Fermi Surface Cross Research Articles

Formation and Tuning of 2D Electron Gas in Perovskite Heterostructures

Oxide interfaces provide very intriguing phenomena, in particular a 2D electron gas (2DEG) emerging between robustly insulating perovskites. The 2DEG was detected in 2004 beneath polar LaAlO3 (LAO) epitaxially grown on TiO2‐terminated SrTiO3 (001) (STO). Herein, recent first‐principles studies of 2DEGs are reviewed. Using a Green function method, the family of the polar/nonpolar (001) interfaces: LAO/STO, LaFeO3/STO, and STO/KTaO3 is computed. In the context of 2DEG, one of two insulating perovskites, at least, must be polar. The effect of a polar/polar interface is modeled for LAO/KTaO3(001) and also for the (110) and (111) interfaces of LAO/STO. Starting from the defectless superlattice with its two differently terminated interfaces, we demonstrate that the 2DEG and 2D hole gas appear there, respectively, due to the presence of excessive electrons or holes. 2DEG is evaluated by its layer‐resolved density profile along [001], as well as the Fermi surface cross sections and effective masses, which are directly related to the transport properties. The effects of intermixed cations, their vacancies, and oxygen vacancies at each interface of LAO/STO are calculated. Finally, we show how to tune reversibly the 2DEG by changing the electronic balance at the LAO surface that mimics the effect of ionic liquid gating.

Deviation from Fermi-liquid transport behavior in the vicinity of a Van Hove singularity

Recent experiments revealed non-Fermi-liquid resistivity in the unconventional superconductor Sr$_{2}$RuO$_{4}$ when strain pushes one of the Fermi surfaces close to a van Hove singularity. The origin of this behavior and whether it can be understood from a picture of well defined quasiparticles is unclear. We employ a Boltzmann transport analysis beyond the single relaxation-time approximation based on a single band which undergoes a Lifshitz transition, where the Fermi surface crosses a van Hove singularity, either due to uni-axial or epitaxial strain. First analytically investigating impurity scattering, we clarify the role of the diverging density of states together with the locally flat band at the point of the Lifshitz transition. Additionally including electron-electron scattering numerically, we find good qualitative agreement with resistivity measurements on uni-axially strained Sr$_{2}$RuO$_{4}$, including the temperature scaling and the temperature dependence of the resistivity peak. Our results imply that even close to the Lifshitz transition, a description starting from well-defined quasiparticles holds. To test the validity of Boltzmann transport theory near a van Hove singularity, we provide further experimentally accessible parameters, such as thermal transport, the Seebeck coefficient, and Hall resistivity and compare different strain scenarios.

Accurate determination of the Fermi surface of tetragonal FeS via quantum oscillation measurements and quasiparticle self-consistent GW calculations

We perform de Haas-van Alphen measurements and quasiparticle self-consistent \textit{GW} (QS\textit{GW}) calculations on FeS. The calculated Fermi surface (FS) consists of two hole and two electron cylinders. We observe all the eight predicted FS cross sections experimentally. With momentum-independent band-energy adjustments of less than 0.1 eV, the maximum deviation between the calculated and observed cross sections is less than 0.2\% of the Brillouin zone area for $B \parallel c$. The carrier density is $\sim$0.5 carriers/Fe. The mass enhancements are nearly uniform across the FS cylinders and moderate, $\sim$2. The absence of a third hole cylinder with $d_{xy}$ character is favorable for the formation of a nodal superconducting gap.

Impact of long-range disorder on the two-dimensional electron gas formation at a LaAlO3/SrTiO3 interface

A two-dimensional electron gas (2DEG) can be formed at an interface between two insulators such as ${\mathrm{LaAlO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$ without any additional doping. Nevertheless, structural imperfections or defects at the interface, which may arise during the growth process or be of another origin, can definitely affect 2DEG properties either increasing or reducing the 2DEG density. In this work, we study 2DEG formation at both perfect and imperfect interfaces of ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ heterostructures in the framework of the density functional theory. Using a first-principles Green function method within a coherent potential approximation, we investigate consistently the development of the 2DEG density starting from a defectless interface and introducing sequentially various kinds of long-range disorder such as cation intermixing and oxygen vacancies. Finally, we evaluate the 2DEG carrier density from the Fermi surface cross sections and effective masses of the carriers, which may be directly related to the multiple transport phenomena in the system.

Topological and trivial magnetic oscillations in nodal loop semimetals

Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is identified separating purely trivial oscillations, arising from the Landau levels of a normal two dimensional (2D) electron gas, to a phase where oscillations of topological and trivial origin coexist, originating from 2D massless Dirac and semi Dirac points, respectively. These could in principle be directly identified in current experiments.

Quantum magnetotransport and de Haas–van Alphen measurements in the three-dimensional Dirac semimetal Pb0.83Sn0.17Se

Magnetoresistance (MR), Hall resistance and magnetization of the Pb0.83Sn0.17Se crystals have been measured in magnetic field up to 15 T and 5 T, respectively, and temperatures from 1.7 K up to 300 K. A large linear and temperature dependent MR is observed in magnetic field up to 15 T. The de Haas–van Alphen (dHvA) and Shubnikov de Haas effects (SdH) of Pb0.83Sn0.17Se crystals have been clearly seen in the temperature range from 30 K down to 1.7 K and magnetic field as low as 2 T. The dHvA and SdH oscillations reveal single frequency of around 8 T which confirms the existence of a single Fermi surface cross section. Influence of isothermal annealing of Pb0.83Sn0.17Se crystals in Se vapours has been investigated. By increasing the annealing temperature from 433 °C up to 440 °C, transition from n to p-type conductivity has been observed. The dHvA and SdH effects clearly reflect the existence of a nontrivial Berry’s phase owing to the linear band dispersion which is the signature of a three-dimensional Dirac fermion in the Pb0.83Sn0.17Se crystals [1].

Three-dimensional Dirac semimetal and magnetic quantum oscillations in Cd3As2

Single crystals of topological Dirac semimetal Cd3As2 were synthesized using a modified vapour transport technique. The magnetization of Cd3As2 single crystals was measured in the temperature range from 4.2-300 K and magnetic field up to 5 T along [001] and [100] directions. In the low temperature region we observed the de Haas van Alphen (dHvA) oscillations which allow us to characterize the three dimensional Fermi surface by extracting its relevant parameters. The dHvA oscillations show the existence of two different Fermi surface cross sections and nontrivial Berry’s phase, which is the signature of Dirac fermion in Cd3As2.

Quantum oscillations in Weyl semimetals: A surface theory approach

We develop an effective surface theory for the surface states of a Weyl semimetal. This theory includes the peculiar Fermi arc states on the surface as well as leakage of the states from the surface to the bulk. Subjecting the model to a magnetic field perpendicular to the surface results in quantum oscillations. The oscillations are different from the usual ones since they do not involve a closed Fermi surface cross section. It has been shown previously that the Quantum oscillations can be understood semiclassically as resulting from motion of electrons on the surface Fermi arcs as well as tunneling through chiral Landau levels associated with the bulk. In this work we develop an effective surface theory and use it to analyze the quantum oscillation in the semiclassical regime and beyond. Specifically, we show that when a pair of Weyl points are close to each other the surface quantum oscillations acquire a phase offset which originates from the bulk. While the surface states are responsible for a large part of the electron motion, tunneling through the bulk is necessary for completing the orbit. This tunneling makes use of the bulk, zero energy, chiral Landau level in each Weyl node. When the nodes are close in momentum space their chiral levels overlap and a gap at zero energy is formed. This gap causes the phase offset in the surface quantum oscillations.

Quantum oscillations in a lead chalcogenide three-dimensional Dirac system

The de Haas–van Alphen (dHvA) and the Shubnikov–de Haas (SdH) oscillations were used to probe the properties of the Fermi surface in single crystals of Pb0.83Sn0.17Se with reduced charge concentration. Pronounced low-frequency oscillations of ∼8 T in the [001] direction were observed, confirming the single Fermi surface cross section. Due to the low effective charge concentration, the ultraquantum limit is reached already at ∼10 T. We observe π-Berry phase shift in the phase of both dHvA and SdH oscillations, which confirms the 3D Dirac nature of the energy band dispersion. In the construction of the Landau level diagram we use a combined indexing method for conductivity, magnetic susceptibility, and magnetization, which is based on the indexing used in the topological insulators. Moreover, the reliability of the indexing method is increased because we use, beside minima and maxima, zeros of the oscillations as well. Different microscopic parameters were calculated from the quantum oscillations in the magnetization, conductivity, and resistivity.

Symmetry-Protected Line Nodes in Non-symmorphic Magnetic Space Groups: Applications to UCoGe and UPd2Al3

We present the group-thoretical classification of gap functions in superconductors coexisting with some magnetic order in non-symmorphic magnetic space groups. Based on the weak-coupling BCS theory, we show that UCoGe-type ferromagnetic superconductors must have horizontal line nodes on either $k_z=0$ or $\pm\pi/c$ plane. Moreover, it is likely that additional Weyl point nodes exist at the axial point. On the other hand, in UPd$_2$Al$_3$-type antiferromagnetic superconductors, gap functions with $A_g$ symmetry possess horizontal line nodes in antiferromagnetic Brillouin zone boundary perpendicular to $c$-axis. In other words, the conventional fully-gapped $s$-wave superconductivity is forbidden in this type of antiferromagnetic superconductors, irrelevant to the pairing mechanism, as long as the Fermi surface crosses a zone boundary. UCoGe and UPd$_2$Al$_3$ are candidates for unconventional superconductors possessing hidden symmetry-protected line nodes, peculiar to non-symmorphic magnetic space groups.

Magnetotransport study of (Sb1−xBix)2Te3 thin films on mica substrate for ideal topological insulator

We deposited high quality (Sb1−xBix)2Te3 on mica substrate by molecular beam epitaxy and investigated their magnetotransport properties. It is found that the average surface roughness of thin films is lower than 2 nm. Moreover, a local maxima on the sheet resistance is obtained with x = 0.043, indicating a minimization of bulk conductivity at this composition. For (Sb0.957Bi0.043)2Te3, weak antilocalization with coefficient of -0.43 is observed, confirming the existence of 2D surface states. Moreover Shubnikov-de Hass oscillation behavior occurs under high magnetic field. The 2D carrier density is then determined as 0.81 × 1016 m−2, which is lower than that of most TIs reported previously, indicating that (Sb0.957Bi0.043)2Te3 is close to ideal TI composition of which the Dirac point and Fermi surface cross within the bulk bandgap. Our results thus demonstrate the best estimated composition for ideal TI is close to (Sb0.957Bi0.043)2Te3 and will be helpful for designing TI-based devices.

Transport signatures of Fermi surface topology change in BiTeI

We report a quantum magnetotransport signature of a change in the Fermi surface topology in the Rashba semiconductor BiTeI with a systematic tuning of the Fermi level ${E}_{F}$. Beyond the quantum limit, we observe a marked increase (decrease) in electrical resistivity when ${E}_{F}$ is above (below) the Dirac node that we show originates from the Fermi surface topology. This effect represents a measurement of the electron distribution on low-index $(n=0,\ensuremath{-}1)$ Landau levels and is uniquely enabled by the finite bulk ${k}_{z}$ dispersion along the $c$ axis and strong Rashba spin-orbit coupling strength of the system. The Dirac node is independently identified by Shubnikov--de Haas oscillations as a vanishing Fermi surface cross section at ${k}_{z}=0$. Additionally, we find that the violation of Kohler's rule allows a distinct insight into the temperature evolution of the observed quantum magnetoresistance effects.

Two-dimensional Fermi surfaces in Kondo insulator SmB₆.

In the Kondo insulator samarium hexaboride (SmB6), strong correlation and band hybridization lead to an insulating gap and a diverging resistance at low temperature. The resistance divergence ends at about 3 kelvin, a behavior that may arise from surface conductance. We used torque magnetometry to resolve the Fermi surface topology in this material. The observed oscillation patterns reveal two Fermi surfaces on the (100) surface plane and one Fermi surface on the (101) surface plane. The measured Fermi surface cross sections scale as the inverse cosine function of the magnetic field tilt angles, which demonstrates the two-dimensional nature of the conducting electronic states of SmB6.

The first molecular superconductor based on BEDT-TTF radical cation salt with paramagnetic tris(oxalato)ruthenate anion

The first molecular superconductor based on BEDT-TTF radical cation salt with the paramagnetic tris(oxalato)ruthenate anion, β′′-(BEDT-TTF)4Kx(H3O)1−x[RuIII(ox)3]C6H5Br (x ∼ 0.8), is synthesized and its crystal and electronic structure as well as transport and magnetotransport properties are studied. The single crystals have monoclinic C2/c symmetry and β′′-packing of the conducting BEDT-TTF layer. The samples were found to be superconductors with Tc = 2.8–6.3 K (depending on the sample). Well pronounced Shubnikov–de Haas oscillations are observed in the field range 7–17 T. The Fourier spectrum of the oscillations mainly consists of two frequencies, which correspond to the Fermi surface cross sections 6.3% and 0.85% of the Brillouin zone. The first one with good accuracy corresponds to the calculated cross section 7.5%, the origin of the second one is discussed. Semiconducting orthorhombic phase ‘pseudo-κ’-(BEDT-TTF)4Kx(H3O)1−x[RuIII(ox)3]C6H5CN is also synthesized and studied.

SU(2) approach to the pseudogap phase of high-temperature superconductors: Electronic spectral functions

We use an SU(2) mean-field theory approach with input from variational wave functions of the $t\text{\ensuremath{-}}J$ model to study the electronic spectra in the pseudogap phase of cuprates. In our model, the intermediate-temperature state of underdoped cuprates is realized by classical fluctuations of the order parameter between the $d$-wave superconductor and the staggered-flux state. The spectral functions of the pure and the averaged states are computed and analyzed. Our model predicts a photoemission spectrum with an asymmetric gap structure interpolating between the superconducting gap centered at the Fermi energy and the asymmetric staggered-flux gap. This asymmetry of the gap changes sign at the points where the Fermi surface crosses the diagonal $(\ensuremath{\pi},0)\text{\ensuremath{-}}(0,\ensuremath{\pi})$.

Electron doping and superconductivity in the two-dimensional Hubbard model

An elaborate variational wave function is used for studying superconductivity in the repulsive twodimensional Hubbard model, including both nearest- and next-nearest-neighbor hoppings. A marked asymmetry is found between the “localized” hole-doped region and the more itinerant electron-doped region. Superconductivity with d-wave symmetry turns out to be restricted to densities where the Fermi surface crosses the magnetic zone boundary. A concomitant peak in the magnetic structure factor at , clearly points to a magnetic mechanism. One of the central issues in the field of high-temperature superconductors has been—and for some researchers still is—the question whether pairing in the cuprates arises from purely repulsive interactions, as proposed by Anderson two decades ago. 1 This question has been studied extensively in the framework of the two-dimensional 2Drepulsive Hubbard model and the related t-J model. Recent progress, both in dynamical mean-field theory 2,3 and in variational calculations, 4 has strengthened the case for the existence of a superconducting phase in the Hubbard model, with a d-wave gap parameter reasonably close to the experimental values for intermediate interaction strengths U of the order of the bandwidth. This conclusion has been challenged on the basis of Monte Carlo simulations, 5 which we believe to be not conclusive, as discussed below. Most previous studies of the Hubbard model have been restricted to nearest-neighbor hopping, where electron doping does not differ from hole doping. Here we show that the addition of second-neighbor hopping which breaks the electron-hole symmetry changes this behavior substantially. While the hole-doped side is “localized” and shows kineticenergy-driven superconductivity with a large condensation energy, the electron-doped side is itinerant with a potentialenergy-driven superconductivity and a small condensation energy.

PRESSURE-INDUCED ELECTRONIC PHASE TRANSITIONS AND SUPERCONDUCTIVITY IN TITANIUM

The electronic band structure, density of states, structural phase transition, superconducting transition and Fermi surface cross section of titanium ( Ti ) under normal and high pressures are reported. The high pressure band structure exhibits significant deviations from the normal pressure band structure due to s → d transition. On the basis of band structure and total energy results obtained using tight-binding linear muffin-tin orbital method (TB LMTO), we predict a phase transformation sequence of α( hcp ) → ω (hexagonal) → γ (distorted hcp) → β (bcc) in titanium under pressure. From our analysis, we predict a δ (distorted bcc) phase which is not stable at any high pressures. At ambient pressure, the superconducting transition occurs at 0.354 K. When the pressure is increased, it is predicted that, Tc increases at a rate of 3.123 K/Mbar in hcp–Ti . On further increase of pressure, Tc begins to decrease at a rate of 1.464 K/Mbar. The highest value of Tc(P) estimated is 5.043 K for hcp–Ti , 4.538 K for ω– Ti and 4.85 K for bcc – Ti . From this, it is inferred that the maximum value of Tc(P) is rather insensitive to the crystal structure of Ti . The nonlinearities in Tc(P) is explained by considering the destruction and creation of new parts of Fermi surface at high pressure. At normal pressure, the hardness of Ti is in the following order: ω- Ti > hcp - Ti > bcc- Ti > γ- Ti .

Magnetoresistance of Co-doped ZnO thin films

Longitudinal, transverse, and perpendicular magnetoresistances were investigated at temperatures 1.2<T<300K in fields of up to 20 T for four ZnO films: one undoped, two with 4% Co (one paramagnetic, the other exhibiting anhysteretic ferromagnetism at room temperature), and one with 25% Co which exhibits hysteretic ferromagnetism, butterfly magnetoresistance, and presence of Co clusters. The magnetoresistance becomes negligibly small above 50–100 K, and magnetic terms are only evident below 20 K, where the mobility is sufficiently high. Quantum oscillations observed below 2 K in the paramagnetic sample with 4% Co give two different extremal Fermi surface cross sections. The data for dilute ferromagnetic samples are consistent with coherent spin transport in a ferromagnetic matrix; data for the x=25% films suggest that spin-polarized electrons can tunnel coherently between well-separated cobalt clusters.

Fermi surface and electron correlation effects of ferromagnetic iron

The electronic band structure of bulk ferromagnetic iron is explored by angle-resolved photoemission for electron correlation effects. Fermi surface cross sections as well as band maps are contrasted with density functional calculations. The Fermi vectors and band parameters obtained from photoemission and their prediction from band theory are analyzed in detail. Generally good agreement is found for the Fermi surface. A bandwidth reduction for shallow bands of $\ensuremath{\sim}30%$ is observed. Additional strong quasiparticle renormalization effects are found near the Fermi level, leading to a considerable mass enhancement. The role of electronic correlation effects and the electronic coupling to magnetic excitations is discussed in view of the experimental results.

Effective Hamiltonian approach for magnetic band structure and additional oscillations in the magnetization originating from the Fermi surface at finite magnetic fields

The one-electron Schr\"odinger equation in a two-dimensional periodic potential and a homogeneous magnetic field $B$ perpendicular to the plane is solved exactly for rational flux quantum numbers per unit cell ${\ensuremath{\Phi}}_{c}∕{\ensuremath{\Phi}}_{0}=p∕q$. For comparison, the spectrum around a certain flux quantum number ${p}_{0}∕{q}_{0}$ has also been obtained by semiclassical quantization of the exact magnetic band structure (MBS) at ${p}_{0}∕{q}_{0}$. To implement and justify this procedure, a generalized effective Hamiltonian theory based on the MBS at finite magnetic fields has been established. The total energy as a function of ${\ensuremath{\Phi}}_{c}∕{\ensuremath{\Phi}}_{0}$ shows a series of kinks, where each kink indicates an insulating state. The kinks of each series converge to a metallic state. The magnetization contains information not only about the band structure (at zero-magnetic field), but also about the magnetic band structures (for finite fields). The period of the oscillations in $M[1∕(B\ensuremath{-}{B}_{0})]$ is determined by the Fermi surface cross sections for the MBS at ${B}_{0}$. The height of the steps in $M(B)$ provides the energy gap in the MBS at $B$. Unlike the standard Lifshitz-Kosevich type approaches, our theoretical de Haas-van Alphen spectra contain the effects of magnetic breakdown, forbidden orbits, and interband coupling implicitly.