Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0803.4208 · Physical Review Letters

Effective Masses in a Strongly Anisotropic Fermi Liquid

Tudor D. Stanescu, Victor M. Galitski, H. D. Drew

Published Aug 8, 2008• 11 citations
arXivHTMLPDF

Abstract

Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z_{q}. Our primary motivation is to explain the relatively large value of the cyclotron mass observed experimentally and its relation with the effective Hall mass. Using a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor 1/Z_{q}, while the effective Hall mass is proportional to Z_{q}/Z_{q};{2}, where cdots, three dots, centered implies an averaging over the Fermi surface. If the Z-factor becomes small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small.

DOI
10.1103/physrevlett.101.066405

Related papers

Cyclotron resonance and quantum oscillations of critical Fermi surfaces

Haoyu Guo, Davide Valentinis, Jörg Schmalian +2 more

Kohn's theorem places strong constraints on the cyclotron response of Fermi liquids. Recent observations of a doping dependence in the cyclotron mass of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ [Legros et al., Phys. Rev. B 106, 195110 (2022)] are therefore surprising because the cyclotron mass can only be renormalized by large momentum umklapp interactions, which are not expected to vary significantly with doping. We show that a version of Kohn's theorem continues to apply to disorder-free non-Fermi-liquids with a critical boson near zero momentum. However, marginal Fermi liquids arising from a spatially random Yukawa coupling between the electrons and bosons do give rise to significant corrections to the cyclotron mass that we compute. This is the same theory that yields linear-in-temperature resistivity and other properties of strange metals at zero fields [Patel et al., Science 381, 790 (2023)].

arXiv:2308.01956•Physical review. B./Physical review. B•Feb 27, 2024•17 citations

ANISOTROPIC PHENOMENA IN STRONGLY CORRELATED ELECTRON SYSTEMS

Edwin Christopher Carter

This thesis is concerned with momentum anisotropy in strongly correlated electron systems, and explores its origin and its consequences through two contrasting projects. The first is a study of the temperature dependences of magnetotransport quantities in the normal state of the cuprate high-temperature superconductors. A phenomenological anisotropic small-angle scattering model is investigated; Hall effect measurements can be reproduced for parameters sufficiently close to particle-hole symmetry, but the experimentally observed magnetoresistance cannot be explained. The second project studies the phase diagram and quasiparticle properties of the square lattice Hubbard model within two-site cluster dynamical mean field theory (DMFT), at zero temperature. The "two-site" approach provides a drastically simplified but physically motivated self-consistency scheme for DMFT. This is combined for the first time with cluster DMFT, within which different magnetic orders and momentum anisotropy may be represented consistently. The extent of antiferromagnetism is determined; phases are discovered where the Fermi surface consists of small hole pockets, and the Mott transition happens as these pockets shrink to points. Anisotropic phenomena observed in the cuprates are reproduced by the theory; a pseudogap destroys the Fermi surface in some places, leaving behind Fermi arcs that closed into hole pockets by lines with very small quasiparticle residue.

•Jan 1, 2005•0 citations

Anisotropic fermionic quasiparticles

Seongjin Ahn, S. Das Sarma

We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.

arXiv:2011.02481•Physical review. B./Physical review. B•Jan 8, 2021•9 citations

Spin stiffness of a Fermi liquid in the ν=1 quantum Hall regime

A. B. Van'kov, Игорь Владимирович Кукушкин

Anomalous behavior of spin stiffness is revealed in ZnO-based two-dimensional electron systems (2DESs) with strong Coulomb interaction and Wigner-Seitz parameter ${r}_{s}>6$. The spin stiffness is extracted directly from the quadratic $k$ dispersion of spin excitons at $\ensuremath{\nu}=1$ probed by inelastic light scattering. The resulting values are found to be dramatically rescaled compared to the case of weakly interacting 2DESs---spin stiffness turned out to be of the order of the cyclotron energy with the effective mass of Fermi-liquid quasiparticles. This result is also confirmed by the exact diagonalization simulations.

Physical review. B./Physical review. B•Dec 21, 2020•9 citations

Fermi-liquid phase of thet-Jmodel and the Hall coefficient in the high-temperature superconductors

C. A. R. Sá de Melo, Ziqiang Wang, Sebastian Doniach

The Hall coefficient in the strongly correlated Fermi-liquid phase of the t-J model is studied for moderate hole concentrations. We find that the quasiparticle self-energy is strongly k dependent due to gauge-field interactions. It leads to corrections to the Fermi-surface curvature and to enhancement of the quasiparticle lifetime in the holelike region. We show that a systematic treatment of the strong local correlations to next to leading order in 1/N is sufficient to give rise to a sign change in the Hall coefficient. This effect occurs near 0.20 doping for J/t=0.2 and may be relevant to the high-${\mathit{T}}_{\mathit{c}}$ materials.

Physical Review Letters•Mar 30, 1992•13 citations

Universal and nonuniversal renormalizations in Fermi liquids

Andrey V. Chubukov, Dmitrii L. Maslov

We discuss an interplay between the Fermi-liquid (FL) theory and diagrammatic perturbative approach to interacting Fermi systems. In the FL theory for Galilean-invariant systems, mass renormalization ${m}^{\ensuremath{\ast}}/m$ comes exclusively from fermions at the Fermi surface. We show that in a diagrammatic perturbation theory the same result for ${m}^{\ensuremath{\ast}}/m$ comes from fermions both at and away from the Fermi surface. The equivalence of the FL and perturbative approaches is based on a particular relation between self-energy contributions from high- and low-energy fermions. We argue that care has to be exercised in the renormalization-group approach to a FL in order not to miss the high-energy contribution to ${m}^{\ensuremath{\ast}}/m$. As particular examples, we discuss ${m}^{\ensuremath{\ast}}/m$ and the quasiparticle residue $Z$ for two-dimensional and three-dimensional systems with both SU(2) and $\text{SU}(N)$ symmetries, and with a short-range interaction. We derive an expression for the anisotropic part of the Fermi-liquid vertex in the large-$N$ limit of the $\text{SU}(N)$ case.

arXiv:1003.4032•Physical Review B•Jun 3, 2010•13 citations
Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z_{q}. Our primary motivation is to explain the relatively large value of the cyclotron mass observed experimentally and its relation with the effective Hall mass. Using a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor 1/Z_{q}, while the effective Hall mass is proportional to Z_{q}/Z_{q};{2}, where cdots, three dots, centered implies an averaging over the Fermi surface. If the Z-factor becomes small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small.
Kohn's theorem places strong constraints on the cyclotron response of Fermi liquids. Recent observations of a doping dependence in the cyclotron mass of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ [Legros et al., Phys. Rev. B 106, 195110 (2022)] are therefore surprising because the cyclotron mass can only be renormalized by large momentum umklapp interactions, which are not expected to vary significantly with doping. We show that a version of Kohn's theorem continues to apply to disorder-free non-Fermi-liquids with a critical boson near zero momentum. However, marginal Fermi liquids arising from a spatially random Yukawa coupling between the electrons and bosons do give rise to significant corrections to the cyclotron mass that we compute. This is the same theory that yields linear-in-temperature resistivity and other properties of strange metals at zero fields [Patel et al., Science 381, 790 (2023)].
This thesis is concerned with momentum anisotropy in strongly correlated electron systems, and explores its origin and its consequences through two contrasting projects. The first is a study of the temperature dependences of magnetotransport quantities in the normal state of the cuprate high-temperature superconductors. A phenomenological anisotropic small-angle scattering model is investigated; Hall effect measurements can be reproduced for parameters sufficiently close to particle-hole symmetry, but the experimentally observed magnetoresistance cannot be explained. The second project studies the phase diagram and quasiparticle properties of the square lattice Hubbard model within two-site cluster dynamical mean field theory (DMFT), at zero temperature. The "two-site" approach provides a drastically simplified but physically motivated self-consistency scheme for DMFT. This is combined for the first time with cluster DMFT, within which different magnetic orders and momentum anisotropy may be represented consistently. The extent of antiferromagnetism is determined; phases are discovered where the Fermi surface consists of small hole pockets, and the Mott transition happens as these pockets shrink to points. Anisotropic phenomena observed in the cuprates are reproduced by the theory; a pseudogap destroys the Fermi surface in some places, leaving behind Fermi arcs that closed into hole pockets by lines with very small quasiparticle residue.
We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.
Anomalous behavior of spin stiffness is revealed in ZnO-based two-dimensional electron systems (2DESs) with strong Coulomb interaction and Wigner-Seitz parameter rs>6{r}_{s}>6rs​>6. The spin stiffness is extracted directly from the quadratic kkk dispersion of spin excitons at $\ensuremath{\nu}=1$ probed by inelastic light scattering. The resulting values are found to be dramatically rescaled compared to the case of weakly interacting 2DESs---spin stiffness turned out to be of the order of the cyclotron energy with the effective mass of Fermi-liquid quasiparticles. This result is also confirmed by the exact diagonalization simulations.
The Hall coefficient in the strongly correlated Fermi-liquid phase of the t-J model is studied for moderate hole concentrations. We find that the quasiparticle self-energy is strongly k dependent due to gauge-field interactions. It leads to corrections to the Fermi-surface curvature and to enhancement of the quasiparticle lifetime in the holelike region. We show that a systematic treatment of the strong local correlations to next to leading order in 1/N is sufficient to give rise to a sign change in the Hall coefficient. This effect occurs near 0.20 doping for J/t=0.2 and may be relevant to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials.
We discuss an interplay between the Fermi-liquid (FL) theory and diagrammatic perturbative approach to interacting Fermi systems. In the FL theory for Galilean-invariant systems, mass renormalization ${m}^{\ensuremath{\ast}}/m$ comes exclusively from fermions at the Fermi surface. We show that in a diagrammatic perturbation theory the same result for ${m}^{\ensuremath{\ast}}/m$ comes from fermions both at and away from the Fermi surface. The equivalence of the FL and perturbative approaches is based on a particular relation between self-energy contributions from high- and low-energy fermions. We argue that care has to be exercised in the renormalization-group approach to a FL in order not to miss the high-energy contribution to ${m}^{\ensuremath{\ast}}/m$. As particular examples, we discuss ${m}^{\ensuremath{\ast}}/m$ and the quasiparticle residue ZZZ for two-dimensional and three-dimensional systems with both SU(2) and SU(N)\text{SU}(N)SU(N) symmetries, and with a short-range interaction. We derive an expression for the anisotropic part of the Fermi-liquid vertex in the large-NNN limit of the SU(N)\text{SU}(N)SU(N) case.