Fermi Surface Topology Research Articles

Magnetoresistance from Fermi surface topology

Extremely large non-saturating magnetoresistance has recently been reported for a large number of both topologically trivial and non-trivial materials. Different mechanisms have been proposed to explain the observed magnetotransport properties, yet without arriving to definitive conclusions or portraying a global picture. In this work, we investigate the transverse magnetoresistance of materials by combining the Fermi surfaces calculated from first principles with the Boltzmann transport theory approach relying on the semiclassical model and the relaxation time approximation. We first consider a series of simple model Fermi surfaces to provide a didactic introduction into the charge-carrier compensation and open-orbit mechanisms leading to non-saturating magnetoresistance. We then address in detail magnetotransport in three representative materials: (i) copper, a prototypical nearly free-electron metal characterized by the open Fermi surface that results in an intricate angular magnetoresistance, (ii) bismuth, a topologically trivial semimetal in which very large magnetoresistance is known to result from charge-carrier compensation, and (iii) tungsten diphosphide WP2, a recently discovered type-II Weyl semimetal that holds the record of magnetoresistance in compounds. In all three cases our calculations show excellent agreement with both the field dependence of magnetoresistance and its anisotropy measured at low temperatures. Furthermore, the calculations allow for a full interpretation of the observed features in terms of the Fermi surface topology. These results will help addressing a number of outstanding questions, such as the role of the topological phase in the pronounced large non-saturating magnetoresistance observed in topological materials.

Observation of superconductivity in the pressurized Weyl-semimetal candidate TaIrTe4

Here we report the observation of superconductivity in pressurized type-II Weyl semimetal (WSM) candidate TaIrTe4 by means of complementary high-pressure transport and synchrotron X-ray diffraction measurements. We find that TaIrTe4 shows superconductivity with transition temperature (TC) of 0.57 K at the pressure of ~23.8 GPa. Then, the TC value increases with pressure and reaches ~2.1 K at 65.7 GPa. In situ high-pressure Hall coefficient (RH) measurements at low temperatures demonstrate that the positive RH increases with pressure until the critical pressure of the superconducting transition is reached, but starts to decrease upon further increasing pressure. Above the critical pressure, the positive magnetoresistance effect disappears simultaneously. Our high pressure X-ray diffraction measurements reveal that, at around the critical pressure the lattice of the TaIrTe4 sample is distorted by the application of pressure and its volume is reduced by ~19.2%, the value of which is predicted to result in the change of the electronic structure significantly. We propose that the pressure-induced distortion in TaIrTe4 is responsible for the change of topology of Fermi surface and such a change favors the emergence of superconductivity. Our results clearly demonstrate the correlation among the lattice distortion, topological physics and superconductivity in the WSM.

Quadratic to linear magnetoresistance tuning in TmB4

The change of a material's electrical resistance (R) in response to an external magnetic field (B) provides subtle information for the characterization of its electronic properties and has found applications in sensor and storage related technologies. In good metals, Boltzmann's theory predicts a quadratic growth in magnetoresistance (MR) at low B, and saturation at high fields. On the other hand, a number of nonmagnetic materials with weak electronic correlation and low carrier concentration for metallicity, such as inhomogeneous conductors, semimetals, narrow gap semiconductors and topological insulators, two-dimensional electron gas (2DEG) show positive, non-saturating linear magnetoresistance (LMR). However, observation of LMR in single crystals of a good metal is rare. Here we present low-temperature, angle dependent magnetotransport in single crystals of the antiferromagnetic metal, TmB4. We observe large, positive and anisotropic MR(B), which can be tuned from quadratic to linear by changing the direction of the applied field. In view of the fact that isotropic, single crystalline metals with large Fermi surface (FS) are not expected to exhibit LMR, we attribute our observations to the anisotropic FS topology of TmB4. Furthermore, the linear MR is found to be temperature-independent, suggestive of quantum mechanical origin.

Evolution of the low-temperature Fermi surface of superconducting FeSe1\u2212xSx across a nematic phase transition

The existence of a nematic phase transition in iron-chalcogenide superconductors poses an intriguing question about its impact on superconductivity. To understand the nature of this unique quantum phase transition, it is essential to study how the electronic structure changes across this transition at low temperatures. Here, we investigate the evolution of the Fermi surfaces and electronic interactions across the nematic phase transition of FeSe1−xSx using Shubnikov-de Haas oscillations in high magnetic fields up to 45 T in the low temperature regime down to 0.4 K. Most of the Fermi surfaces of FeSe1−xSx monotonically increase in size except for a prominent low frequency oscillation associated with a small, but highly mobile band, which disappears at the nematic phase boundary near x ~ 0.17, indicative of a topological Lifshitz transition. The quasiparticle masses are larger inside the nematic phase, indicative of a strongly correlated state, but they become suppressed outside it. The experimentally observed changes in the Fermi surface topology, together with the varying degree of electronic correlations, will change the balance of electronic interactions in the multi-band system FeSe1−xSx and promote different kz-dependent superconducting pairing channels inside and outside the nematic phase.

Disappearance of Superconductivity and a Concomitant Lifshitz Transition in Heavily Overdoped Bi2Sr2CuO6 Superconductor Revealed by Angle-Resolved Photoemission Spectroscopy**Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0300300 and 2017YFA0302900, the Strategic Priority Research Program (B) of Chinese Academy of Sciences under Grant Nos XDB07020300 and XDB25000000, the National Basic Research Program of China under Grant

By partially doping Pb to effectively suppress the superstructure in single-layered cuprate Bi2Sr2CuO6+δ (Pb-Bi2201) and annealing them in vacuum or in high pressure oxygen atmosphere, a series of high quality Pb-Bi2201 single crystals are obtained with Tc covering from 17 K to non-superconducting in the overdoped region. High resolution angle resolved photoemission spectroscopy measurements are carried out on these samples to investigate the evolution of the Fermi surface topology with doping in the normal state. Clear and complete Fermi surfaces are observed and quantitatively analyzed in all of these overdoped Pb-Bi2201 samples. A Lifshitz transition from hole-like Fermi surface to electron-like Fermi surface with increasing doping is observed at a doping level of ∼0.35. This transition coincides with the change that the sample undergoes superconducting-to-non-superconducting states. Our results reveal the emergence of an electron-like Fermi surface and the existence of a Lifshitz transition in heavily overdoped Bi2201 samples. This provides important information in understanding the connection between the disappearance of superconductivity and the Lifshitz transition in the overdoped region.

Significant change in the electronic behavior associated with structural distortions in monocrystalline SrAg4As2

We report a combined study of transport and thermodynamic measurements on the layered pnictide material SrAg4As2. Upon cooling, a drop in electrical and Hall resistivity, a jump in heat capacity and an increase in susceptibility and magnetoresistance (MR) are observed around 110 K. These observations suggest that non-magnetic phase transitions emerge at around 110 K, that are likely associated with structural distortions. In sharp contrast with the first-principles calculations based on the crystal structure at room temperature, quantum oscillations reveal small Fermi pockets with light effective masses, suggesting a significant change in the Fermi surface topology caused by the low temperature structural distortion. No superconductivity emerges in SrAg$_4$As$_2$ down to 2 K and under pressures up to 2.13 GPa; instead, the low temperature structural distortion increases linearly with temperature at a rate of ~13 K/GPa above 0.89 GPa.

Fermi surface topology in a metallic phase of VO2 thin films grown on TiO2(001) substrates

Since the first observation of the metal-to-insulator transition (MIT), VO2 has attracted substantial attention in terms of whether this transition is impelled by electron–phonon interaction (Peierls transition) or electron–electron interaction. Regarding Peierls transition, it has been theoretically predicted that the Fermi surface (FS) cross-section exhibits certain nesting features for a metallic phase of VO2. Various experimental studies related to the nesting feature have been reported. Nevertheless, there is no experimental result on FS topology. In this work, we determine the FS topology of the metallic phase of VO2 through studies of VO2 epitaxial thin films on TiO2(001) substrates, using synchrotron radiation angle-resolved photoemission spectroscopy (ARPES). Three electron pockets around Γ are observed in band structures along the Γ–X direction. These three bands form electron surfaces around Γ in the ΓXRZ plane. Furthermore, the lowest energy band FS exhibits the nesting feature corresponding to a nesting vector overrightarrow{q} = ΓR, as predicted by the calculation. Our results strongly indicate the formation of the charge-density wave with overrightarrow{q} = ΓR and thus, the importance of Peierls transition for the mechanism of the MIT in VO2.

Correlation-driven Lifshitz transition in electron-doped iron selenides (Li,Fe)OHFeSe

Effects of electronic correlation and spin-orbit coupling (SOC) on electronic structure of iron selenides (${\mathrm{Li}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}$)OHFeSe have been investigated with the combination of density functional theory (DFT) and dynamical mean-field theory. It is found that the electronic correlation substantially changes the Fermi surface topology for $x=0.2$, resulting in a tiny electron pocket around the zone center $\mathrm{\ensuremath{\Gamma}}$ and two large electron pockets around the zone corner $M$, respectively. Moreover, the SOC also considerably affects the low-energy electronic structure near the Fermi level, especially inducing a gap in the Dirac-like dispersion around $\mathrm{\ensuremath{\Gamma}}$ for $x=0.2$. Our calculations show a correlation-driven Lifshitz transition from FeSe to the heavily electron-doped compound, leading to a transition of the nesting wave vector from ($\ensuremath{\pi}$, 0) to ($\ensuremath{\pi}$, $0.5\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}$) accompanied by an orbital-weight redistribution between the ${d}_{xy}$ and ${d}_{xz}/{d}_{yz}$ orbitals. These correlation-driven electronic structures enrich the understanding of different DFT and experimental results, suggesting a quite distinct superconducting state of (${\mathrm{Li}}_{0.8}{\mathrm{Fe}}_{0.2}$)OHFeSe in comparison with FeSe.

Impurity Effects in Nodal Extendeds- and Nodelessd-Wave Superconductors: Gap Symmetry of BiS2-Based Layered Superconductors

In BiS$_2$-based layered superconductors,the existence of gap nodes on Fermi-surface curves has been suggested from angle-resolved photoemission spectroscopy measurements, whereas the conventional $s$-wave gap has been proposed from measurements of superfluid density and thermal conductivity. To reconcile these two distinct experimental results of the gap node, we investigate nonmagnetic impurity effects in the superconductor with a disconnected pocketlike Fermi-surface structure. Then, we claim that the seemingly contradictory situation concerning the gap node is resolved by a concept of dirty nodal extended $s$-wave superconductivity. Provided that it is unnecessary to consider the nodes of the gap, at first glance, the conventional $s$-wave gap seems to be a unique solution, but in the pocketlike Fermi-surface topology, a nontrivial possibility of a nodeless $d$-wave superconductor is pointed out. To clarify the gap symmetry, we propose to perform experiments on nuclear magnetic relaxation rate $T_{1}^{-1}$ in BiS$_2$-based layered superconductors.

Anisotropic Dirac Fermions in BaMnBi2 and BaZnBi2

We investigate the electronic structure of BaMnBi2 and BaZnBi2 using angle-resolved photoemission spectroscopy and first-principles calculations. Although they share similar structural properties, we show that their electronic structure exhibit dramatic differences. A strong anisotropic Dirac dispersion is revealed in BaMnBi2 with a decreased asymmetry factor compared with other members of AMnBi2 (A = alkali earth or rare earth elements) family. In addition to the Dirac cones, multiple bands crossing the Fermi energy give rise to a complex Fermi surface topology for BaZnBi2. We further show that the strength of hybridization between Bi-p and Mn-d/Zn-s states is the main driver of the differences in electronic structure for these two related compounds.

Emergent Dirac Gullies and Gully-Symmetry-Breaking Quantum Hall States in ABA Trilayer Graphene.

We report on quantum capacitance measurements of high quality, graphite and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At a high displacement field and low density, strong trigonal warping gives rise to three new emergent Dirac cones in each valley, which we term "gullies." The gullies are centered around the corners of a hexagonal Brillouin zone and related by threefold rotation symmetry. At low magnetic fields of B=1.25 T, the gullies manifest as a change in the degeneracy of the Landau levels from two to three. Weak incompressible states are also observed at integer filling within these triplet Landau levels, which a Hartree-Fock analysis indicates are associated with Coulomb-driven nematic phases that spontaneously break rotation symmetry.

Emergent Dirac carriers across a pressure-induced Lifshitz transition in black phosphorus

The phase diagrams of correlated systems like cuprates or pnictides high-temperature superconductors are characterized by a topological change of the Fermi surface under continuous variation of an external parameter, the so-called Lifshitz transition. However, the large number of low-temperature instabilities and the interplay of multiple energy scales complicate the study of this phenomenon. Here we first identify the optical signatures of a pressure-induced Lifshitz transition in a clean elemental system, black phosphorus. By applying external pressures above 1.5 GPa, we observe a change in the pressure dependence of the Drude plasma frequency due to the appearance of massless Dirac fermions. At higher pressures, optical signatures of two structural phase transitions are also identified. Our findings suggest that a key fingerprint of the Lifshitz transition in solid state systems, and in absence of structural phase transitions, is a discontinuity of the Drude plasma frequency due to the change of Fermi surface topology.

Impurity-induced bound states as a signature of pairing symmetry in multiband superconducting CeCu2Si2

The notion of multiband superconductivity with dominant two-gap features has been recently applied to the unconventional superconductor CeCu2Si2 for challenging the previously accepted concept of nodal d-wave pairing. In the proposed study, the realistic multiband Fermi surface topology of CeCu2Si2 was obtained through first-principles calculations, and analysis was conducted with an effective two-band hybridization model including detailed band structure. Within the T-matrix approximation, the obtained calculation results show that different pairing candidates, including fully gapped s-wave, loop-nodal s-wave, and d-wave pairings, could yield qualitatively distinct features characterized by impurity-induced bound states. These features can be verified through high-resolution scanning tunneling microscopy or spectroscopy and provide corroborative justification that would be beneficial for the ongoing research regarding the superconducting gap symmetry of CeCu2Si2 at ambient pressure.

Magnetic fluctuations under pressure on S-doped FeSe studied via 77Se NMR

FeSe1-xSx has attracted much attention among iron-based superconductors because the pure sample undergoes nematic and superconducting (SC) phase transitions without magnetism. A pressure-induced antiferromagnetic (AFM) phase emerges upon applying pressure. In the pressure (P)-temperature (T) phase diagram for the 12%-S doped sample, the AFM phase is separated from the nematic phase at around 3.0 GPa, and SC transition temperature (Tc) takes a maximum (∼30 K). We measured T1 of 77Se for the 12%-S doped FeSe at 3.0 GPa. We found from 1/T1T that low-energy AFM fluctuations are not so much enhanced under pressure compared with those at ambient pressure. The result suggests changes of topology and nesting of Fermi surfaces during pressurizing process.

Extremely large magnetoresistance and the complete determination of the Fermi surface topology in the semimetal ScSb

We report the magnetoresistance of ScSb, which is a semimetal with a simple rocksalt-type structure. We found that the magnetoresistance reaches $\sim$28000 % at 2 K and 14 T in our best sample, and it exhibits a resistivity plateau at low temperatures. The Shubnikov-de Haas oscillations extracted from the magnetoresistance data allow the full construction of the Fermi surface, including the so-called $\alpha_3$ pocket which has been missing in other closely related monoantimonides, and an additional hole pocket centered at $\Gamma$. The electron concentration ($n$) and the hole concentration ($p$) are extracted from our analysis, which indicate that ScSb is a nearly compensated semimetal with $n/p\approx0.93$. The calculated band structure indicates the absence of a band inversion, and the large magnetoresistance in ScSb can be attributed to the nearly perfect compensation of electrons and holes, despite the existence of the additional hole pocket.

Multi-Valley Superconductivity in Ion-Gated MoS2 Layers.

Layers of transition metal dichalcogenides (TMDs) combine the enhanced effects of correlations associated with the two-dimensional limit with electrostatic control over their phase transitions by means of an electric field. Several semiconducting TMDs, such as MoS2, develop superconductivity (SC) at their surface when doped with an electrostatic field, but the mechanism is still debated. It is often assumed that Cooper pairs reside only in the two electron pockets at the K/K' points of the Brillouin Zone. However, experimental and theoretical results suggest that a multivalley Fermi surface (FS) is associated with the SC state, involving six electron pockets at Q/Q'. Here, we perform low-temperature transport measurements in ion-gated MoS2 flakes. We show that a fully multivalley FS is associated with the SC onset. The Q/Q' valleys fill for doping ≳ 2 × 1013 cm-2, and the SC transition does not appear until the Fermi level crosses both spin-orbit split sub-bands Q 1 and Q 2. The SC state is associated with the FS connectivity and promoted by a Lifshitz transition due to the simultaneous population of multiple electron pockets. This FS topology will serve as a guideline in the quest for new superconductors.

Raman and ARPES combined study on the connection between the existence of the pseudogap and the topology of the Fermi surface in Bi2Sr2CaCu2O8+δ

We study the behavior of the pseudogap in overdoped Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+d}$ by electronic Raman scattering (ERS) and angle-resolved photoemission spectroscopy (ARPES) on the same single crystals. Using both techniques we find that, unlike the superconducting gap, the pseudogap related to the anti-bonding band vanishes above the critical doping p$_c$ = 0.22. Concomitantly, we show from ARPES measurements that the Fermi surface of the anti-bonding band is hole-like below pc and becomes electron-like above p$_c$. This reveals that the appearance of the pseudogap depends on the Fermi surface topology in Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+d}$ , and more generally, puts strong constraint on theories of the pseudogap phase.

Topological kinematics of origami metamaterials

A variety of electronic phases in solid-state systems can be understood by abstracting away microscopic details and refocusing on how Fermi surface topology interacts with band structure to define available electron states 1 . In fact, topological concepts are broadly applicable to non-electronic materials and can be used to understand a variety of seemingly unrelated phenomena2–6. Here, we apply topological principles to origami-inspired mechanical metamaterials7–12, and demonstrate how to guide bulk kinematics by tailoring the crease configuration-space topology. Specifically, we show that by simply changing the crease angles, we modify the configuration-space topology, and drive origami structures to dramatically change their kinematics from being smoothly and continuously deformable to mechanically bistable and rigid. In addition, we examine how a topologically disjointed configuration space can be used to constrain the locally accessible deformations of a single folded sheet. While analyses of origami structures are typically dependent on the energetics of constitutive relations11–14, the topological abstractions introduced here are a separate and independent consideration that we use to analyse, understand and design these metamaterials.

Extremely large magnetoresistance induced by Zeeman effect-driven electron-hole compensation and topological protection in MoSi2

The magnetoresistance is the magnetic field induced change of electrical resistivity of a material. Recent studies have revealed extremely large magnetoresistance in several non-magnetic semimetals, which has been explained on the basis of either electron-hole compensation or the Fermi surface topology, or the combination of both. Here, we present a single crystal study on MoSi$_2$, which exhibits extremely large magnetoresistance, approaching almost 10$^7$ % at 2 K and 14 T magnetic field. It is found that the electron-hole compensation level in MoSi$_2$ evolves with magnetic field, which is resulted from strong Zeeman effect, and found beneficial in boosting the large non-saturating magnetoresistance. The non-trivial Berry phase in the de Haas-van Alphen oscillations and the moderate suppression of backward scattering of the charge carriers lend support for the topological nature of this semimetal. The ultra-large carrier mobility of the topologically protected charge carriers reinforces the magnetoresistance of MoSi2 to an unprecedented large value.

Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model

One of the distinctive features of hole-doped cuprate superconductors is the onset of a `pseudogap' below a temperature $T^*$. Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the two-dimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is hole-like and that, for a broad range of parameters, its opening is concomitant with a Fermi surface topology change from electron- to hole-like. We identify a common link between these observations: the pole-like feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this pole-like feature, and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.