Bare Electron Mass Research Articles

Decoupling of the many-body effects from the electron mass in GaAs by means of reduced dimensionality

Determining the (bare) electron mass ${m}_{0}$ in crystals is often hindered by many-body effects since Fermi-liquid physics renormalizes the band mass, making the observed effective mass ${m}^{*}$ depend on density. Here, we use a one-dimensional (1D) geometry to amplify the effect of interactions, forcing the electrons to form a nonlinear Luttinger liquid with separate holon and spinon bands, therefore separating the interaction effects from ${m}_{0}$. Measuring the spectral function of gated quantum wires formed in GaAs by means of magnetotunnelling spectroscopy and interpreting them using the 1D Fermi-Hubbard model, we obtain ${m}_{0}=(0.0525\ifmmode\pm\else\textpm\fi{}0.0015){m}_{\text{e}}$ in this material, where ${m}_{\text{e}}$ is the free-electron mass. By varying the density in the wires, we change the interaction parameter ${r}_{\text{s}}$ in the range from $\ensuremath{\sim}1$--4 and show that ${m}_{0}$ remains constant. The determined value of ${m}_{0}$ is $\ensuremath{\sim}22%$ lighter than observed in GaAs in geometries of higher dimensionality $D$ ($D>1$), consistent with the quasiparticle picture of a Fermi liquid that makes electrons heavier in the presence of interactions.

Topological Dirac semimetal BaAuSb

Dirac semimetals feature Dirac cones with topologically nontrivial states in the bulk that are protected by crystalline symmetries. They attract considerable attention due to rich quantum states and properties of interest, such as high Fermi velocities, mobility, and small effective masses. Here, we show that a ternary intermetallic BaAuSb crystal hosts both trivial and nontrivial topological Dirac states in the bulk. The nontrivial Fermi-surface pocket at the Brillouin zone center is characterized with only a few hundredths of a bare electron mass and with very high mobility. All parts of the Fermi surface detected by quantum oscillations, topologically trivial or nontrivial, have carriers with unusually high Fermi velocities and small masses. These conducting states may be coupled with magnetic moments in materials where Ba is replaced by magnetic rare-earth atoms.

Evolution of the cyclotron mass with doping in La2−xSrxCuO4

The recent observation of cyclotron resonance in optimally-doped La$_{2-x}$Sr$_x$CuO$_4$ using time-domain THz spectroscopy in high magnetic field has given new possibilities for the study of cuprate superconductors. One can measure the cyclotron mass in more disordered cuprates possesing short scattering times therefore expanding the study to materials and dopings in which quantum oscillations have not been observed. Here we present the measurement of the carrier mass of the hole doped cuprate La$_{2-x}$Sr$_x$CuO$_4$ across a a range of dopings spanning the slightly underdoped ($x=0.13$) to highly overdoped ($x=0.26$), near to the termination of the superconducting dome. These results reveal a systematic increase of $m_c$ with doping, up to values greater than thirteen times the bare electron mass. This is in contrast with those masses extracted from the heat capacity, which show a peak near the pseudogap critical point $p^*$ and/or Lifshitz transition. The cyclotron frequency is linear in field up to 31 T for all dopings giving no evidence for field induced Fermi surface reconstructions. The cyclotron mass is found to be positive for all dopings, but with a magnitude systematically below the heat capacity mass for under and optimally doped samples, while exceeding it for overdoped samples. Among other aspects, these results are surprising as photoemission reveals a Lifshitz transition in the middle of our doping range and the sign of the cyclotron mass determined from a finite frequency resonance is -- in conventional theories -- a {\it topological quantity} only sensitive to whether or not the Fermi surface is closed around holes or electrons. We see no sign of a divergence of the mass near $p^*$ nor near the Lifshitz transition, showing that any singularity -- if it exists -- is not strong enough to affect the cyclotron mass.

Fermi Surface and Mass Renormalization in the Iron-Based Superconductor YFe_{2}Ge_{2}.

Interaction-enhanced carrier masses are central to the phenomenology of iron-based superconductors. Quantum oscillation measurements in the new unconventional superconductor YFe_{2}Ge_{2} resolve all four Fermi surface pockets expected from band structure calculations, which predict an electron pocket in the Brillouin zone corner and three hole pockets enveloping the centers of the top and bottom of the Brillouin zone. Carrier masses reach up to 20 times the bare electron mass and are among the highest ever observed in any iron-based material, accounting for the enhanced heat capacity Sommerfeld coefficient ≃100 mJ/mol K^{2}. Mass renormalization is uniform across reciprocal space, suggesting predominantly local correlations, as in the Hund's metal scenario.

Breakdown of the equivalence between gravitational mass and energy due to quantum effects

We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in the semiclassical variant of general relativity, where the gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom — a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is the inequivalence between passive gravitational mass and energy at the microscopic level. Indeed, the quantum measurement of gravitational mass can give a result which is different from the expected one, [Formula: see text], where the electron is initially in its ground state; [Formula: see text] is the bare electron mass. The second effect is that the expectation values of both the passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of the energy. The most spectacular effects are the inequivalence of the passive and active gravitational masses and the energy at the macroscopic level for an ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by Einstein’s famous equation, [Formula: see text]. In this paper, we also improve several drawbacks of the original pioneering works.

Characterization of the superconducting phase in tellurium hydride at high pressure

At present, hydrogen-based compounds constitute one of the most promising classes of materials for applications as phonon-mediated high-temperature superconductors. Herein, the behavior of the superconducting phase in tellurium hydride (HTe) at high pressure (p = 300 GPa) is analyzed in detail, by using the isotropic Migdal–Eliashberg equations. The chosen pressure conditions are considered here as a case study which corresponds to the highest critical temperature value [Formula: see text] in the analyzed material, as determined within recent density functional theory simulations. It is found that the Migdal–Eliashberg formalism, which constitutes a strong-coupling generalization of the Bardeen–Cooper–Schrieffer (BCS) theory, predicts that the critical temperature value ([Formula: see text] K) is higher than previous estimates of the McMillan formula. Further investigations show that the characteristic dimensionless ratios for the thermodynamic critical field, the specific heat for the superconducting state, and the superconducting band gap exceed the limits of the BCS theory. In this context, also the effective electron mass is not equal to the bare electron mass as provided by the BCS theory. On the basis of these findings it is predicted that the strong-coupling and retardation effects play pivotal role in the superconducting phase of HTe at 300 GPa, in agreement with similar theoretical estimates for the sibling hydrogen and hydrogen-based compounds. Hence, it is suggested that the superconducting state in HTe cannot be properly described within the mean-field picture of the BCS theory.

Anomalous transport properties of Re3Ge7

Single crystals of intermetallic Re$_3$Ge$_7$ were grown and characterized by measuring magnetization, electrical resistivity, Hall coefficient, and specific heat. Magnetization measurements show the material is weakly diamagnetic. A phase transition is indicated by a kink in magnetic susceptibility at $T_{c} = 58.5$K and is confirmed by a $\lambda$-like anomaly in specific heat. In zero-field, the temperature dependence of electrical resistivity $\rho(T)$ follows a typical metallic behavior above $T_c$ and sharply increases below $T_c$, showing a metal-to-insulator-like transition. When a magnetic field is applied, strong effects on the transport properties are observed. The temperature dependence of magnetoresistivity $\Delta\rho$ = $\rho (T, H)$ - $\rho (T, H=0)$ develops a maximum around 30 K, deviating from ordinary metallic behavior. Analysis of the Hall coefficient measurements indicates that the carrier density is 0.04 per formula unit at 300 K and drops by two orders of magnitude below $T_c$. The effective mass of charge carriers is inferred from the analysis of the Shubnikov-de Haas quantum oscillations to be close to the bare electron mass.

Moment of inertia of superconductors

We find that the bulk moment of inertia per unit volume of a metal becoming superconducting increases by the amount me/(πrc), with me the bare electron mass and rc=e2/mec2 the classical electron radius. This is because superfluid electrons acquire an intrinsic moment of inertia me(2λL)2, with λL the London penetration depth. As a consequence, we predict that when a rotating long cylinder becomes superconducting its angular velocity does not change, contrary to the prediction of conventional BCS-London theory that it will rotate faster. We explain the dynamics of magnetic field generation when a rotating normal metal becomes superconducting.

Detailed study of the Fermi surfaces of the type-II Dirac semimetallic candidates XTe2 ( X =Pd, Pt)

We present a detailed quantum oscillatory study on the Dirac type-II semimetallic candidates PdTe$_{2}$ and PtTe$_{2}$ \emph{via} the temperature and the angular dependence of the de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) effects. In high quality single crystals of both compounds, i.e. displaying carrier mobilities between $10^3$ and $10^4$ cm$^2$/Vs, we observed a large non-saturating magnetoresistivity (MR) which in PtTe$_2$ at a temperature $T = 1.3$ K, leads to an increase in the resistivity up to $5 \times 10^{4}$ % under a magnetic field $\mu_0 H = 62$ T. These high mobilities correlate with their light effective masses in the range of 0.04 to 1 bare electron mass according to our measurements. For PdTe$_{2}$ the experimentally determined Fermi surface cross-sectional areas show an excellent agreement with those resulting from band-structure calculations. Surprisingly, this is not the case for PtTe$_{2}$ whose agreement between calculations and experiments is relatively poor even when electronic correlations are included in the calculations. Therefore, our study provides a strong support for the existence of a Dirac type-II node in PdTe$_2$ and probably also for PtTe$_2$. Band structure calculations indicate that the topologically non-trivial bands of PtTe$_2$ do not cross the Fermi-level ($\varepsilon_F$). In contrast, for PdTe$_2$ the Dirac type-II cone does intersect $\varepsilon_F$, although our calculations also indicate that the associated cyclotron orbit on the Fermi surface is located in a distinct $k_z$ plane with respect to the one of the Dirac type-II node. Therefore it should yield a trivial Berry-phase.

Large effective mass and interaction-enhanced Zeeman splitting of K -valley electrons in MoSe2

We study the magnetotransport of high-mobility electrons in monolayer and bilayer MoSe$_2$, which show Shubnikov-de Haas (SdH) oscillations and quantum Hall states in high magnetic fields. An electron effective mass of 0.8$m_e$ is extracted from the SdH oscillations' temperature dependence; $m_e$ is the bare electron mass. At a fixed electron density the longitudinal resistance shows minima at filling factors (FFs) that are either predominantly odd, or predominantly even, with a parity that changes as the density is tuned. The SdH oscillations are insensitive to an in-plane magnetic field, consistent with an out-of-plane spin orientation of electrons at the $K$-point. We attribute the FFs parity transitions to an interaction enhancement of the Zeeman energy as the density is reduced, resulting in an increased Zeeman-to-cyclotron energy ratio.

Tunable Γ-K Valley Populations in Hole-Doped Trilayer WSe_{2}.

We present a combined experimental and theoretical study of valley populations in the valence bands of trilayer WSe_{2}. Shubnikov-de Haas oscillations show that trilayer holes populate two distinct subbands associated with the K and Γ valleys, with effective masses 0.5m_{e} and 1.2m_{e}, respectively; m_{e} is the bare electron mass. At a fixed total hole density, an applied transverse electric field transfers holes from Γ orbitals to K orbitals. We are able to explain this behavior in terms of the larger layer polarizability of the K orbital subband.

Renormalized Landau quasiparticle dispersion revealed by photoluminescence spectra from a two-dimensional Fermi liquid at the MgZnO/ZnO heterointerface

We analyze the low-temperature photoluminescence spectra from two-dimensional electron systems (2DESs) confined at ${\mathrm{Mg}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}\mathrm{O}$/ZnO heterojunctions as the electron density is decreased from $2.3\ifmmode\times\else\texttimes\fi{}{10}^{12}$ to $3.5\ifmmode\times\else\texttimes\fi{}{10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}2}$. The value of the quasiparticle optical density-of-states mass is directly extracted from the width of the 2DES photoluminescence band and is shown to renormalize and double from the value close to that of bulk ZnO material, $0.3{m}_{0}$ (${m}_{0}$ is the bare electron mass), to $0.6{m}_{0}$ due to electron-electron interactions as the interaction parameter ${r}_{s}$ increases from 2.4 to 6.5. The experimentally probed quasiparticle energies far exceed the limits of Landau's Fermi-liquid theory.

Partial hybridisation of electron-hole states in an InAs/GaSb double quantum well heterostructure

InAs/GaSb coupled quantum well heterostructures are important semiconductor systems with applications ranging from spintronics to photonics. Most recently, InAs/GaSb heterostructures have been identified as candidate two-dimensional topological insulators, predicted to exhibit helical edge conduction via fully spin-polarised carriers. We study an InAs/GaSb double quantum well heterostructure with an AlSb barrier to decouple partially the 2D electrons and holes, and find conduction consistent with a 2D hole gas, with an effective mass of 0.235 ± 0.005 m0, existing simultaneously with hybridised carriers with an effective mass of 0.070 ± 0.005 m0, where m0 is the bare electron mass.

Quasi-two-dimensional Fermi surfaces with localized f electrons in the layered heavy-fermion compound CePt2In7

We report measurements of the de Haas-van Alphen effect in the layered heavy-fermion compound CePt$_2$In$_7$ in high magnetic fields up to 35 T. Above an angle-dependent threshold field, we observed several de Haas-van Alphen frequencies originating from almost ideally two-dimensional Fermi surfaces. The frequencies are similar to those previously observed to develop only above a much higher field of 45 T, where a clear anomaly was detected and proposed to originate from a change in the electronic structure [M. M. Altarawneh et al., Phys. Rev. B 83, 081103 (2011)]. Our experimental results are compared with band structure calculations performed for both CePt$_2$In$_7$ and LaPt$_2$In$_7$, and the comparison suggests localized $f$ electrons in CePt$_2$In$_7$. This conclusion is further supported by comparing experimentally observed Fermi surfaces in CePt$_2$In$_7$ and PrPt$_2$In$_7$, which are found to be almost identical. The measured effective masses in CePt$_2$In$_7$ are only moderately enhanced above the bare electron mass $m_0$, from 2$m_0$ to 6$m_0$.

Thermodynamics of the CaLi2 Superconductor in the Vicinity of Structural Phase Transition

Eliashberg formalism is used to investigate the thermodynamic properties of the high-pressure superconducting phase of the CaLi2 compound. In particular, our calculations are conducted in the vicinity of the C2/c → P21/c pressure-induced structural phase transition. We show that, in the considered case, the value of the Coulomb pseudopotential is high and equals 0.26. Moreover, we give the analysis of the thermodynamic parameters such as the superconducting transition temperature (TC), the energy gap at the Fermi level (2Δ(0)), the thermodynamic critical field (HC), and the specific heat of superconducting (CS) and normal (CN) states. We emphasize that the characteristic dimensionless ratios RΔ ≡ 2Δ(0)/kBTC, RH ≡ TCCN(TC)/HC2(0), and RC ≡ ΔC(TC)/CN (TC), have values that are beyond the predictions of the BCS theory in the case of the considered material. In particular, RΔ = 3.85, RH = 0.161, and RC = 1.86. Furthermore, it is proved that the effective electron mass is high and equals 2.02me, where me denotes the bare electron mass.

Spectral-edge mode in interacting one-dimensional systems

A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles and between Bose particles (with and without spin) using Bethe-Ansatz techniques and find that the dispersions of the corresponding spectral edge modes are close to a parabola in all cases. Based on this emergent phenomenon we propose an empirical model of a free, non-relativistic particle with an effective mass identified at low energies as the bare electron mass renormalised by the dimensionless Luttinger parameter $K$ (or $K_\sigma$ for particles with spin). The relevance of the Luttinger parameters beyond the low energy limit provides a more robust method for extracting them experimentally using a much wide range of data from the bottom of the one-dimensional band to the Fermi energy. The empirical model of the spectral edge mode complements the mobile impurity model to give a description of the excitations in proximity of the edge at arbitrary momenta in terms of only the low energy parameters and the bare electron mass. Within such a framework, for example, exponents of the spectral function are expressed explicitly in terms of only a few Luttinger parameters.

Tunneling in Heavy-Fermion Junctions

In this paper I review recent theoretical and experimental advances in understanding of tunneling processes between normal metals and metals containing electrons which occupy partially filled f-orbitals. In heavy-fermion materials the effective mass of the quasiparticles far exceeds the bare electron mass due to strong hybridization between conduction and f-orbital states. Kondo lattices form a class of heavy-fermion systems in which an average occupation number of f-electron states is close to an integer. Therefore, the tunneling into a Kondo lattice necessarily involves co-tunneling process of a tip electron into an f-electron state of a Kondo lattice. This co-tunneling process is manifested in the Fano-lineshape of differential conductance as a function of an applied voltage, which has been routinely observed in recent experiments on various Kondo lattice systems. To illustrate these ideas, I discuss the problem of the tunneling junction when the single particle states in the tip are also a product of hybridization between conduction and f-states, i.e., tunneling between two heavy-fermion materials.

Thermodynamic evidence for valley-dependent density of states in bulk bismuth

Electron-like carriers in bismuth are described by the Dirac Hamiltonian, with a band mass becoming a thousandth of the bare electron mass along one crystalline axis. The existence of three anisotropic valleys offers electrons an additional degree of freedom, a subject of recent attention. Here, we map the Landau spectrum by angle-resolved magnetostriction, and quantify the carrier number in each valley: while the electron valleys keep identical spectra, they substantially differ in their density of states at the Fermi level. Thus, the electron fluid does not keep the rotational symmetry of the lattice at low temperature and high magnetic field, even in the absence of internal strain. This effect, reminiscent of the Coulomb pseudogap in localized electronic states, affects only electrons in the immediate vicinity of the Fermi level. It presents the most striking departure from the non-interacting picture of electrons in bulk bismuth.

Diameter-selective alignment of carbon nanotubes on Si(001) stepped surfaces.

We report total-energy electronic-structure calculations based on the density-functional theory that provide stable adsorption sites, structural characteristics, and energy bands of carbon nanotubes (CNTs) adsorbed on the Si(001) stepped surfaces. We choose (5,5), (9,9), and (13,13) armchair CNTs with the diameters of 6.8Å, 12.2Å, and 17.6Å, respectively, as representatives of CNTs and explore all the possible adsorption sites either on the terrace or at step edges. We find that the (9,9) CNT is most favorably adsorbed at the edge of the double-layer step DB along the ⟨110⟩ direction, whereas the (5,5) and (13,13) CNTs favor the terrace site where the CNTs are perpendicular to the Si dimer rows. This finding is indicative of the diameter-selective self-organized alignment of CNTs by exploiting the Si surface steps along the particular direction. We also find that the electronic structure of each CNT is modified upon adsorption depending on the adsorption site and the diameter of the CNTs. In particular, the (9,9) CNT at the most stable step edge site becomes semiconducting and the resultant valence and conduction bands exhibit nearly linear dispersion with the effective mass of 0.085 m0 (m0: bare electron mass), preserving the characteristics of the Dirac electrons. We also find that the flat bands appear near the Fermi level (EF) when the (13,13) CNT is adsorbed at the metastable DB step edge, inferring that spin polarization is possible for the CNT on the Si(001) stepped surface.

Superconductivity of calcium in phase VI

The properties of the superconducting state of calcium in phase VI were analyzed. By using the imaginary axis Eliashberg equations it has been shown, that the Coulomb pseudopotential reaches the high value equal to 0.215. In the considered case, the critical temperature is not properly described by the Allen–Dynes formula and it should be calculated with an use of the modified expression. In the paper the exact solutions of the Eliashberg equations on the real axis were also obtained. On this basis it was stated, that the effective potential of the electron–electron interaction is attractive for the frequencies lower or equal to the maximum phonon frequency. Then, the dimensionless parameter 2 Δ(0)/ k B T C = 4.10 was calculated. In the last step it has been proven, that the ratio of the electron effective mass to the bare electron mass is high and reaches its maximum equal to 2.36 for the critical temperature.