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Effective Masses in a Strongly Anisotropic Fermi Liquid

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

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.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.

arXiv:0803.4208Physical Review LettersAug 8, 200811 citations

THE THEORY OF A FERMI LIQUID

Elsevier eBooksJan 1, 196512 citations

The Theory of a Fermi Liquid

D. ter Haar

Elsevier eBooksJan 1, 19650 citations

The Fermi Liquid

Hui Zhai

1. Introduce density distribution and momentum distribution of non-interacting Fermi gas. 2. Discuss the transport property of a Fermi gas through a quantum point contact. 3. Discuss Fermi surface as a key of a non-interacting Fermi gas and its generalization to a Fermi liquid. 4. Introduce the effective mass and the quasi-particle residue as two key parameters of the Fermi liquid. 5. Introduce the self-energy and the universal relations between the effective mass, the quasi-particle residue and the self-energy. 6. Discuss Fermi polaron as an example of the Fermi liquid, and show these universal relations with this example. 7. Discuss the divergence of the effective mass and vanishing of quasi-particle residue when Fermi liquid description fails. 8. Introduce the radio-frequency spectroscopy and how it measures the polaron energy and the quasi-particle residue. 9. Summarize different spectroscopy measurements in ultracold atomic systems.1. Introduce density distribution and momentum distribution of non-interacting Fermi gas. 2. Discuss the transport property of a Fermi gas through a quantum point contact. 3. Discuss Fermi surface as a key of a non-interacting Fermi gas and its generalization to a Fermi liquid. 4. Introduce the effective mass and the quasi-particle residue as two key parameters of the Fermi liquid. 5. Introduce the self-energy and the universal relations between the effective mass, the quasi-particle residue and the self-energy. 6. Discuss Fermi polaron as an example of the Fermi liquid, and show these universal relations with this example. 7. Discuss the divergence of the effective mass and vanishing of quasi-particle residue when Fermi liquid description fails. 8. Introduce the radio-frequency spectroscopy and how it measures the polaron energy and the quasi-particle residue. 9. Summarize different spectroscopy measurements in ultracold atomic systems.

Cambridge University Press eBooksJan 30, 20210 citations

Finite-size analysis of the Fermi liquid properties of the homogeneous electron gas

Markus Holzmann, B. Bernu, David M. Ceperley

We analyze the extrapolation to the thermodynamic limit of Fermi liquid properties of the homogeneous electron gas in two and three dimensions. Using field theory, we explicitly calculate finite-size effects of the total energy, the renormalization factor, and the effective mass at the Fermi surface within the random phase approximation (RPA) and discuss the validity for general metallic systems.

arXiv:1105.2964Journal of Physics Conference SeriesSep 16, 201120 citations

Fermions and the Fermi surface

Lecture notes in physics. M, MonographsJan 1, 19970 citations

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