Fermi Pockets Research Articles

Topologically protected surface states in TaPdTe5

By combining angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations, we have studied the electronic band structure of a topological material candidate TaPdTe5.Two inverted bulk gaps determined through the parity analysis were observed in TaPdTe5 near the Fermi level, which causes the appearance of topologically protected surface states on the (010) surface. Beside the surface state, we also observed strong surface resonance state. The hybridization between the surface resonance state and the surface state changes the quasi-one-dimensional like Fermi surface sheets of the surface resonance state into two-dimensional Fermi pockets. Our findings provide comprehensive understanding about the interesting surface states in TaPdTe5.

Electronic structure, magnetic order and Lifshitz transition in electron doped new structure 12442 type Fe-based superconductors

We investigate in detail the electronic structure of very recently discovered electron doped 12442-type iron based BaTh2Fe4As4(N1−xOx)2 compounds (x = 0.1–0.6), using Density Functional Theory (DFT) based first principles calculations. Unlike in many iron-based superconducting compounds, absence of As-4pZ orbital character, and dominant contributions from Fe-3d orbitals close to the Fermi level are noted. Formation energy calculations indicate x = 0.3 structure is the most stable which is consistent with experimental observation. Incorporating magnetic order at Fe sites in compound x = 0.3, our calculations predict stripe AFM as ground state magnetic structure. Calculated Arsenic height from the Fe square plane (hAs) for striped AFM configuration agrees well with the experiment. An important outcome of this calculation is the prediction of occurrence of Lifshitz transition at the same doping level (x = 0.6) for which the highest critical temperature is reported in literature. Detailed analysis of electronic structure results like estimation of radii of various Fermi pockets, orbital characters of Fermi surfaces lead to prediction of mixed d and s pairing symmetry.

Temperature-driven changes in the Fermi surface of graphite

We report on temperature-dependent size and anisotropy of the Fermi pockets in graphite revealed by magnetotransport measurements. The magnetoresistances obtained in fields along the c-axis obey an extended Kohler's rule, with the carrier density following prediction of a temperature-dependent Fermi energy, indicating a change in the Fermi pocket size with temperature. The angle-dependent magnetoresistivities at a given temperature exhibit a scaling behavior. The scaling factor that reflects the anisotropy of the Fermi surface is also found to vary with temperature. Our results demonstrate that temperature-driven changes in Fermi surface can be ubiquitous and need to be considered in understanding the temperature-dependent carrier density and magnetoresistance anisotropy in semimetals.

Analysis of unconventional chiral fermions in a noncentrosymmetric chiral crystal PtAl

Symmetry protected nontrivial states in chiral topological materials hold immense potential for fundamental science and technological advances. Here, we report electrical transport, quantum oscillations, and electronic structure results of a single crystal of chiral quantum material PtAl. Based on the de Haas-van Alphen (dHvA) oscillations, we show that the smallest Fermi pocket $(\ensuremath{\alpha})$ possesses a nontrivial Berry phase $1.16\ensuremath{\pi}$. The band associated with this Fermi pocket carries a linear energy dispersion over a substantial energy window of $\ensuremath{\sim}700\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ that is further consistent with the calculated optical conductivity. First principles calculations unfold that PtAl is a higher fold chiral fermion semimetal where structural chirality drives the chiral fermions to lie at the high symmetry $\mathrm{\ensuremath{\Gamma}}$ and $R$ points of the cubic Brillouin zone. In the absence of spin orbit coupling, the band crossings at $\mathrm{\ensuremath{\Gamma}}$ and $\mathrm{R}$ points are three and fourfold degenerate with a chiral charge of $\ensuremath{-}2$ and $+2$, respectively. The inclusion of spin orbit coupling transforms these crossing points into four and sixfold degenerate points with a chiral charge of $\ensuremath{-}4$ and $+4$. Nontrivial surface states on the (001) surface connect the bulk projected chiral points through the long helical Fermi arcs that spread over the entire surface Brillouin zone.

Observation of anisotropic Dirac cones in the topological material Ti2Te2P

Anisotropic bulk Dirac (or Weyl) cones in three-dimensional systems have recently gained intense research interest as they are examples of materials with tilted Dirac (or Weyl) cones indicating the violation of Lorentz invariance. In contrast, the studies on anisotropic surface Dirac cones in topological materials which contribute to anisotropic carrier mobility have been limited. By employing angle-resolved photoemission spectroscopy and first-principles calculations, we reveal the anisotropic surface Dirac dispersion in a tetradymite material ${\mathrm{Ti}}_{2}{\mathrm{Te}}_{2}\mathrm{P}$ on the (001) plane of the Brillouin zone. We observe quasielliptical Fermi pockets at the $\overline{M}$ point of the Brillouin zone forming the anisotropic surface Dirac cones. Our calculations of the ${\mathbb{Z}}_{2}$ indices confirm that the system is topologically nontrivial with multiple topological phases in the same material. In addition, the observed nodal-line-like feature formed by bulk bands makes this system topologically rich.

Behavior of gapped and ungapped Dirac cones in the antiferromagnetic topological metal SmBi

We studied the behavior of nontrivial Dirac fermion states in the antiferromagnetic metal SmBi using angle-resolved photoemission spectroscopy (ARPES). The experimental results exhibit multiple Fermi pockets around the $\overline{\mathrm{\ensuremath{\Gamma}}}$ and $\overline{M}$ points along with a band inversion in the spectrum along the $\overline{\mathrm{\ensuremath{\Gamma}}}\text{\ensuremath{-}}\overline{M}$ line consistent with the density functional theory results. In addition, ARPES data reveal Dirac cones at the $\overline{\mathrm{\ensuremath{\Gamma}}}$ and $\overline{M}$ points within the energy gap of the bulk bands. The Dirac cone at $\overline{M}$ exhibits a distinct Dirac point and is intense in the high-photon-energy data, while the Dirac cone at $\overline{\mathrm{\ensuremath{\Gamma}}}$ is intense at low photon energies. Employing ultrahigh-resolution ARPES, we discover destruction of a Fermi surface constituted by the surface states across the Ne\'el temperature of 9 K. Interestingly, the Dirac cone at $\overline{\mathrm{\ensuremath{\Gamma}}}$ is found to be gapped at 15 K, and the behavior remains similar across the magnetic transition. These results reveal complex momentum-dependent gap formation and Fermi surface destruction across the magnetic transition in an exotic correlated topological material; the interplay between magnetism and topology in this system calls for ideas beyond the existing theoretical models.

Orbital angular momentum driven anomalous Hall effect

Orbital angular momentum (OAM) plays a central role in regulating the magnetic state of electrons in nonperiodic systems such as atoms and molecules. In solids, on the other hand, OAM is usually quenched by the crystal field, and thus has a negligible effect on magnetization. Accordingly, it is generally neglected in discussions around band topology such as Berry curvature and intrinsic anomalous Hall effect (AHE). Here, we present a theoretical framework demonstrating that crystalline OAM can be directionally unquenched in transition metal oxides via energetic proximity of the conducting $d$ electrons to the local magnetic moments. We show that this leads to ``composite'' Fermi pockets with topologically nontrivial OAM textures. This enables a giant Berry curvature and a resultant intrinsic nonmonotonic AHE, even in collinearly ordered spin states. We use this model to explain the origin of the giant AHE observed in the forced ferromagnetic state of ${\mathrm{EuTiO}}_{3}$ and propose it as a general scheme for OAM driven AHE.

Temperature dependence of resistivity and temperature coefficient of a single-crystal bismuth nanowire based on the varying scattering mechanism

Temperature dependence of resistivity and temperature coefficient of a single-crystal bismuth nanowire was investigated considering the scattering mechanism for each Fermi pocket of the carrier using relaxation time approximation based on the Boltzmann equation. The scattering mechanism of each bismuth carrier was determined according to the relationship between the mean free path of bulk bismuth and nanowire (diameter: 595 and 345 nm). The calculation and experimental results revealed the dominant contribution of the bulk segment in the room-temperature region, influencing the scattering mechanism, whereas the dominant contribution of the wire segment was observed in the lower-temperature region owing to the substantially larger mean free path of the carrier than the wire diameter. Moreover, the temperature coefficient in the lower-temperature region was determined by the effective masses parallel and perpendicular to the wire length, verifying the unique behavior of the temperature dependence of bismuth nanowires with three-dimensional density of state.

Doped Mott insulators in the triangular-lattice Hubbard model

We investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping $\delta$ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping $\delta\lesssim 10\%$, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave-vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well defined Fermi surface. On further doping, $\delta \approx 10\%\sim 20\%$ SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping $\delta \gtrsim 20\%$, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

Orbital-Selective High-Temperature Cooper Pairing Developed in the Two-Dimensional Limit.

For multiband superconductors, the orbital multiplicity yields orbital differentiation in normal-state properties and can lead to orbital-selective spin-fluctuation Cooper pairing. The orbital-selective phenomenon has become increasingly pivotal in clarifying the pairing "enigma", particularly for multiband high-temperature superconductors. Meanwhile, in one-unit-cell (1-UC) FeSe/SrTiO3, since the standard electron-hole Fermi pocket nesting scenario is inapplicable, the actual pairing mechanism is subject to intense debate. Here, by measuring high-resolution Bogoliubov quasiparticle interference, we report observations of highly anisotropic magnetic Cooper pairing in 1-UC FeSe. Theoretically, it is important to incorporate orbitally selective effects of electronic correlations within a spin-fluctuation pairing calculation, where the dxy orbital becomes coherence-suppressed. The resulting pairing gap is compatible with the experimental findings, which suggests that high-Tc Cooper pairing with orbital selectivity applies to 2D-limit 1-UC FeSe. Our findings imply the general existence of orbital selectivity in iron-based superconductors and the universal significance of electron correlations in high-Tc superconductors.

Doping induced band renormalization in 122-type Fe-based superconductor

We study the electronic structure of a superconducting composition of 122-type Fe-based pnictide material, CaFe1.9Co0.1As2 employing high resolution angle resolved photoemission spectroscopy technique. The experimental results exhibit three bands close to Fermi level at Γ-point of the Brillouin zone among which only one band crosses the Fermi level. In the parent compound, CaFe2As2, all the three bands cross the Fermi level and form three hole pockets. While the destruction of Fermi pockets due to electron doping (Co-substitution dopes electrons into the system) is expected, we observe significant orbital selective band renormalization with respect to the parent compound. It appears that the effect of spin-orbit coupling is stronger in the doped compound.

Pair-density-wave in the strong coupling limit of the Holstein-Hubbard model

A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effective t-J-V model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the K and {K}^{prime} points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge c ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.

Anisotropic surface state in a topological semimetal candidate Ta3SiTe6

Using high-resolution angle-resolved photoemission spectroscopy, we studied the surface state of Ta3SiTe6, a candidate of topological semimetal protected by nonsymmorphic symmetry. Through photon-energy dependent measurements, the surface state near the Fermi level was detected. By determining the band dispersions, we found that the surface state is topological trivial. Around the surface Brillouin zone center, the surface bands disperse linear-like, forming a band crossing (zero energy gap) point at about 0.2 eV below the Fermi level. In Ta3SiTe6's rectangular surface Brillouin zone, the surface bands only cross the Fermi level along one axis, forming two hole-like Fermi pockets near surface Brillouin zone boundaries. Although the observed surface state is not topological, we proposed that its anisotropic Fermi surface topography could be potentially useful for future applications.

Searching for a promising topological Dirac nodal-line semimetal by angle resolved photoemission spectroscopy

Topological semimetals, in which conduction and valence bands cross each other at either discrete points or along a closed loop with symmetry protected in the momentum space, exhibited great potential in applications of optical devices as well as heterogeneous catalysts or antiferromagnetic spintronics, especially when the crossing points/lines matches Fermi level (E F). It is intriguing to find the ‘ideal’ topological semimetal material, in which has a band structure with Dirac band-crossing located at E F without intersected by other extraneous bands. Here, by using angle resolved photoemission spectroscopy, we investigate the band structure of the so-called ‘square-net’ topological material ZrGeS. The Brillouin zone (BZ) mapping shows the Fermi surface of ZrGeS is composed by a diamond-shaped nodal line loop at the center of BZ and small electron-like Fermi pockets around X point. The Dirac nodal line band-crossing located right at E F, and shows clearly the linear Dirac band dispersions within a large energy range >1.5 eV below E F, without intersected with other bands. The obtained Fermi velocities and effective masses along Γ–X, Γ–M and M–X high symmetry directions were 4.5–5.9 eV Å and 0–0.50 m e, revealing an anisotropic electronic property. Our results suggest that ZrGeS, as a promising topological nodal line semimetal, could provide a promising platform to investigate the Dirac-fermions related physics and the applications of topological devising.

Multiband Superconductivity with Sign-Preserving Order Parameter in Kagome Superconductor CsV_{3}Sb_{5}.

The superconductivity of a kagome superconductor CsV_{3}Sb_{5} is studied by scanning tunneling microscopy and spectroscopy at ultralow temperature with high resolution. Two kinds of superconducting gaps with multiple sets of coherent peaks and residual zero-energy density of states (DOS) are observed on both half-Cs and Sb surfaces, implying multiband superconductivity. In addition, in-gap states can be induced by magnetic impurities but not by nonmagnetic impurities, suggesting a sign-preserving or s-wave superconducting order parameter. Moreover, the interplay between charge density waves (CDW) and superconductivity differs on various bands, resulting in different density-of-states distributions. Our results suggest that the superconducting gap is likely isotropic on the sections of Fermi surface that play little roles in CDW, and the superconducting gaps on the sections of Fermi surface with anisotropic CDW gaps are likely anisotropic as well. The residual spectral weights at zero energy are attributed to the extremely small superconducting gap on the tiny oval Fermi pockets. Our study provides critical clues for further understanding the superconductivity and its relation to CDW in CsV_{3}Sb_{5}.

Ground-state phase diagram of the t-t′-J model

We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.

Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions

Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here, we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently-reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\alpha$-RuCl$_3$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed.

Competing phases and critical behaviour in three coupled spinless Luttinger liquids

We study electronic phase competition in a strongly correlated system of three coupled spinless Luttinger liquids—one of the simplest models where topologically nontrivial chiral orders may be realized. We study the problem as a coupled sine-Gordon model, using a perturbative renormalization group (RG) approach. In contrast with counterparts with fewer fermionic species, here the scaling procedure generates off-diagonal contributions to the phase stiffness matrix, which require both rescaling as well as large rotations of the bosonic fields. These rotations, generally non-abelian in nature, introduce a coupling between different interaction channels even at the tree-level order in the coupling constant scaling equations. We study competing phases in this system, taking into account the aforementioned rotations, and determine its critical behaviour in a variety of interaction parameter regimes where perturbative RG is possible. The phase boundaries are found to be of the Berezinskii–Kosterlitz–Thouless type, and we specify the parameter regimes where symmetry breaking between the three flavours of bosonic fields, orders involving different flavours, and chiral orders may be observed. Our approach and findings may be relevant for understanding phases and transitions at high magnetic fields in semimetals such as bismuth featuring three Fermi pockets.

Charge Density Wave and Electron-Phonon Interaction in Epitaxial Monolayer NbSe2 FilmsSupported by the National Natural Science Foundation of China (Grant Nos. 11774154, 11790311, and 12004172), the National Key Research and Development Program of China (Grant No. 2018YFA0306800), the Fundamental Research Funds for the Central Universities (Grant No. 0204-14380186), the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 2020Z172), the

Understanding the interplay between superconductivity and charge-density wave (CDW) in NbSe2 is vital for both fundamental physics and future device applications. Here, combining scanning tunneling microscopy, angle-resolved photoemission spectroscopy and Raman spectroscopy, we study the CDW phase in the monolayer NbSe2 films grown on various substrates of bilayer graphene (BLG), SrTiO3(111), and Al2O3(0001). It is found that the two stable CDW states of monolayer NbSe2 can coexist on NbSe2/BLG surface at liquid-nitrogen temperature. For the NbSe2/SrTiO3(111) sample, the unidirectional CDW regions own the kinks at ±41 meV and a wider gap at 4.2 K. It is revealed that the charge transfer from the substrates to the grown films will influence the configurations of the Fermi surface, and induce a 130 meV lift-up of the Fermi level with a shrink of the Fermi pockets in NbSe2/SrTiO3(111) compared with the NbSe2/BLG. Combining the temperature-dependent Raman experiments, we suggest that the electron-phonon coupling in monolayer NbSe2 dominates its CDW phase transition.

Demonstration of valley anisotropy utilized to enhance the thermoelectric power factor

Valley anisotropy is a favorable electronic structure feature that could be utilized for good thermoelectric performance. Here, taking advantage of the single anisotropic Fermi pocket in p-type Mg3Sb2, a feasible strategy utilizing the valley anisotropy to enhance the thermoelectric power factor is demonstrated by synergistic studies on both single crystals and textured polycrystalline samples. Compared to the heavy-band direction, a higher carrier mobility by a factor of 3 is observed along the light-band direction, while the Seebeck coefficient remains similar. Together with lower lattice thermal conductivity, an increased room-temperature zT by a factor of 3.6 is found. Moreover, the first-principles calculations of 66 isostructural Zintl phase compounds are conducted and 9 of them are screened out displaying a pz-orbital-dominated valence band, similar to Mg3Sb2. In this work, we experimentally demonstrate that valley anisotropy is an effective strategy for the enhancement of thermoelectric performance in materials with anisotropic Fermi pockets.