Fermi Surface Deformation Research Articles

Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, QN, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from QN is given by χ−1∝|Δq|. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ−1∝|Δq|2 dependence yields a robust finite-T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the (t−t′) Hubbard model and found that at large U/t>5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ−1∝|Δq|2. Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024

Van Hove annihilation and nematic instability on a kagome lattice.

A nematic phase breaks the point-group symmetry of the crystal lattice and is known to emerge in correlated materials. Here we report the observation of an intra-unit-cell nematic order and associated Fermi surface deformation in the kagome metal ScV6Sn6. Using scanning tunnelling microscopy and scanning tunnelling spectroscopy, we reveal a stripe-like nematic order breaking the crystal rotational symmetry within the kagome lattice itself. Moreover, we identify a set of Van Hove singularities adhering to the kagome-layer electrons, which appear along one direction of the Brillouin zone and are annihilated along other high-symmetry directions, revealing rotational symmetry breaking. Via detailed spectroscopic maps, we further observe an elliptical deformation of the Fermi surface, which provides direct evidence for an electronically mediated nematic order. Our work not only bridges the gap between electronic nematicity and kagome physics but also sheds light on the potential mechanism for realizing symmetry-broken phases in correlated electron systems.

Asymptotic Pomeranchuk instability of Fermi liquids in half-filled Landau levels

We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form nu =2 , n+1/2). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the n rightarrow infty limit.

Collective modes in interacting two-dimensional tomographic Fermi liquids

We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless. We derive expressions for both the longitudinal and the transverse conductivity and discuss the collective mode spectrum along the collisionless-tomographic-hydrodynamic crossover. Longitudinal modes cross over from zero sound in the collisionless regime to hydrodynamic first sound in the tomographic and hydrodynamic regime, where odd-parity damping appears as a subleading correction to the lifetime. In charged Fermi liquids with long-range Coulomb coupling, these modes reduce to plasmons with a strongly suppressed odd-parity correction to the damping. The transverse response, by contrast, has a specific tomographic transport regime with two imaginary odd-parity modes, one of which requires a finite repulsive interaction, distinct from both the shear sound in the collisionless regime and an overdamped diffusive current mode in the hydrodynamic limit. Our work demonstrates that there are deep many-body aspects of interacting Fermi liquids, which are often thought to be well understood theoretically, remaining unexplored.

Multipolar Fermi-surface deformation in a Rydberg-dressed Fermi gas with long-range anisotropic interactions

We study theoretically the deformation of the Fermi surface (FS) of a three-dimensional gas of Rydberg-dressed $^6$Li atoms. The laser dressing to high-lying Rydberg $D$ states results in angle-dependent soft-core-shaped interactions whose anisotropy is described by multiple spherical harmonics. We show that this can drastically modify the shape of the FS and that its deformation depends on the interplay between the Fermi momentum $k_F$ and the reciprocal momentum $\bar{k}$ corresponding to the characteristic soft-core radius of the dressing-induced potential. When $k_F< \bar{k}$, the dressed interaction stretches a spherical FS into an ellipsoid. When $k_F\gtrsim \bar{k}$, complex deformations are encountered which exhibit multipolar characteristics. We analyze the formation of Cooper pairs around the deformed FS and show that they occupy large orbital angular momentum states ($p$, $f$, and $h$ wave) coherently. Our study demonstrates that Rydberg dressing to high angular momentum states may pave a route toward the investigation of unconventional Fermi gases and multiwave superconductivity.

Fermi surface in La-based cuprate superconductors from Compton scattering imaging

Compton scattering provides invaluable information on the underlying Fermi surface (FS) and is a powerful tool complementary to angle-resolved photoemission spectroscopy and quantum oscillation measurements. Here we perform high-resolution Compton scattering measurements for La2−xSrxCuO4 with x = 0.08 (Tc = 20 K) at 300 K and 150 K, and image the momentum distribution function in the two-dimensional Brillouin zone. We find that the observed images cannot be reconciled with the conventional hole-like FS believed so far. Instead, our data imply that the FS is strongly deformed by the underlying nematicity in each CuO2 plane, but the bulk FSs recover the fourfold symmetry. We also find an unusually strong temperature dependence of the momentum distribution function, which may originate from the pseudogap formation in the presence of the reconstructed FSs due to the underlying nematicity. Additional measurements for x = 0.15 and 0.30 at 300 K suggest similar FS deformation with weaker nematicity, which nearly vanishes at x = 0.30.

Generating Giant Vortex in a Fermi Superfluid via Spin-Orbital-Angular-Momentum Coupling

Spin-orbital-angular-momentum (SOAM) coupling has been realized in recent experiments of Bose-Einstein condensates [Chen etal., Phys. Rev. Lett. 121, 113204 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.113204 and Zhang etal., Phys. Rev. Lett. 122, 110402 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.110402], where the orbital angular momentum imprinted upon bosons leads to quantized vortices. For fermions, such an exotic synthetic gauge field can provide fertile ground for fascinating pairing schemes and rich superfluid phases, which are yet to be explored. Here we demonstrate how SOAM coupling stabilizes vortices in Fermi superfluids through a unique mechanism that can be viewed as the angular analog to that of the spin-orbit-coupling-induced Fulde-Ferrell state under a Fermi surface deformation. Remarkably, the vortex size is comparable with the beam waist of Raman lasers generating the SOAM coupling, which is typically much larger than previously observed vortices in Fermi superfluids. With tunable size and core structure, these giant vortex states provide unprecedented experimental access to topological defects in Fermi superfluids.

Fermionic order by disorder in a van der Waals antiferromagnet

CeTe3 is a unique platform to investigate the itinerant magnetism in a van der Waals (vdW) coupled metal. Despite chemical pressure being a promising route to boost quantum fluctuation in this system, a systematic study on the chemical pressure effect on Ce3+(4f1) states is absent. Here, we report on the successful growth of a series of Se doped single crystals of CeTe3. We found a fluctuation driven exotic magnetic rotation from the usual easy-axis ordering to an unusual hard-axis ordering. Unlike in localized magnetic systems, near-critical magnetism can increase itinerancy hand-in-hand with enhancing fluctuation of magnetism. Thus, seemingly unstable hard-axis ordering emerges through kinetic energy gain, with the self-consistent observation of enhanced magnetic fluctuation (disorder). As far as we recognize, this order-by-disorder process in fermionic system is observed for the first time within vdW materials. Our finding opens a unique experimental platform for direct visualization of the rich quasiparticle Fermi surface deformation associated with the Fermionic order-by-disorder process. Also, the search for emergent exotic phases by further tuning of quantum fluctuation is suggested as a promising future challenge.

Neutron-star deformation due to anisotropic momentum distribution of neutron-star matter

Herein, we present a theoretical study of how Fermi-surface distortion affects symmetric nuclear matter, pure neutron matter, and neutron-star matter. The results indicate that, for the binding energy of symmetric nuclear matter, the generally accepted value extracted from the Bethe-Weiz\acker mass formula for nuclei can constrain the degree of anisotropy because of Fermi-surface deformation $\ensuremath{\delta}\phantom{\rule{0.16em}{0ex}}\ensuremath{\lesssim}0.05$. The value of $\ensuremath{\delta}$ starts to affect the stiffness of the equation of state for symmetric nuclear matter and pure neutron matter when $\ensuremath{\delta}\phantom{\rule{0.16em}{0ex}}\ensuremath{\gtrsim}0.01$. Moreover, if the Fermi surface is distorted, the results indicate that neutron stars can be deformed into an oblate shape. This deformation depends on two factors: the stiffness of the corresponding equation of state and value of $\ensuremath{\delta}$. The corresponding deformation near the maximum neutron-star mass comes from the anisotropic pressure within these stars, which is caused by the distortion of Fermi surface predicted by the equation of state of the models.

Stability of quantum degenerate Fermi gases of tilted polar molecules

A recent experimental realization of quantum degenerate gas of $^{40}$K$^{87}$Rb molecules opens up prospects of exploring strong dipolar Fermi gases and many-body phenomena arising in that regime. Here we derive a mean-field variational approach based on the Wigner function for the description of ground-state properties of such systems. We show that the stability of dipolar fermions in a general harmonic trap is universal as it only depends on the trap aspect ratios and the dipoles' orientation. We calculate the species-independent stability diagram and the deformation of the Fermi surface (FS) for polarized molecules, whose electric dipoles are oriented along a preferential direction. Compared to atomic magnetic species, the stability of a molecular electric system turns out to strongly depend on its geometry and the FS deformation significantly increases.

Nonequilibrium susceptibility in photoinduced Floquet states

Nonequilibrium susceptibility in photoinduced Floquet states is studied. We analyze an electron system coupled with a heat bath in a time-periodic oscillating electric field. Spin/charge susceptibility is formulated on the basis of the Floquet Green function method, and is calculated numerically in a wide range of amplitude and frequency of light. When the frequency is larger than the bandwidth, the susceptibility is enhanced due to the dynamical localization effect, and their peak positions in the momentum space are shifted by the Fermi surface deformation. In the case of the small frequency and amplitude, multiple-peak structure emerges in the susceptibility, originating from the multiple Floquet bands which cross the Fermi level. To confirm those numerical results and provide the interpretation, an approximated expression of the susceptibility is derived for small electric-field amplitude.

Impact of an elliptical Fermi surface deformation on the energy of a spinless two-dimensional electron gas

We study the effects of an elliptical Fermi surface deformation on the energy of a two-dimensional electron gas. We consider a standard model for fully spin-polarized (spinless) electrons embedded in a uniformly charged neutralizing jellium background and treat the system in the thermodynamic (bulk) limit. We calculate exactly the energy changes of the system as a function of a parameter that gauges the elliptic deformation of the Fermi surface. The results obtained give insight on various scenarios and competing tendencies that may arise in such a system in presence of some form of internal anisotropy originating from factors such as electron’s anisotropic effective mass, anisotropic interaction potential or both.

Effect of hexagonal warping of the Fermi surface on the thermoelectric properties of a topological insulator irradiated with linearly polarized radiation

We investigate the effect of the hexagonal warped anisotropic Fermi surface on the anomalous thermoelectric properties of the topological insulator surface illuminated with linearly polarized off-resonant electromagnetic radiation. Upon irradiation of the TI surface, the linearly polarized (LP) off-resonant radiation couples with the Dirac surface states. By explicitly finding the off-resonant quasistatic Hamiltonian we show that this coupling occurs only in the presence of the hexagonal warping of the Fermi surface of the topological insulator. We calculate the spin texture of the surface states, Berry curvature, Berry phase, orbital magnetic moment, and magnetization associated with the band structure, which we find strongly depends on the angle of polarization and the amplitude of radiation. For the anomalous thermoelectric effects generated by the Berry curvature, it is found that due to the hexagonal warping induced Fermi surface deformation and the radiation parameter dependent spin texture of the surface states, the transverse Hall, Ettingshausen, Nernst, and thermal conductivities show significant variation with the change in polarization angle, chemical potential, temperature, and the amplitude of radiation. As a consequence, the thermoelectric coefficient of performance ($ZT$) of the topological insulator is found to be increased in the presence of LP off-resonant irradiation compared to the absence of radiation.

Collective dynamics of Fermi surface fluctuations in an interacting Weyl metal phase

Instabilities in a Landau's Fermi-liquid state occur, increasing the strength of interaction parameters in the Landau's Fermi-liquid theory. Introducing both the Berry curvature and chiral anomaly into this theoretical framework, we investigate collective dynamics of Fermi surface fluctuations and reveal their instabilities in an interacting Weyl metal phase with broken time reversal symmetry. Recently, a topological Fermi-liquid theory has been proposed to describe this interacting Weyl metal phase, where not only the Berry curvature but also the chiral anomaly is introduced into the Landau's Fermi-liquid theory [Phys. Rev. B 95, 205113 (2017)]. Based on the Boltzmann-equation framework, we find criteria for the stability of the topological Fermi-liquid state as a function of forward-scattering Landau's interaction parameters and the distance of a pair of Weyl points given by an external magnetic field. In addition to these instability criteria for general angular momentum channels, we investigate the dispersion relation of the zero-sound mode as the simplest example of such Fermi surface fluctuations. Zero-sound modes are well-defined collective excitations in a Landau's Fermi-liquid state, given by the collective dynamics of Fermi surface deformations in the spin-singlet channel with zero angular momentum, where their instability is related with phase separation. We find that the role of the Berry curvature changes the instability criteria of the Landau's Fermi-liquid state. Even if the zero-sound mode is stable in the region of the forward-scattering amplitude, the Berry curvature gives rise to Landau damping beyond the Landau's Fermi-liquid theory. Based on the instability criterion of the zero-sound mode, we propose a phase diagram for a topological Fermi-liquid state against the phase separation in the plane of Landau's interaction parameter and effective Berry curvature, which generalizes the one-dimensional phase diagram of the Landau's Fermi-liquid theory.

Topological features of the thermal Hall conductivity in a chiral p-wave superconductor under strain

Motivated by experimental studies on the effect of tensile and compressive strain or uniaxial pressure in the superconducting phase of the transition metal oxide Sr2RuO4, the pairing symmetry assuming the chiral p-wave superconducting state and the transport property are investigated theoretically by means of the self-consistent Bogoliubov-de Gennes approach. The uniaxial strain leads to the Fermi surface deformation. The topological properties are sensitive to the Fermi surface geometry induced by the strain and switch around the Lifshitz transition in the γ band. The temperature dependence of the thermal Hall conductivity is connected with the amplitude of the strain. While the topological number is reflected in the temperature linear contribution in the low-temperature limit of the thermal Hall conductivity, the deviation from this behavior depends on the pairing channel. Our result may enable us to provide information on the gap function of the chiral p-wave phase.

Ground state of an ultracold Fermi gas of tilted dipoles in elongated traps

Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS). Recently it was experimentally observed in a sample of erbium atoms that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole–dipole interaction Aikawa et al (2014 Science 345 1484). Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the FS follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles. Here we generalise a previous Hartree–Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap. With this we study for the first time the effects of the dipoles’ arbitrary orientation on the ground-state properties of the system. Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion. We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations. The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation. Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles, but softens showing a change in the aspect ratio depending on the dipoles’ orientation relative to the trap geometry, as well as on the trap anisotropy itself. Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.

Spin-imbalanced pairing and Fermi surface deformation in flat bands

We study the attractive Hubbard model with spin imbalance on two lattices featuring a flat band: the Lieb and kagome lattices. We present mean-field phase diagrams featuring exotic superfluid phases, similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose stability is confirmed by dynamical mean-field theory. The nature of the pairing is found to be richer than just the Fermi surface shift responsible for the usual FFLO state. The presence of a flat band allows for changes in the particle momentum distributions at null energy cost. This facilitates formation of nontrivial superfluid phases via multiband Cooper pair formation: the momentum distribution of the spin component in the flat band deforms to mimic the Fermi surface of the other spin component residing in a dispersive band. The Fermi surface of the unpaired particles that are typical for gapless superfluids becomes deformed as well. The results highlight the profound effect of flat dispersions on Fermi surface instabilities, and provide a potential route for observing spin-imbalanced superfluidity and superconductivity.

Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime

A recent time-of-flight (TOF) expansion experiment with polarized fermionic erbium atoms measured a Fermi surface deformation from a sphere to an ellipsoid due to dipole-dipole interaction, thus confirming previous theoretical predictions. Here we perform a systematic study of the ground-state properties and TOF dynamics for trapped dipolar Fermi gases from the collisionless to the hydrodynamic regime at zero temperature. To this end we solve analytically the underlying Boltzmann-Vlasov equation within the relaxation-time approximation in the vicinity of equilibrium by using a suitable rescaling of the equilibrium distribution. The resulting ordinary differential equations for the respective scaling parameters are then solved numerically for experimentally realistic parameters and relaxation times that correspond to the collisionless, collisional, and hydrodynamic regime. The equations for the collisional regime are first solved in the approximation of a fixed relaxation time, and then this approach is extended to include a self-consistent determination of the relaxation time. The presented analytical and numerical results are relevant for a detailed quantitative understanding of ongoing experiments and the design of future experiments with ultracold fermionic dipolar atoms and molecules. In particular, the obtained results are relevant for systems with strong dipole-dipole interaction, which turn out to affect significantly the aspect ratios during the TOF expansion.

Interaction-driven Lifshitz transition with dipolar fermions in optical lattices

Anisotropic dipole-dipole interactions between ultracold dipolar fermions break the symmetry of the Fermi surface and thereby deform it. Here we demonstrate that such a Fermi surface deformation induces a topological phase transition -- so-called Lifshitz transition -- in the regime accessible to present-day experiments. We describe the impact of the Lifshitz transition on observable quantities such as the Fermi surface topology, the density-density correlation function, and the excitation spectrum of the system. The Lifshitz transition in ultracold atoms can be controlled by tuning the dipole orientation and -- in contrast to the transition studied in crystalline solids -- is completely interaction-driven.

Spin-fermion model with overlapping hot spots and charge modulation in cuprates

We study particle-hole instabilities in the framework of the spin-fermion (SF) model. In contrast to previous studies, we assume that adjacent hot spots can overlap due to a shallow dispersion of the electron spectrum in the antinodal region. In addition, we take into account effects of a remnant low energy and momentum Coulomb interaction. We demonstrate that at sufficiently small values $|\varepsilon (\pi ,0)-E_{F}|\lesssim \Gamma $, where $E_{F}$ is the Fermi energy, $\varepsilon \left( \pi ,0\right) $ is the energy in the middle of the Brillouin zone edge, and $\Gamma $ is a characteristic energy of the fermion-fermion interaction due to the antiferromagnetic fluctuations, the leading particle-hole instability is a d-form factor Fermi surface deformation (Pomeranchuk instability) rather than the charge modulation along the Brillouin zone diagonals predicted within the standard SF model previously. At lower temperatures, we find that the deformed Fermi surface is further unstable to formation of a d-form factor charge density wave (CDW) with a wave vector along the Cu-O-Cu bonds (axes of the Brillouin zone). We show that the remnant Coulomb interaction enhances the d-form factor symmetry of the CDW. These findings can explain the robustness of this order in the cuprates. The approximations made in the paper are justified by a small parameter that allows one an Eliashberg-like treatment. Comparison with experiments suggests that in many cuprate compounds the prerequisites for the proposed scenario are indeed fulfilled and the results obtained may explain important features of the charge modulations observed recently.