Anisotropic Fermi Surface Research Articles

Electronic structure investigation and anisotropic phonon anharmonicity in ternary ZrGeTe4 single crystals

Ternary two-dimensional (2D) transition metal chalcogenides have gained immense attention because of their ability to overcome the intrinsic limitations of their binary counterparts. Layered 2D materials are important for future electronic and photonic devices owing to their low structural symmetry and in-plane anisotropy with tunable bandgap. Herein, the electronic structure and detailed vibrational properties of bulk ZrGeTe4 layered single crystals were investigated using angle-resolved photoemission spectroscopy (ARPES) and Raman scattering (RS). The ARPES results revealed an anisotropic Fermi surface of different momentum along kx and ky from the zone center and an anisotropic band structure with varying band curvatures along the high-symmetry directions. Furthermore, the RS of ZrGeTe4 was investigated under different polarizations and varying temperatures. The polarized RS exhibited twofold and fourfold symmetry orientations in different configurations, revealing the anisotropic phonon dispersions for bulk ZrGeTe4. The observed softening of Raman modes was corroborated with the anharmonic phonon dispersion, which was further supported by our third-order force constant calculations of thermal transport using density functional theory. Low lattice thermal conductivity with increasing temperature is linked with enhanced phonon–phonon scattering, which is evident from the decreased phonon lifetime and peak linewidth. In addition to these fundamental aspects, the anisotropic nature and unique layered structure of such materials reveal their bright future for next-generation nanoelectronic applications.

Magnetic field-dependent thermopower: Insights into spin and quantum interactions

This study explores the impact of external magnetic fields on thermoelectric properties, focusing on the interplay of spin and quantum effects. Using gadolinium (Gd) as a case study, we observed anomalous magneto-thermopower trends, with a reduction in thermopower at ∼35 K and an enhancement at TC ≈ 293 K under high magnetic fields. Comprehensive temperature and field-dependent measurements, including specific heat capacity, magnetic susceptibility, and Hall effect, were performed to uncover the underlying mechanisms. We derived a relation for the total thermopower of an uncompensated ferromagnetic metal and calculated multi-band carrier characteristics, such as concentration and mobility, using the maximum entropy principle. Our findings reveal a ∼70 % suppression of the magnetic contribution to specific heat capacity under a 12 T field and a positive magnon-drag contribution to the total thermopower. Field-dependent Hall measurements indicate that the anomalous Hall effect is dominated by intrinsic contributions from Berry curvature. Additionally, transverse magnetoresistance data suggest anisotropic Fermi surfaces, domain movement, suppression of spin-flip effects, and Fermi surface modifications. First-principles calculations based on Density Functional Theory (DFT) further support these findings. These calculations reveal significant Berry curvature contributions, leading to an anomalous Hall conductivity of approximately 1260 S/cm at the Fermi level. The enhancement of thermopower near TC is primarily attributed to the suppression of magnon-drag and the imbalance in carrier mobility and relaxation times, driven by spin and quantum effects. These combined effects result in a ∼50 % increase in thermopower and a ∼150 % improvement in zT at 12 T. The notable peak in zT at cryogenic temperatures highlights a potential pathway for designing efficient thermoelectric materials for cryogenic cooling applications. Our results demonstrate the significance of field-dependent spin and quantum effects in enhancing thermoelectric performance, offering new directions for thermoelectric research and material design.

Electronic Transport and Interaction of Lattice Dynamics in Topological Nodalline Semimetal HfAs2 Single Crystals

AbstractTopological semimetals represent a novel class of quantum materials displaying non‐trivial topological states that host Dirac/Weyl fermions. The intersection of Dirac/Weyl points gives rise to essential properties in a wide range of innovative transport phenomena, including extreme magnetoresistance, high mobilities, weak antilocalization, electron hydrodynamics, and various electro‐optical phenomena. In this study, the electronic, transport, phonon scattering, and interrelationships are explored in single crystals of the topological semimetal HfAs2. It reveals a weak antilocalization effect at low temperatures with high carrier density, which is attributed to perfectly compensated topological bulk and surface states. The angle‐resolved photoemission spectroscopy (ARPES) results show anisotropic Fermi surfaces and surface states indicative of the topological semimetal, further confirmed by first‐principle density functional theory (DFT) calculations. Moreover, the lattice dynamics in HfAs2 are investigated both with the Raman scattering and density functional theory. The phonon dispersion, density of states, lattice thermal conductivity, and the phonon lifetimes are computed to support the experimental findings. The softening of phonons, the broadening of Raman modes, and the reduction of phonon lifetimes with temperature suggest the enhancement of phonon anharmonicity in this new topological material, which is crucial for boosting the thermoelectric performance of topological semimetals.

Toward 1D Transport in 3D Materials: SOC-Induced Charge-Transport Anisotropy in Sm3ZrBi5.

1D charge transport offers great insight into strongly correlated physics, such as Luttinger liquids, electronic instabilities, and superconductivity. Although 1D charge transport is observed in nanomaterials and quantum wires, examples in bulk crystalline solids remain elusive. In this work, it is demonstrated that spin-orbit coupling (SOC) can act as a mechanism to induce quasi-1D charge transport in the Ln3MPn5 (Ln = lanthanide; M = transition metal; Pn = Pnictide) family. From three example compounds, La3ZrSb5, La3ZrBi5, and Sm3ZrBi5, density functional theory calculations with SOC included show a quasi-1D Fermi surface in the bismuthide compounds, but an anisotropic 3D Fermi surface in the antimonide structure. By performing anisotropic charge transport measurements on La3ZrSb5, La3ZrBi5, and Sm3ZrBi5, it is demonstrated that SOC starkly affects their anisotropic resistivity ratios (ARR) at low temperatures, with an ARR of ≈4 in the antimonide compared to ≈9.5 and ≈22 (≈32 after magnetic ordering) in La3ZrBi5 and Sm3ZrBi5, respectively. This report demonstrates the utility of spin-orbit coupling to induce quasi-low-dimensional Fermi surfaces in anisotropic crystal structures, and provides a template for examining othersystems.

Probing the Anisotropic Fermi Surface in Tetralayer Graphene via Transverse Magnetic Focusing.

Bernal-stacked tetralayer graphene (4LG) exhibits intriguing low-energy properties, featuring two massive sub-bands and showcasing diverse features of topologically distinct, anisotropic Fermi surfaces, including Lifshitz transitions and trigonal warping. Here, we study the influence of the band structure on electron dynamics within 4LG using transverse magnetic focusing. Our analysis reveals two distinct focusing peaks corresponding to the two sub-bands. Furthermore, we uncover a pronounced dependence of the focusing spectra on crystal orientations, indicative of an anisotropic Fermi surface. Utilizing the semiclassical model, we attribute this orientation-dependent behavior to the trigonal warping of the band structure. This phenomenon leads to variations in electron trajectories based on crystal orientation. Our findings not only enhance our understanding of the dynamics of electrons in 4LG but also offer a promising method for probing anisotropic Fermi surfaces in other materials.

Influence of High Surfactant Concentrations on the Morphology and Crystallinity of Electrodeposited Antimony and Bismuth Nanowires

Antimony and bismuth nanowires are excellent model systems to investigate the interplay of various size-dependent transport phenomena relevant for applications in thermoelectrics, spintronics, or catalysis. The properties of these nanowires can be significant influenced by size effects due to the large mean free path and Fermi wavelength of charge carriers and phonons. Since antimony and bismuth possess highly anisotropic Fermi surfaces, the transport is also strongly dependent on the crystallographic orientation. Therefore, it is very important to develop and control suitable electrodeposition processes that allow us to understand the nanowire growth and to accordingly adjust preferred orientation and morphology of the synthesized nanowires.The so called template route employed in the presented work allows to control number density, alignment, geometry, length and diameter of the nanowires. The electrolytes and plating processes influence crystallinity, crystal orientation, and morphology of the electrodeposited materials. Here, antimony and bismuth nanowires are grown by potentiostatic electrodeposition in polycarbonate etched ion-track membranes using SbCl3 and BiCl3 in aqueous electrolytes.In this talk, we will show the influence of the presence of nonionic and anionic surfactants in high concentrations in the electrolyte during the electrodeposition of Bi and Sb nanowires. The recorded current-time curves of the plating process will be presented. Systematic characterization of the nanowires by scanning- and transmission electron microscopy, and X-ray diffraction reveal a strong change in crystallinity as a function of surfactant concentration, which will be discussed in detail.

On non-local electrical transport in anisotropic metals

We discuss various aspects of nonlocal electrical transport in anisotropic metals. For a metal with circular Fermi surface, the scattering rates entering the local conductivity and viscosity tensors are well-defined, corresponding to eigenfrequencies of the linearized collision operator. For anisotropic metals, we provide generalized formulas for these scattering rates and use a variational approximation to show how they relate to microscopic transition probabilities. We develop a simple model of a collision operator for a metal of arbitrary Fermi surface with finite number of quasi-conserved quantities, and derive expressions for the wavevector-dependent conductivity σ(q) and the spatially-varying conductivity σ(x) for a long, narrow channel. We apply this to the case of different rates for momentum-conserving and momentum-relaxing scattering, deriving closed-form expressions for σ(q) and σ(x) — beyond generalizing from circular to arbitrary Fermi surface geometry, this represents an improvement over existing methods which solve the relevant differential equation numerically rather than in closed form. For the specific case of a diamond Fermi surface, we show that, if transport signatures were interpreted via a model for a circular Fermi surface, the diagnosis of the underlying transport regime would differ based on experimental orientation and based on whether σ(q) or σ(x) was considered. Finally, we discuss the bulk conductivity. While the common lore is that “momentum”-conserving scattering does not affect bulk resistivity, we show that crystal momentum-conserving scattering — such as normal electron-electron scattering — can affect the bulk resistivity for an anisotropic Fermi surface. We derive a simple formula for this contribution.

Origin of the Anomalous Electrical Transports in Quasi-One-Dimensional Ta2NiSe7.

Exploration of exotic transport behavior is of great interest and importance for revealing the properties of the CDW phase of quasi-one-dimensional Ta2NiSe7. We report the anisotropic electrical transport properties of Ta2NiSe7 single crystals in the CDW phase. The anisotropic constant (γ = ρb/ρc) increased rapidly at TCDW = 60 K upon cooling. The results of the Hall resistivity show that both the concentrations and mobilities of carriers change abruptly at TCDW. The out-of-plane AMR exhibits C2 and C4 symmetry components while the in-plane AMR exhibits C2, C4, and C6 at the CDW state. The planar Hall effect is observed in Ta2NiSe7 at low temperature, which is suggested to originate from the anisotropic orbital magnetoresistance. The calculated results show that the Fermi surface of Ta2NiSe7 was slightly reconstructed due to the CDW transition. This work highlights the enhancement of Fermi surface anisotropy during CDW formation and provides a novel approach to study the CDW materials.

Magneto-electronic coupling to the anomalous lattice expansion in Bi1.8Sb0.2Te[formula omitted] crystal

Our low-temperature synchrotron diffraction studies reveal an anomalous thermal expansion below ∼ 25 K (Tm). Below Tm, the Shubnikov-de Haas (SdH) oscillations are evident and anisotropic with respect to magnetic field, suggesting an anisotropic Fermi surface. Thermal variation of magnetization result shows a minimum around Tm, pointing to a significant magnetoelastic coupling. Paramagnetic singularities in the magnetization curve indicate the robust topologically-protected surface state. Careful comparison of the resistivity and magnetization results link the elastic coupling to the magnetic and electronic structure in Bi1.8Sb0.2Te3, which has not been explored in the well-studied pristine compound Bi2Te3.

Influence of Magnetic and Electric Fields on Universal Conductance Fluctuations in Thin Films of the Dirac Semimetal Cd3As2.

Time-reversal invariance (TRS) and inversion symmetry (IS) are responsible for the topological band structure in Dirac semimetals (DSMs). These symmetries can be broken by applying an external magnetic or electric field, resulting in fundamental changes to the ground state Hamiltonian and a topological phase transition. We probe these changes using universal conductance fluctuations (UCF) in the prototypical DSM, Cd3As2. With increasing magnetic field, the magnitude of the UCF decreases by a factor of , in agreement with numerical calculations of the effect of broken TRS. In contrast, the magnitude of the UCF increases monotonically when the chemical potential is gated away from the charge neutrality point. We attribute this to Fermi surface anisotropy rather than broken IS. The concurrence between experimental data and theory provides unequivocal evidence that UCF are the dominant source of fluctuations and offers a general methodology for probing broken-symmetry effects in topological quantum materials.

Fermi-Arc Metals.

We predict a novel metallic state of matter that emerges in a Weyl-semimetal superstructure withspatially varying Weyl-node positions. In the new state, the Weyl nodes are stretched into extended, anisotropic Fermi surfaces, which can be understood as being built from Fermi arclike states. This "Fermi-arc metal" exhibits the chiral anomaly of the parental Weyl semimetal. However, unlike in the parental Weyl semimetal, in the Fermi-arc metal the "ultraquantum state," in which the anomalous chiral Landau level is the only state at the Fermi energy, is already reached for a finite energy window at zero magnetic field. Thedominance of the ultraquantum state implies a universal low-field ballistic magnetoconductance and the absence of quantum oscillations, making the Fermi surface "invisible" to de Haas-van Alphen and Shubnikov-de Haas effects, although it signifies its presence in other response properties.

Kinetic theory of the nonlocal electrodynamic response in anisotropic metals: Skin effect in 2D systems

The electrodynamic response of ultrapure materials at low temperatures becomes spatially nonlocal. This nonlocality gives rise to phenomena such as hydrodynamic flow in transport and the anomalous skin effect in optics. In systems characterized by an anisotropic electronic dispersion, the nonlocal dynamics becomes dependent on the relative orientation of the sample with respect to the applied field, in ways that go beyond the usual, homogeneous response. Such orientational dependence should manifest itself not only in transport experiments, as recently observed, but also in optical spectroscopy. In this paper, we develop a kinetic theory for the distribution function and the transverse conductivity of two- and three-dimensional Fermi systems with anisotropic electronic dispersion. By expanding the collision integral into the eigenbasis of a collision operator, we include momentum-relaxing scattering as well as momentum-conserving collisions. We examine the isotropic 2D case as a reference, as well as anisotropic hexagonal and square Fermi-surface shapes. We apply our theory to the quantitative calculation of the skin depth and the surface impedance, in all regimes of skin effect. We find qualitative differences between the frequency dependence of the impedance in isotropic and anisotropic systems. Such differences are shown to persist even for more complex 2D Fermi surfaces, including the ``supercircle'' geometry and an experimental parametrization for ${\mathrm{PdCoO}}_{2}$, which deviate from an ideal polygonal shape. We study the orientational dependence of skin effect due to Fermi-surface anisotropy, thus providing guidance for the experimental study of nonlocal optical effects.

Large 3D anisotropy of magnetoresistance in MoAlB

Materials with large three-dimensional (3D) anisotropic magnetoresistance (MR) have very important applications in anisotropic magnetoresistance sensors and magnetometers. Herein, we have observed a large 3D anisotropy of MR in nonmagnetic MoAlB single crystal. Specially, the MR ratio (MRa: MRb: MRc) reaches up to 140.5 : 1: 22, when electric current is along a-/b-/c-axis with an applied magnetic field of 8.5 T at 5 K. To clarify the origins of 3D anisotropic MR, angular MR and direction-dependent Hall coefficient measurements as well as first-principles calculations were performed. The nearly electron-hole compensation and the mixed d-p orbital texture are the important origins of the MR effect along a-/c-axis, and the anisotropy of MR originates from the anisotropic Fermi surface and carrier scattering along a-/c-axis in MoAlB. Whereas, the open orbit is a dominant origin along b-axis of MoAlB. Furthermore, the factors affecting the magnitude of MR are given by using two-band model, and possible control strategies are proposed. This work not only proposes a new idea for exploring single-phase nonmagnetic 3D anisotropic MR material, but also provides a key material for the design and development of new 3D anisotropic magnetoresistance sensors and magnetometers in the future.

Phonon-limited resistivity of multilayer graphene systems

We calculate the theoretical contribution to the doping and temperature ($T$) dependence of electrical resistivity due to scattering by acoustic phonons in Bernal bilayer graphene (BBG) and rhombohedral trilayer graphene (RTG). We focus on the role of nontrivial geometric features of the detailed, anisotropic $k\cdot p$ band structures of these systems - e.g. Van Hove singularities, Lifshitz transitions, Fermi surface anisotropy, and band curvature near the gap - whose effects on transport have not yet been systematically studied. We find that these geometric features strongly influence the temperature and doping dependencies of the resistivity. In particular, the band geometry leads to a nonlinear $T$-dependence in the high-$T$ equipartition regime, complicating the usual $T^4$ to $T$ Bloch-Gr\"{u}neisen crossover. Our focus on BBG and RTG is motivated by recent experiments in these systems that have discovered several exotic low-$T$ superconductivity proximate to complicated hierarchies of isospin-polarized phases. These interaction-driven phases are intimately related to the geometric features of the band structures, highlighting the importance of understanding the influence of band geometry on transport. While resolving the effects of the anisotropic band geometry on the scattering times requires nontrivial numerical solution, our approach is rooted in intuitive Boltzmann theory. We compare our results with recent experiment and discuss how our predictions can be used to elucidate the relative importance of various scattering mechanisms in these systems.

Resistivity scaling in CuTi determined from transport measurements and first-principles simulations

The resistivity size effect in the ordered intermetallic CuTi compound is quantified using in situ and ex situ thin film resistivity ρ measurements at 295 and 77 K, and density functional theory Fermi surface and electron–phonon scattering calculations. Epitaxial CuTi(001) layers with thickness d = 5.8–149 nm are deposited on MgO(001) at 350 °C and exhibit ρ vs d data that are well described by the classical Fuchs and Sondheimer model, indicating a room-temperature effective electron mean free path λ = 12.5 ± 0.6 nm, a bulk resistivity ρo = 19.5 ± 0.3 μΩ cm, and a temperature-independent product ρoλ = 24.7 × 10−16 Ω m2. First-principles calculations indicate a strongly anisotropic Fermi surface with electron velocities ranging from 0.7 × 105 to 6.6 × 105 m/s, electron–phonon scattering lengths of 0.8–8.5 nm (with an average of 4.6 nm), and a resulting ρo = 20.6 ± 0.2 μΩ cm in the (001) plane, in excellent agreement (7% deviation) with the measurements. However, the measured ρoλ is almost 2.4 times larger than predicted, indicating a break-down of the classical transport models. Air exposure causes a 6%–30% resistivity increase, suggesting a transition from partially specular (p = 0.5) to completely diffuse surface scattering due to surface oxidation as detected by x-ray photoelectron spectroscopy. Polycrystalline CuTi layers deposited on SiO2/Si substrates exhibit a 001 texture, a grain width that increases with d, and a 74%–163% larger resistivity than the epitaxial layers due to electron scattering at grain boundaries. The overall results suggest that CuTi is a promising candidate for highly scaled interconnects in integrated circuits only if it facilitates liner-free metallization.

First-principles-based screening method for resistivity scaling of anisotropic metals

The resistivity scaling of metals is a crucial limiting factor for further downscaling of interconnects in nanoelectronic devices that affects signal delay, heat production, and energy consumption. Here, we generalize a commonly considered figure of merit for selecting promising candidate metals with highly anisotropic Fermi surfaces in terms of their electronic transport properties at the nanoscale. For this, we introduce a finite-temperature transport tensor, based on band structures obtained from first principles. This transport tensor allows for a straightforward comparison between highly anisotropic metals in nanostructures with different lattice orientations and arbitrary transport directions. By evaluating the temperature dependence of the tensor components, we also assess the validity of a Fermi surface-based evaluation of the transport properties at zero temperature, rather than considering standard operating temperature conditions.

Fermi surface anisotropy in plasmonic metals increases the potential for efficient hot carrier extraction

Realizing the potential of plasmonic hot carrier harvesting for energy conversion and photodetection requires new materials that resolve the bottleneck of extracting carriers prior to energy relaxation within the metal. Using first-principles calculations of optical response and carrier transport properties, we show that directional conductors with Fermi velocities restricted predominantly to one or two directions present significant advantages for efficient hot carrier harvesting. We show that the optical response of film-like conductors, PtCoO$_2$ and Cr$_2$AlC, resemble that of 2D metals, while that of wire-like conductors, CoSn and YCo$_3$B$_2$, resemble that of 1D metals, which can lead to high mode confinement and efficient light collection in small dimensions, while still working with 3D materials with high carrier densities. Carrier lifetimes and transport distances in these materials, especially in PtCoO$_2$ and CoSn, are competitive with noble metals. Most importantly, we predict that carrier injection efficiency from all of these materials into semiconductors can exceed 10% due to the small component of carrier velocity parallel to the metal surface, substantially improving upon the typical less than 0.1% injection efficiency from noble metals into semiconductors.

Anisotropic spin-to-charge conversion in bismuth

Many intriguing physical phenomena have emerged from the Bi-containing materials due to the interplay of band topology and strong spin-orbit coupling (SOC). In this work, we report anisotropic spin-to-charge conversion in Bi, a semimetal endowed with highly anisotropic Fermi surfaces in addition to strong SOC. The value of spin Hall angle ${\ensuremath{\theta}}_{\mathrm{SH}}$ in Bi, that measures the spin-to-charge conversion efficiency, varies from ${\ensuremath{\theta}}_{\mathrm{SH}}\ensuremath{\approx}0$ to ${\ensuremath{\theta}}_{\mathrm{SH}}\ensuremath{\approx}2.6%$ for two predominant crystal orientations. In addition, the propensity of oxidation and interface quality also affect the spin-to-charge conversion in Bi. The highly anisotropic spin-to-charge conversion between Bi(003) and Bi(012) provide significant insights into the exploration and development of Bi-based topological quantum materials and spintronics.

Non-Majorana modes in diluted spin chains proximitized to a superconductor

Spin chains proximitized with superconducting condensates have emerged as one of the most promising platforms for the realization of Majorana modes. Here, we craft diluted spin chains atom by atom following a seminal theoretical proposal suggesting indirect coupling mechanisms as a viable route to trigger topological superconductivity. Starting from single adatoms hosting deep Shiba states, we use the highly anisotropic Fermi surface of the substrate to create spin chains characterized by different magnetic configurations along distinct crystallographic directions. By scrutinizing a large set of parameters we reveal the ubiquitous emergence of boundary modes. Although mimicking signatures of Majorana modes, the end modes are identified as topologically trivial Shiba states. Our work demonstrates that zero-energy modes in spin chains proximitized to superconductors are not necessarily a link to Majorana modes while simultaneously identifying other experimental platforms, driving mechanisms, and test protocols for the determination of topologically nontrivial superconducting phases.

Vortex bound states influenced by the Fermi surface anisotropy

The spatial distribution of vortex bound states is often anisotropic, which is correlated with the underlying property of materials. In this work, we examine the effects of Fermi surface anisotropy on vortex bound states. The large-scale calculation of vortex bound states is introduced in the presence of fourfold or twofold Fermi surface by solving the Bogoliubov–de Gennes (BdG) equations. Two kinds of quasiparticles' behaviors can be extracted from the local density of states (LDOS) around a vortex. The angle-dependent quasiparticles will move from high energy to low energy when the angle varies from curvature maxima to minima of the Fermi surface, while the angle-independent quasiparticles tend to stay at a relatively higher energy. In addition, the weight of angle-dependent quasiparticles can be enhanced by the increasing anisotropy degree of Fermi surface.