experimental studies that suggest phonon-mediated mechanism of superconductivity in BKBO. However, they also point out that this phase cannot be properly described with the BCS theory due to the existence of somewhat unusual effects.

Exotic Superconducting States in FeSe-based Materials

High-temperature superconductivity and a wide variety of exotic superconducting states discovered in FeSe-based materials have been at the frontier of research on condensed matter physics over the past decade. Unique properties originating from the multiband electronic structure, strongly orbital-dependent phenomena, extremely small Fermi energy, electronic nematicity, and topological aspects give rise to many distinct and fascinating superconducting states. Here, we provide an overview of our current understanding of the superconductivity of {\it bulk} FeSe-based materials, focusing on FeSe and the isovalent substituted FeSe$_{1-x}$S$_{x}$ and FeSe$_{1-x}$Te$_{x}$. We discuss the highly nontrivial superconducting properties in FeSe, including extremely anisotropic pairing states, crossover phenomena from Bardeen--Cooper--Schrieffer (BCS) to Bose--Einstein condensation (BEC) states, a novel field-induced superconducting phase, and broken time-reversal symmetry. We also discuss the evolution of the superconducting gap function with sulfur and tellurium doping, paying particular attention to the impact of quantum critical nematic fluctuations and the topological superconductivity. FeSe-based materials provide an excellent playground to study various exotic superconducting states.

Emergence of a non-Fowler-Nordheim-type behavior for a general planar tunneling barrier

In this work we investigate a generalized tunneling barrier for planar emitters at zero-temperature. We present the evidence of the emergence of a non-Fowler-Nordheim-type general behavior for the field emission current density in the case that the Fermi energy (μ) is comparable with or smaller that the decay width (dF). Therefore, for some non-metals or materials that have very small Fermi energy the standard Fowler-Nordheim-type theory may require a correction. In the opposite regime, i.e., for μ much larger that dF, we confirm that the conventional theory is suitable for metals.

Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe.

We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35T applied parallel to the ab plane. At low temperatures, the upper critical field μ_{0}H_{c2}^{ab} shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at μ_{0}H^{*}≈24 T well below μ_{0}H_{c2}^{ab}, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the high-field phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe.

Charge state switching of the divacancy defect in 4H -SiC

Optical charge state switching was previously observed in photoluminescence experiments for the divacancy defect in $4H$-SiC. The participating dark charge state could not be identified with certainty. We use constrained density-functional theory to investigate the mechanism of charge state conversion from the bright neutral charge state of the divacancy defect to the positive and negative charge states including corresponding recovery of the neutral charge state. While we can confirm that the positive charge state is dark, we do not find evidence that the negative charge state is dark. We compute similar absorption energies required for conversion of the neutral defect to both charge states. However, the formation of the positive charge state requires a series of excitations involving a 2-photon excitation, while the creation of the negative charge state is achieved through a single 2-photon process. Calculated absorption energies for the recovery of the neutral defect from the positive charge state fit the experimental value better than those from the negative charge state. Defect formation energies as a function of the Fermi energy show a very small Fermi energy range in which the negative charge state is most stable, while the positive charge state exhibits a wide stability range. Overall, our computational results give more support to the identification of the dark charge state as the positive over the negative charge state in the mechanism of optical charge state switching.

Anisotropic Zeeman Splitting in YbNi4P2

The electronic structure of heavy-fermion materials is highly renormalised at low temperatures with localised moments contributing to the electronic excitation spectrum via the Kondo effect. Thus, heavy-fermion materials are very susceptible to Lifshitz transitions due to the small effective Fermi energy arising on parts of the renormalised Fermi surface. Here, we study Lifshitz transitions that have been discovered in YbNi_44P_22 in high magnetic fields. We measure the angular dependence of the critical fields necessary to induce a number of Lifshitz transitions and find it to follow a simple Zeeman-shift model with anisotropic g-factor. This highlights the coherent nature of the heavy quasiparticles forming a renormalised Fermi surface. We extract information on the orientation of the Fermi surface parts giving rise to the Lifshitz transitions and we determine the anisotropy of the effective gg-factor to be \eta \approx 3.8η≈3.8 in good agreement with the crystal field scheme of YbNi_44P_22.

Shubnikov-de Haas oscillations of massive Dirac fermions in a Dirac antiferromagnet SrMnSb2

We investigate the physical properties of massive Dirac fermions in SrMnSb2 using transport, specific heat, electronic structure calculations, and Shubnikov-de Haas (SdH) oscillations. SrMnSb2 is a candidate Dirac antiferromagnet, consisting of the MnSb layers and the distorted square net of Sb atoms with a zigzag chain structure. This structural distortion leads to gap opening at the band crossing point found in the square lattice of the sister compound SrMnBi2 but leaves another Dirac band crossing near the Brillouin zone boundary. The small 2D Fermi surface with a light electron mass and a small Fermi energy is confirmed by the large resistivity anisotropy, the large Seebeck coefficient, and also the angle and temperature dependent SdH oscillations. The Berry phase obtained from the SdH oscillations is trivial, in contrast to the case of SrMnBi2. The relatively large spin orbit coupling gap and the small Fermi energy in SrMnSb2 is found to be essential to understand this contrasting behavior of the massive Dirac fermions as compared to SrMnBi2. Our observations demonstrate that the Berry phase of the mobile electrons in SrMnSb2 is sensitive to the Fermi level change and can be tuned by doping or deficiency.

Ultrathin Bismuth Film on High-Temperature Cuprate Superconductor Bi2Sr2CaCu2O8+δ as a Candidate of a Topological Superconductor.

One of the key challenges in condensed-matter physics is to establish a topological superconductor that hosts exotic Majorana fermions. Although various heterostructures consisting of conventional BCS (Bardeen-Cooper-Schrieffer) superconductors as well as doped topological insulators were intensively investigated, no conclusive evidence for Majorana fermions has been provided. This is mainly because of their very low superconducting transition temperatures ( Tc) and small superconducting-gap magnitude. Here, we report a possible realization of topological superconductivity at very high temperatures in a hybrid of Bi(110) ultrathin film and copper oxide superconductor Bi2Sr2CaCu2O8+δ (Bi2212). Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we found that three-bilayer-thick Bi(110) on Bi2212 exhibits a proximity-effect-induced s-wave energy gap as large as 7.5 meV which persists up to Tc of Bi2212 (85 K). The small Fermi energy and strong spin-orbit coupling of Bi(110), together with the large pairing gap and high Tc, make this system a prime candidate for exploring stable Majorana fermions at very high temperatures.

Combination Law for Drude–Sommerfeld's Electron Damping in Multilayer Thin Metal Films

A combination rule for electron damping in multilayer thin metal films is derived from a mean‐field picture and is applied to optical experimental data. The overall coefficient obeys a parallel law of pure materials damping, , chemical specificity being involved by averaging over densities of low energy states in the free electron model. Geometric and static electromagnetic features of single layers couple via small Fermi's energy fractions (αi). An application is developed for thin Cu/Au and Au/Ag films, showing an apparently irregular damping trend in the film thickness (di = 2.5–7.5 nm). The inferred ⟨γ⟩'s agree in both cases with our data when |αi| = 10−2 ÷ 10−3 linearly increases with decreasing di, suggesting a coupling phenomenology that can bring new insights in the optics and plasmonics of nanostructures.

Published Tunneling Results of Binnig et al Interpreted as Related to Surface Superconductivity in SrTiO3

In 1980, Binnig et al. reported tunneling measurements on Nb-doped SrTiO3, and interpreted their results as indicating two-band superconductivity in the bulk of SrTiO3. However, (1) effective masses determined from tunneling results in the normal state by Sroubek in 1969 and 1970 are much smaller than those determined by most other methods. The much smaller masses were attributed to properties of a surface layer by the present author in 1971. (2) The only other reports of two-band superconductivity in bulk SrTiO3 can be used to infer much smaller values for the band separations than found by Binnig et al. In this paper, we give an alternative explanation of the results of Binnig et al. in terms of superconductivity in a surface layer. We obtain fair fits to the band gaps versus Fermi energy for the two bands in the three samples where two surface subbands are occupied and to the temperature dependence of the gaps in one crystal, using a model with three adjustable interaction parameters, an adjustable energy for the phonons which dominate the pairing, and an adjustable ratio of the mean-field T c to the actual T c . We show results for a combined fit to the low-temperature band gaps and to the T-dependence in one crystal. The phonon energy which gives the best fit is 21 meV. This is probably an appropriate average over the three longitudinal polar modes and acoustic modes in the material. A large value of about two is found for the ratio T c m f /T c , and we conjecture that this arises because a band with a small Fermi energy, not seen in the tunneling results, plays a part in increasing T c m f /T c .

Effects of heavy-ion irradiation on FeSe

We report the effects of heavy-ion irradiation on FeSe single crystals by irradiating Uranium up to a dose equivalent matching field of $B_\phi$ = 16 T. Almost continuous columnar defects along the $c$-axis with a diameter $\sim$10 nm are confirmed by high-resolution transmission electron microscopy. $T_c$ is found to be suppressed by introducing columnar defects at a rate of d$T_c$/d$B_\phi$ $\sim$ -0.29KT$^{-1}$, which is much larger than those observed in iron pnictides. This unexpected large suppression of $T_c$ in FeSe is discussed in relation to the large diameter of the columnar defects as well as its unique band structure with a remarkably small Fermi energy. The critical current density is first dramatically enhanced with irradiation reaching a value over $\sim$2$\times$10$^5$ A/cm$^2$ ($\sim$5 times larger than that of the pristine sample) at 2 K (self-field) with $B_\phi$ = 2 T, then gradually suppressed with increasing $B_\phi$. The $\delta$$l$-pinning associated with charge-carrier mean free path fluctuations, and the $\delta$$T_c$-pinning associated with spatial fluctuations of the transition temperature are found to coexist in the pristine FeSe, while the irradiation increases the contribution from $\delta$$l$-pinning, and makes it dominant over $B_\phi$ = 4 T.

Spatially inhomogeneous electron state deep in the extreme quantum limit of strontium titanate.

When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the extreme quantum limit (EQL) and becomes susceptible to a number of instabilities. Bringing a three-dimensional electronic system deeply into the EQL can be difficult however, since it requires a small Fermi energy, large magnetic field, and low disorder. Here we present an experimental study of the EQL in lightly-doped single crystals of strontium titanate. Our experiments probe deeply into the regime where theory has long predicted an interaction-driven charge density wave or Wigner crystal state. A number of interesting features arise in the transport in this regime, including a striking re-entrant nonlinearity in the current–voltage characteristics. We discuss these features in the context of possible correlated electron states, and present an alternative picture based on magnetic-field induced puddling of electrons.

Band structure reconstruction across nematic order in high quality FeSe single crystal as revealed by optical spectroscopy study

We perform an in-plane optical spectroscopy measurement on high quality FeSe single crystals grown by a vapor transport technique. Below the structural transition at Ts ∽90K, the reflectivity spectrum clearly shows a gradual suppression around 400cm−1 and the conductivity spectrum shows a peak at higher frequency. The energy scale of this gap-like feature is comparable to the width of the band splitting observed by ARPES. The low-frequency conductivity consists of two Drude components and the overall plasma frequency is smaller than that of the FeAs based compounds, suggesting a lower carrier density or stronger correlation effect. The plasma frequency becomes even smaller below Ts which agrees with the very small Fermi energy estimated by other experiments. Similar to iron pnictides, a clear temperature-induced spectral weight transfer is observed for FeSe, being indicative of strong correlation effect.

Superconductivity versus bound-state formation in a two-band superconductor with small Fermi energy: Applications to Fe pnictides/chalcogenides and dopedSrTiO3

We analyze the interplay between superconductivity and the formation of bound pairs of fermions (BCS-BEC crossover) in 2D models of interacting fermions with small Fermi energy EF and weak attractive interaction, which extends to energies well above EF. The 2D case is special because one has to distinguish between bound state formation and superconductivity already at weak coupling. We briefly review the situation in the one-band model and then consider two different two-band models: the one with a hole and an electron band, and the one with two electron bands. In each case we obtain the bound state energy 2 E0 for two fermions in a vacuum and solve the set of coupled equations for the pairing gaps and the chemical potentials to obtain the onset temperature of the pairing, Tins and the quasiparticle dispersion. We then compute the superfluid stiffness and obtain the actual Tc. We show that, at EF >> E0 the behavior of both two-band models is BCS-like in the sense that Tc almost coincides with Tins and both are much smaller than EF. At EF < E0, the two models behave differently: in the model with two electron bands, Tins ~E0/log(E0/EF) and Tc ~EF << Tins. In between Tins and Tc the system displays preformed pair behavior. In the model with a hole and an electron band, Tins ~ Tc and both remain finite at EF=0 The preformed pair behavior still exists in this model because Tc is numerically smaller than Tins. For both models we re-express Tins in terms of the fully renormalized two-particle scattering amplitude by extending to two-band case the method pioneered by Gorkov and Melik-Barkhudarov back in 1961. We apply our results to to Nb-doped SrTiO3 and to Fe-pnictides and Fe-chalcogenides, particularly to FeSe, in which superconducting gap is comparable to the Fermi energy.

Non-Fermi-liquid scattering rates and anomalous band dispersion in ferropnictides

Angle-resolved photoemission spectroscopy (ARPES) is used to study the band dispersion and the quasiparticle scattering rates in two ferropnictides systems. Our ARPES results show linear-in-energy dependent scattering rates which are constant in a wide range of control parameter and which depend on the orbital character of the bands. We demonstrate that the linear energy dependence gives rise to weakly dispersing band with a strong mass enhancement when the band maximum crosses the chemical potential. In the superconducting phase the related small effective Fermi energy favors a Bardeen-Cooper-Schrieffer (BCS)\,\cite{Bardeen1957}-Bose-Einstein (BE)\,\cite{Bose1924} crossover state.

Electronic structure of a superconducting topological insulator Sr-doped Bi2Se3

Using high-resolution angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy, the atomic and low energy electronic structure of the Sr-doped superconducting topological insulators (SrxBi2Se3) was studied. Scanning tunneling microscopy shows that most of the Sr atoms are not in the van der Waals gap. After Sr doping, the Fermi level was found to move further upwards when compared with the parent compound Bi2Se3, which is consistent with the low carrier density in this system. The topological surface state was clearly observed, and the position of the Dirac point was determined in all doped samples. The surface state is well separated from the bulk conduction bands in the momentum space. The persistence of separated topological surface state combined with small Fermi energy makes this superconducting material a very promising candidate for the time reversal invariant topological superconductor.

On mobility of electrons in a shallow Fermi sea over a rough seafloor

Several doped semiconductors, in contrast to heavily-doped silicon and germanium, host extremely mobile carriers, which give rise to quantum oscillations detectable in relatively low magnetic fields. The small Fermi energy in these dilute metals quantifies the depth of the Fermi sea. When the carrier density exceeds a threshold, accessible thanks to the long Bohr radius of the parent insulator, the local seafloor is carved by distant dopants. In such conditions, with a random distribution of dopants, the probability of finding an island or a trench depends on on the effective Bohr radius, and the carrier density, n. This picture yields an expression for electron mobility with a random distribution of dopants: , in reasonable agreement with the magnitude and concentration dependence of the low-temperature mobility in three dilute metals whose insulating parents are a wide-gap (SrTiO3), a narrow-gap (PbTe) and a ‘zero’-gap (TlBiSSe) semiconductor.