Fermi Surface Nesting Research Articles

Fully Two-Dimensional Incommensurate Charge Modulation on the Pd-Terminated Polar Surface of PdCoO2.

Here, we use low-temperature scanning tunneling microscopy and spectroscopy to study the polar surfaces of PdCoO2. On the CoO2-terminated polar surface, we detect the quasiparticle interference pattern originating from the Rashba-like spin-split surface states. On the well-ordered Pd-terminated polar surface, we observe a regular lattice that has a larger lattice constant than the atomic lattice of PdCoO2. In comparison with the shape of the hexagonal Fermi surface on the Pd-terminated surface, we identify this regular lattice as a fully two-dimensional incommensurate charge modulation that is driven by the Fermi surface nesting. More interestingly, we also find the moiré pattern induced by the interference between the two-dimensional incommensurate charge modulation in the Pd layer and its atomic lattice. Our results not only show a new charge modulation on the Pd surface of PdCoO2 but also pave the way for fully understanding the novel electronic properties of this material.

Structural instability and charge modulations in the kagome superconductor AV3Sb5

Recently, both charge density wave (CDW) and superconductivity have been observed in the kagome compounds $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$. However, the nature of the CDW that results in many novel charge modulations is still under hot debate. Based on the first-principles calculations, we discover two kinds of CDW states in $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$, namely, the trimerized-hexamerized $2\ifmmode\times\else\texttimes\fi{}2$ phase and the dimerized $4\ifmmode\times\else\texttimes\fi{}1$ phase. Our phonon spectrum and electronic Lindhard function calculations reveal that the most intensive structural instability in $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ originates from a combined in-plane vibration mode of V atoms through the electron-phonon coupling, rather than the Fermi surface nesting effect. More importantly, a metastable $4\ifmmode\times\else\texttimes\fi{}1$ phase with the V-V dimer pattern and twofold symmetric bow-tie-shaped charge modulation is revealed in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$. Further analyses demonstrate that both the in-plane phonon instability and $c$ direction interaction play important roles during the $4\ifmmode\times\else\texttimes\fi{}1$ phase formation, which provides key understanding for the mechanism of the $4\ifmmode\times\else\texttimes\fi{}1$ CDW and relative novel phenomena in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.

Origin and strain tuning of charge density wave in LaTe3

We study the origin of charge density wave (CDW) in rare-earth tritelluride LaTe3 and the strain tuning effect on CDW in monolayer LaTe3 by first-principles calculations. The calculations of the electronic structure, phonon spectrum, electron susceptibility, and electron-phonon coupling (EPC) matrix show that the origin of CDW in LaTe3 is momentum-dependent EPC rather than Fermi-surface nesting. The unidirectional CDW with a wave-vector QCDW≈2/7c∗ is the most stable state. We study the biaxial strain effect on CDW in monolayer LaTe3 by evaluating the total energy, CDW-related lattice distortions, and phonon spectra. Our results show that the tensile strain can enhance CDW order, while the compressive strain can inhibit CDW order. As the CDW order is fully suppressed, superconductivity could be induced. Our study may help to clarify the mechanism of CDW in LaTe3 and find the effective tuning method of CDW in monolayer or few-layer configuration.

Fermi-Surface Origin of Skyrmion Lattices in Centrosymmetric Rare-Earth Intermetallics.

We show from first principles that barrel-shaped structures within the Fermi surface of the centrosymmetric intermetallic compounds GdRu_{2}Si_{2} and Gd_{2}PdSi_{3} give rise to Fermi surface nesting, which determines the strength and sign of quasi-two-dimensional Ruderman-Kittel-Kasuya-Yosida pairwise exchange interactions between the Gd moments. This is the principal mechanism leading to their helical single-q spin-spiral ground states, providing transition temperatures and magnetic periods in good agreement with experiment. Using atomistic spin-dynamic simulations, we draw a direct line between the subtleties of the three-dimensional Fermi surface topology and the stabilization of a square skyrmion lattice in GdRu_{2}Si_{2} at applied magnetic fields as observed in experiment.

Fermi surface nesting and the Lindhard response function in the kagome superconductor CsV3Sb5

The recently discovered kagome net compounds AV3Sb5 (A = K, Rb, and Cs) become superconducting on cooling, in addition to displaying interesting topological features in the electronic structure. They also exhibit charge density wave ordering, which manifests as a breathing-mode distortion in the kagome layers. It has been suggested that such ordering derives from nesting between saddle points on the Fermi surface. In aid of the evolving understanding of this intriguing materials class, we present calculations of Fermi surface nesting and Lindhard susceptibility of CsV3Sb5. The breathing mode distortions appear to not display a simple link with Fermi surface nesting (FSN) and do not display the signatures of a Peierls-like transition. The FSN is agnostic to changes along kz and is only mildly impacted by small shifts of the Fermi level. The results suggest that FSN is largely independent of specific features in the saddle point.

Nested Fermi surfaces and correlated electronic phases in hole-doped semiconductor quantum wells

We demonstrate the existence of novel interaction effects in hole-doped semiconductor quantum wells which are connected to dramatic changes in the Fermi surface geometry occurring upon variation of the doping. We present band structure calculations showing that quantum wells formed in $p$-type cubic semiconductors develop perfectly nested Fermi surfaces at a critical hole density $p\ensuremath{\sim}1/{d}^{2}$ set by the width $d$ of the quantum well. Nesting gives rise to competing superconducting and charge or spin density wave order, which we analyze using the perturbative renormalization group method. The correlated phases may be created or destroyed by tuning the hole density towards or away from the critical density. Our results establish $p$-type semiconductor quantum wells as a platform for novel correlated phases, which may be precisely controlled using electrostatic gating and external magnetic fields.

Non-Maxwell–Boltzmann dependence of channel carrier concentration in a quasi one dimensional charge density wave channel in the ballistic transport regime

With the aid of a coherent transport model utilizing the non-equilibrium Green function approach, a three terminal device with metallic gate, source and drain and a quasi one dimensional charge density wave (CDW) channel is simulated focussing on the transistor behaviour brought about by a sweep of the channel potential or equivalently the chemical potential in the channel. The channel is strongly insulating only at half-filling and moving to lower and higher carrier concentrations both incur a mean field phase transition to a conducting state. With the aid of conductance calculations for a pinned CDW condensate, we present calculations for the sub-threshold slope in terms of the hopping parameter or equivalently the width of the tight-binding chain. The effects of source to drain bias and length are examined. The conductance profiles are analyed in relation to transmission profiles. The observed CDW profiles are explained in terms of filling and Fermi surface nesting. Boundary conditions, gap equations and response functions are shown to reveal the commensurability conditions and size of the transport gap. The channel carrier concentration is modulated in an athermal (non-Maxwellian–Boltzmann) fashion, thereby making it an interesting prospect for steep transistors.

Charge ordering mechanism in silver difluoride

Using Density Functional Theory, competition between Mott-Hubbard and intervalence charge transfer mechanism of electron localization is revealed in AgF$_2$, an important silver analogue of oxocuprates. We show that at reduced temperature and electron correlations AgF$_2$ becomes metallic and dynamically unstable in respect to CDW phonon modes that promote charge ordering. The CDW instability is closely related to Kohn anomaly and Fermi surface nesting. The long advocated KBrF$_4$ type CDW Ag$^{1+/3+}$F$_2$ structure and its facile transformation to the ground state Ag$^{2+}$F$_2$ phase is explained. Our results point out to intimate interplay between lattice, charge and spin degrees of freedom in seemingly simplistic binary metal fluoride.

Correlated physics in an artificial triangular anti-dot lattice

This work considers a two-dimensional artificial triangular anti-dot lattice (TAL): a semiconductor-based artificial crystal hosting Dirac cones, flat bands, and Fermi surface nesting. All such single-particle features have dramatic implications for the emergent correlated phases. This work predominantly focuses on the existence of a robust flat band and enumerates the possible correlated phases that follow. We find that the flat band is generated, in the single-particle theory, when charges align themselves along a kagome lattice with the same period as the TAL. The correlated phases are studied using complementary techniques of expansion in strong and weak Coulomb interactions. Our microscopic modeling shows that for the purpose of generating strongly correlated phases, hole-doped TALs have significant advantages over electron-doped ones.

Origin of charge density wave in the layered kagome metal CsV3Sb5

Using first-principles calculations, we identify the origin of the observed charge density wave (CDW) formation in a layered kagome metal ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$. It is revealed that the structural distortion of kagome lattice forming the trimeric and hexameric V atoms is accompanied by the stabilization of quasimolecular states, which gives rise to the opening of CDW gaps for the V-derived multibands lying around the Fermi level. We, thus, propose the Jahn-Teller-like instability having the local lattice distortion and its derived quasimolecular states as a driving force of the CDW order. Specifically, the saddle points of multiple Dirac bands near the Fermi level, located at the $M$ point, are hybridized to disappear along the ${k}_{z}$ direction, therefore, not supporting the widely accepted Peierls-like electronic instability due to Fermi surface nesting. It is further demonstrated that applied hydrostatic pressure significantly reduces the interlayer spacing to destabilize the quasimolecular states, leading to a disappearance of the CDW phase at a pressure of $\ensuremath{\sim}2\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$. The presently proposed underlying mechanism of the CDW order in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ can also be applicable to other isostructural kagome lattices, such as ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$ and ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$.

Real-space observation of incommensurate spin density wave and coexisting charge density wave on Cr (001) surface

In itinerant magnetic systems, a spin density wave (SDW) state can be induced by Fermi surface nesting and electron-electron interaction. It may intertwine with other orders such as charge density wave (CDW), while their relation is still yet to be understood. Here via spin-polarized scanning tunneling microscopy, we directly observed long-range spin modulation on Cr(001) surface, which corresponds to the well-known incommensurate SDW of bulk Cr. It displays 6.0 nm in-plane period and anti-phase behavior between adjacent (001) planes. Meanwhile, we simultaneously observed the coexisting CDW with half the period of SDW. Such SDW/CDW have highly correlated domain structures and are in-phase. Surprisingly, the CDW displays a contrast inversion around a density-of-states dip at −22 meV, indicating an anomalous CDW gap opened below EF. These observations support that the CDW is a secondary order driven by SDW. Our work is not only a real-space characterization of incommensurate SDW, but also provides insights on how SDW and CDW coexist.

Charge-Density-Wave-Induced Peak-Dip-Hump Structure and the Multiband Superconductivity in a Kagome Superconductor CsV_{3}Sb_{5}.

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal AV_{3}Sb_{5} (A=K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV_{3}Sb_{5}. The spectra around K[over ¯] is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below E_{F}. The peak-dip-hump line shape is contributed by linearly dispersive Dirac bands in the lower branch and a dispersionless flat band close to E_{F} in the upper branch. The electronic instability via Fermi surface nesting could play a role in determining these CDW-related features. The superconducting gap of ∼0.4 meV is observed on both the electron band around Γ[over ¯] and the flat band around K[over ¯], implying the multiband superconductivity. The finite density of states at E_{F} in the CDW phase is most likely in favor of the emergence of multiband superconductivity, particularly the enhanced density of states associated with the flat band. Our results not only shed light on the controversial origin of the CDW, but also offer insights into the relationship between CDW and superconductivity.

Orbital- and atom-dependent linear dispersion across the Fermi level induces charge density wave instability in EuTe4

In the Peierls description of a charge density wave (CDW), Fermi surface nesting (FSN)---defined by the divergence of the imaginary part of electronic susceptibility, i.e., $\mathrm{Im}{{\ensuremath{\chi}}_{0}}$---leads to divergence of the real part, thus inducing CDW instability at wave vector ${\mathbf{q}}_{\mathrm{CDW}}$. Here we show that the divergence of $\mathrm{Im}{{\ensuremath{\chi}}_{0}}$ implying a divergence of $\mathrm{Re}{{\ensuremath{\chi}}_{0}}$ at the same ${\mathbf{q}}_{\mathrm{CDW}}$ breaks down for three-dimensional Fermi surfaces and is particularly severe for linearly dispersing electronic bands across the Fermi level (${E}_{\mathrm{F}}$), as exemplified by rare-earth tellurides $R{\mathrm{Te}}_{n}$. By calculating the orbital-, atom-, and momentum-resolved contribution to ${\ensuremath{\chi}}_{0}$ of ${\mathrm{EuTe}}_{4}$, we find that FSN and CDW instability are not driven by the same atoms and orbitals but from different ones. This unique behavior is enabled by linearly dispersing bands across ${E}_{\mathrm{F}}$ with constant Fermi surface velocity that assists electron-hole pairs to form not only at ${E}_{\mathrm{F}}$ but also across ${E}_{\mathrm{F}}$ at ${\mathbf{q}}_{\mathrm{CDW}}$, hence allowing different orbitals to contribute to the divergence of $\mathrm{Re}{{\ensuremath{\chi}}_{0}}$ and $\mathrm{Im}{{\ensuremath{\chi}}_{0}}$. The above scenario is general and applicable to recent observations of CDWs and spin density waves (SDWs) from linearly dispersing bands in several Dirac and Weyl semimetals and kagome metals. Moreover, as we demonstrate, such component-resolved analysis provides focused input to engineer CDW and SDW states.

Twofold van Hove singularity and origin of charge order in topological kagome superconductor CsV3Sb5

The layered vanadium antimonides AV3Sb5 (A = K, Rb, Cs) are a recently discovered family of topological kagome metals that exhibit a range of strongly correlated electronic phases including charge order and superconductivity. However, it is not yet understood how the distinctive electronic structure of the kagome lattice is linked to the observed many-body phenomena. Here we combine angle-resolved photoemission spectroscopy and density functional theory to reveal multiple kagome-derived van Hove singularities (vHS) coexisting near the Fermi level of CsV3Sb5 and analyse their contribution to electronic symmetry breaking. The vHS are characterized by two distinct sublattice flavours (p-type and m-type), which originate, respectively, from their pure and mixed sublattice characters. These twofold vHS flavours of the kagome lattice critically determine the pairing symmetry and unconventional ground states emerging in the AV3Sb5 series. We establish that, among the multiple vHS in CsV3Sb5, the m-type vHS of the dxz/dyz kagome band and the p-type vHS of the dxy/dx2–y2 kagome band are located very close to the Fermi level, setting the stage for electronic symmetry breaking. The former band is characterized by pronounced Fermi surface nesting, while the latter exhibits a higher-order vHS. Our work reveals the essential role of kagome-derived vHS for the collective phenomena realized in the AV3Sb5 family. Spectroscopic measurements show how the features of the band structure related to the kagome lattice in CsV3Sb5 contribute to the observed strongly correlated phases.

Electron-momentum dependence of electron-phonon coupling underlies dramatic phonon renormalization in YNi2B2C

Electron-phonon coupling, i.e., the scattering of lattice vibrations by electrons and vice versa, is ubiquitous in solids and can lead to emergent ground states such as superconductivity and charge-density wave order. A broad spectral phonon line shape is often interpreted as a marker of strong electron-phonon coupling associated with Fermi surface nesting, i.e., parallel sections of the Fermi surface connected by the phonon momentum. Alternatively broad phonons are known to arise from strong atomic lattice anharmonicity. Here, we show that strong phonon broadening can occur in the absence of both Fermi surface nesting and lattice anharmonicity, if electron-phonon coupling is strongly enhanced for specific values of electron-momentum, k. We use inelastic neutron scattering, soft x-ray angle-resolved photoemission spectroscopy measurements and ab-initio lattice dynamical and electronic band structure calculations to demonstrate this scenario in the highly anisotropic tetragonal electron-phonon superconductor YNi2B2C. This new scenario likely applies to a wide range of compounds.

Emergence of high superconductivity in a layered TaS3 crystal

A novel layered P21/m TaS3 is revealed to have the highest superconducting Tc of 23.6 K at 50 GPa among the reported transition metal chalcogenides. The high Tc mainly arises from the nested Fermi surface and induced softened low-frequency phonons.

Nearly fully opened charge density wave gap in the quasi-two-dimensional conductor γ−Mo4O11 : A comparative study with η−Mo4O11

The accommodation of Luttinger liquid behavior and unique quasiparticles in the charge density wave (CDW) state has led to renewed interest in the low-dimensional molybdenum bronzes. Here, the authors report a comprehensive experimental study on the quasi-two-dimensional CDW oxide bronzes Mo${}_{4}$O${}_{11}$, in which the CDW instability is dominated by hidden Fermi surface nesting, resulting in magnetic field induced quantum oscillations. Different from the monoclinic $\ensuremath{\eta}$ phase, the orthorhombic $\ensuremath{\gamma}$ phase shows a flexible CDW transition with a nearly fully opened gap, as seen in nonlinear transport behavior related to the CDW sliding motion, which is only observed in quasi-one-dimensional systems.

Collapse of a region of the magnetic phase diagram of elemental terbium under a strain-induced Lifshitz transition

AC susceptibility and neutron scattering measurements are used to study the magnetic field-temperature magnetic phase diagram of a Tb single crystal under uniaxial tension along its hexagonal $c$ axis. An external magnetic field is applied in the basal plane. We focus on the region in the phase diagram that corresponds to the helical antiferromagnetic phase and find that this region collapses when the uniaxial tension is increased beyond a critical value as low as 600 bar. There are strong reasons to associate this collapse with an underlying Lifshitz transition in the Fermi surface of Tb's valence electrons. We use a finite-temperature ab initio theory to analyze our measurements, obtaining a pressure-temperature magnetic phase diagram in very good agreement with experiment. Our calculations indicate that short- and long-range magnetic order has a crucial effect on the Fermi surface nesting and consequent magnetism of Tb.

Controllable phase transitions between multiple charge density waves in monolayer 1T-VSe2 via charge doping

Two-dimensional materials are known to possess emergent properties that are not found in their bulk counterparts. Recent experiments have shown a 7×3 charge density wave (CDW) in monolayer 1 T-VSe2, in contrast to the 4×4×3 phase in bulk. Here, via first-principles calculations, we show that multiple CDW phases compete in monolayer VSe2, the ground state of which can be tuned by charge doping. With doping, the 7×3 CDW of the pristine VSe2 transfers to a 4×4 or 3×3 phase, at critical doping concentrations of around 0.2 electrons per formula unit and 0.2 holes per formula unit, respectively. These transitions are further understood by analyzing the role of Fermi surface nesting and momentum-dependent electron–phonon coupling in monolayer 1T-VSe2. These results make VSe2 an appealing material for electronic devices based on controllable CDW phase transitions.

Martensitic transformation mechanism of Mg-Sc lightweight shape memory alloys

Mg-Sc alloys are known as novel and promising lightweight shape memory alloys (LWSMAs), which have outstanding performance. Yet, a precise understanding of the microscopic picture and interactions governing the martensitic transformation (MT) remains elusive. We systematically investigate the MT of Mg-Sc alloys using first-principles methods. The result of generalized solid-state nudged elastic band methods confirms that no energy barrier inhibits the MT. We show that the bcc structure of Mg26Sc6 is dynamical instability at 0 K caused by electron-phonon coupling and Fermi surface nesting. Particularly, the high-temperature stability of Mg26Sc6 is revealed for the first time using the temperature-dependent effective potential method. The softening of the acoustic mode at Γ-R corresponds to two neighboring (1 0 1) planes moving towards each other, and forms martensite phase. Our calculations provide the complete and atomic-level mechanism for the MT of Mg-Sc alloys and shed some light on the design of new LWSMAs.