- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Fulde-Ferrell-Larkin-Ovchinnikov transition and quantum criticality in polarized Fermi gases

Francesco Pirolo*, Leonardo Pisani†, and Pierbiagio Pieri‡

  • *Contact author: francesco.pirolo2@unibo.it
  • †Contact author: leonardo.pisani2@unibo.it
  • ‡Contact author: pierbiagio.pieri@unibo.it
PDF

Phys. Rev. B 114, 254507 – Published 6 November, 2026

DOI: https://doi.org/10.1103/4wwz-xg5q

Abstract

We investigate the zero-temperature transition from the polarized normal phase to the FFLO state in a two-dimensional Fermi gas by means of a diagrammatic t-matrix approach. We first show that the standard non-self-consistent theory produces an unphysical critical polarization because of a severe violation of the Luttinger theorem. Motivated by this observation, we introduce a minimal self-consistent extension that largely restores compliance with the Luttinger theorem while preserving the analytical simplicity of the original formalism. This leads to a physically consistent critical polarization over the whole interaction range. Building on this improved description, we characterize the quantum critical behavior of the FFLO transition through the quasiparticle decay rates, quasiparticle weights, momentum distributions, and the critical dynamics of both fermionic and bosonic degrees of freedom. We further compare the two- and three-dimensional systems, showing that their critical properties can be understood within a unified geometrical picture based on the nesting of the majority and minority Fermi surfaces. Finally, for a three-dimensional lattice, we demonstrate within the Hertz–Millis framework that vertex corrections are irrelevant, thereby placing the FFLO quantum phase transition in the mean-field universality class, in close analogy with the itinerant antiferromagnet transition.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (152)

  1. C. M. Varma, Z. Nussinov, and W. van Saarloos, Singular or non-Fermi liquids, Phys. Rep. 361, 267 (2002).
  2. H. v. Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79, 1015 (2007).
  3. T. Senthil, Critical Fermi surfaces and non-Fermi liquid metals, Phys. Rev. B 78, 035103 (2008).
  4. M. A. Metlitski, D. F. Mross, S. Sachdev, and T. Senthil, Cooper pairing in non-Fermi liquids, Phys. Rev. B 91, 115111 (2015).
  5. M. Brando, D. Belitz, F. M. Grosche, and T. R. Kirkpatrick, Metallic quantum ferromagnets, Rev. Mod. Phys. 88, 025006 (2016).
  6. J. A. Hertz, Quantum critical phenomena, Phys. Rev. B 14, 1165 (1976).
  7. A. V. Chubukov and D. L. Maslov, Nonanalytic corrections to the Fermi-liquid behavior, Phys. Rev. B 68, 155113 (2003).
  8. D. Belitz and T. Vojta, How generic scale invariance influences quantum and classical phase transitions, Rev. Mod. Phys. 77, 579 (2005).
  9. S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, 2011)
  10. D. Belitz, T. R. Kirkpatrick, and T. Vojta, Nonanalytic behavior of the spin susceptibility in clean Fermi systems, Phys. Rev. B 55, 9452 (1997).
  11. A. V. Chubukov, C. Pépin, and J. Rech, Instability of the quantum-critical point of itinerant ferromagnets, Phys. Rev. Lett. 92, 147003 (2004).
  12. A. Abanov and A. Chubukov, Anomalous scaling at the quantum critical point in itinerant antiferromagnets, Phys. Rev. Lett. 93, 255702 (2004).
  13. D. Bergeron, D. Chowdhury, M. Punk, S. Sachdev, and A.-M. S. Tremblay, Breakdown of Fermi liquid behavior at the (π,π)=2kF spin-density wave quantum-critical point: The case of electron-doped cuprates, Phys. Rev. B 86, 155123 (2012).
  14. E. Berg, M. A. Metlitski, and S. Sachdev, Sign-Problem–Free quantum Monte Carlo of the onset of antiferromagnetism in metals, Science 338, 1606 (2012).
  15. T. Holder and W. Metzner, Non-Fermi-liquid behavior at the onset of incommensurate 2kF charge- or spin-density wave order in two dimensions, Phys. Rev. B 90, 161106 (2014).
  16. T. Holder and W. Metzner, Anomalous dynamical scaling from nematic and U(1) gauge field fluctuations in two-dimensional metals, Phys. Rev. B 92, 041112 (2015).
  17. B. S. Chandrasekhar, A note on the maximum critical field of high-field superconductors, Appl. Phys. Lett. 1, 7 (1962).
  18. A. M. Clogston, Upper limit for the critical field in hard superconductors, Phys. Rev. Lett. 9, 266 (1962).
  19. M. W. Zwierlein, A. Schirotzek, C. H. Schunck, and W. Ketterle, Fermionic superfluidity with imbalanced spin populations, Science 311, 492 (2006).
  20. G. B. Partridge, W. Li, R. I. Kamar, Y.-A. Liao, and R. G. Hulet, Pairing and phase separation in a polarized Fermi gas, Science 311, 503 (2006).
  21. Y. Shin, M. W. Zwierlein, C. H. Schunck, A. Schirotzek, and W. Ketterle, Observation of phase separation in a strongly interacting imbalanced Fermi gas, Phys. Rev. Lett. 97, 030401 (2006).
  22. P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135, A550 (1964).
  23. A. I. Larkin and Y. N. Ovchinnikov, Nonuniform state of superconductors, Zh. Eksp. Teor. Fiz. 47, 1136 (1964) [Sov. Phys. JETP 20, 762 (1965)].
  24. R. Casalbuoni and G. Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys. 76, 263 (2004).
  25. Y. Matsuda and K. Shimahara, Fulde–Ferrell–Larkin–Ovchinnikov state in heavy fermion superconductors, J. Phys. Soc. Jpn. 76, 051005 (2007).
  26. R. Combescot, Introduction to FFLO phases and collective modes in the BEC-BCS crossover, in Ultra-Cold Fermi Gases, edited by M. Inguscio, W. Ketterle, and C. Salomon (IOS Press, Amsterdam, 2007), pp. 697–714.
  27. J. J. Kinnunen, J. E. Baarsma, J.-P. Martikainen, and P. Törmä, The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review, Rep. Prog. Phys. 81, 046401 (2018).
  28. G. C. Strinati, P. Pieri, G. Röpke, P. Schuck, and M. Urban, The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems, Phys. Rep. 738, 1 (2018).
  29. A. Bianchi, R. Movshovich, C. Capan, P. G. Pagliuso, and J. L. Sarrao, Possible Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in CeCoIn5, Phys. Rev. Lett. 91, 187004 (2003).
  30. M. Kenzelmann, T. Strässle, C. Niedermayer, M. Sigrist, B. Padmanabhan, M. Zolliker, A. D. Bianchi, R. Movshovich, E. D. Bauer, J. L. Sarrao, and J. D. Thompson, Coupled superconducting and magnetic order in CeCoIn5, Science 321, 1652 (2008).
  31. R. Lortz, Y. Wang, A. Demuer, P. H. M. Böttger, B. Bergk, G. Zwicknagl, Y. Nakazawa, and J. Wosnitza, Calorimetric evidence for a Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in the layered organic superconductor κ-(BEDT-TTF)2Cu(NCS)2, Phys. Rev. Lett. 99, 187002 (2007).
  32. J. A. Wright, E. Green, P. Kuhns, A. Reyes, J. Brooks, J. Schlueter, R. Kato, H. Yamamoto, M. Kobayashi, and S. E. Brown, Zeeman-driven phase transition within the superconducting state of κ-(BEDT-TTF)2Cu(NCS)2, Phys. Rev. Lett. 107, 087002 (2011).
  33. H. Mayaffre, S. Krämer, M. Horvatić, C. Berthier, K. Miyagawa, K. Kanoda, and V. F. Mitrović, Evidence of Andreev bound states as a hallmark of the FFLO phase in κ−(BEDT−TTF)2Cu(NCS)2, Nat. Phys. 10, 928 (2014).
  34. G. Koutroulakis, H. Kühne, J. A. Schlueter, J. Wosnitza, and S. E. Brown, Microscopic study of the Fulde-Ferrell-Larkin-Ovchinnikov state in an all-organic superconductor, Phys. Rev. Lett. 116, 067003 (2016).
  35. C. W. Cho, J. H. Yang, N. F. Q. Yuan, J. Shen, T. Wolf, and R. Lortz, Thermodynamic evidence for the Fulde-Ferrell-Larkin-Ovchinnikov state in the KFe2As2 superconductor, Phys. Rev. Lett. 119, 217002 (2017).
  36. S. Kasahara, Y. Sato, S. Licciardello, M. Čulo, S. Arsenijević, T. Ottenbros, T. Tominaga, J. Böker, I. Eremin, T. Shibauchi, J. Wosnitza, N.E. Hussey, and Y. Matsuda, Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov state with segmented vortices in the BCS-BEC-crossover superconductor FeSe, Phys. Rev. Lett. 124, 107001 (2020).
  37. Y.-A. Liao, A. S. C. Rittner, T. Paprotta, W. Li, G. B. Partridge, R. G. Hulet, S. K. Baur, and E. J. Mueller, Spin-imbalance in a one-dimensional Fermi gas, Nature (London) 467, 567 (2010).
  38. B. A. Olsen, M. C. Revelle, J. A. Fry, D. E. Sheehy, and R. G. Hulet, Phase diagram of a strongly interacting spin-imbalanced Fermi gas, Phys. Rev. A 92, 063616 (2015).
  39. M. C. Revelle, J. A. Fry, B. A. Olsen, and R. G. Hulet, 1D to 3D crossover of a spin-imbalanced Fermi gas, Phys. Rev. Lett. 117, 235301 (2016).
  40. W. Ong, C. Cheng, I. Arakelyan, and J. E. Thomas, Spin-imbalanced quasi-two-dimensional Fermi gases, Phys. Rev. Lett. 114, 110403 (2015).
  41. D. Mitra, P. T. Brown, P. Schauß, S. S. Kondov, and W. S. Bakr, Phase separation and pair condensation in a spin-imbalanced 2D Fermi gas, Phys. Rev. Lett. 117, 093601 (2016).
  42. B. Sundar, J. A. Fry, M. C. Revelle, R. G. Hulet, and K. R. A. Hazzard, Spin-imbalanced ultracold Fermi gases in a two-dimensional array of tubes, Phys. Rev. A 102, 033311 (2020).
  43. R. Yao, S. Chi, M. Wang, R. J. Fletcher, and M. Zwierlein, Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy, Phys. Rev. Lett. 134, 183402 (2025).
  44. L. Radzihovsky and A. Vishwanath, Quantum liquid crystals in an imbalanced Fermi gas: Fluctuations and fractional vortices in Larkin-Ovchinnikov states, Phys. Rev. Lett. 103, 010404 (2009).
  45. L. Radzihovsky, Fluctuations and phase transitions in Larkin-Ovchinnikov liquid-crystal states of a population-imbalanced resonant Fermi gas, Phys. Rev. A 84, 023611 (2011).
  46. P. Jakubczyk, Renormalization theory for the Fulde-Ferrell-Larkin-Ovchinnikov states at T>0, Phys. Rev. A 95, 063626 (2017).
  47. S. A. Brazovskii, Phase transition of an isotropic system to a nonuniform state, Zh. Eksp. Teor. Fiz. 68, 175 (1975) [Sov. Phys. JETP 41, 85 (1975)].
  48. H. Shimahara, Phase fluctuations and Kosterlitz-Thouless transition in two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov superconductors, J. Phys. Soc. Jpn. 67, 1872 (1998).
  49. Y. Ohashi, On the Fulde–Ferrell State in spatially isotropic superconductors, J. Phys. Soc. Jpn. 71, 2625 (2002).
  50. M. Pini, P. Pieri, and G. Calvanese Strinati, Strong Fulde-Ferrell Larkin-Ovchinnikov pairing fluctuations in polarized Fermi systems, Phys. Rev. Res. 3, 043068 (2021).
  51. G. Sarma, On the influence of a uniform exchange field acting on the spins of the conduction electrons in a superconductor, J. Phys. Chem. Solids 24, 1029 (1963).
  52. D. E. Sheehy and L. Radzihovsky, BEC-BCS crossover in “Magnetized” Feshbach-resonantly paired superfluids, Phys. Rev. Lett. 96, 060401 (2006).
  53. D. E. Sheehy and L. Radzihovsky, BEC–BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids, Ann. Phys. 322, 1790 (2007).
  54. M. M. Parish, F. M. Marchetti, A. Lamacraft, and B. D. Simons, Finite-temperature phase diagram of a polarized Fermi condensate, Nat. Phys. 3, 124 (2007).
  55. F. Chevy and C. Mora, Ultra-cold polarized Fermi gases, Rep. Prog. Phys. 73, 112401 (2010).
  56. L. Radzihovsky and D. E. Sheehy, Imbalanced Feshbach-resonant Fermi gases, Rep. Prog. Phys. 73, 076501 (2010).
  57. C. Lobo, A. Recati, S. Giorgini, and S. Stringari, Normal state of a polarized Fermi gas at unitarity, Phys. Rev. Lett. 97, 200403 (2006).
  58. S. Pilati and S. Giorgini, Phase separation in a polarized Fermi gas at zero temperature, Phys. Rev. Lett. 100, 030401 (2008).
  59. J. Gukelberger, S. Lienert, E. Kozik, L. Pollet, and M. Troyer, Fulde-Ferrell-Larkin-Ovchinnikov pairing as leading instability on the square lattice, Phys. Rev. B 94, 075157 (2016).
  60. E. Vitali, P. Rosenberg, and S. Zhang, Exotic superfluid phases in spin-polarized Fermi gases in optical lattices, Phys. Rev. Lett. 128, 203201 (2022).
  61. Y. He, C.-C. Chien, Q. Chen, and K. Levin, Single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell state in BCS-BEC crossover, Phys. Rev. A 75, 021602(R) (2007).
  62. T. Kashimura, R. Watanabe, and Y. Ohashi, Spin susceptibility and fluctuation corrections in the BCS-BEC crossover regime of an ultracold Fermi gas, Phys. Rev. A 86, 043622 (2012).
  63. M. Urban and P. Schuck, Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem, Phys. Rev. A 90, 023632 (2014).
  64. H. Tajima, T. Kashimura, R. Hanai, R. Watanabe, and Y. Ohashi, Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas, Phys. Rev. A 89, 033617 (2014).
  65. B. Frank, J. Lang, and W. Zwerger, Universal phase diagram and scaling functions of imbalanced Fermi gases, J. Exp. Theor. Phys. 127, 812 (2018).
  66. A. Perali, P. Pieri, G. C. Strinati, and C. Castellani, Pseudogap and spectral function from superconducting fluctuations to the bosonic limit, Phys. Rev. B 66, 024510 (2002).
  67. P. Pieri, L. Pisani, and G. C. Strinati, BCS-BEC crossover at finite temperature in the broken-symmetry phase, Phys. Rev. B 70, 094508 (2004).
  68. M. Pini, P. Pieri, and G. C. Strinati, Fermi gas throughout the BCS-BEC crossover: Comparative study of t-matrix approaches with various degrees of self-consistency, Phys. Rev. B 99, 094502 (2019).
  69. M. Pini, P. Pieri, and G. Calvanese Strinati, Evolution of an attractive polarized Fermi gas: From a Fermi liquid of polarons to a non-Fermi liquid at the Fulde-Ferrell-Larkin-Ovchinnikov quantum critical point, Phys. Rev. B 107, 054505 (2023).
  70. P.-A. Pantel, D. Davesne, and M. Urban, Polarized Fermi gases at finite temperature in the BCS-BEC crossover, Phys. Rev. A 90, 053629 (2014).
  71. G. J. Conduit, P. H. Conlon, and B. D. Simons, Superfluidity at the BEC-BCS crossover in two-dimensional Fermi gases with population and mass imbalance, Phys. Rev. A 77, 053617 (2008).
  72. D. E. Sheehy, Fulde-Ferrell-Larkin-Ovchinnikov state of two-dimensional imbalanced Fermi gases, Phys. Rev. A 92, 053631 (2015).
  73. K. V. Samokhin and M. S. Mar'enko, Quantum fluctuations in Larkin-Ovchinnikov-Fulde-Ferrell superconductors, Phys. Rev. B 73, 144502 (2006).
  74. F. Piazza, W. Zwerger, and P. Strack, FFLO strange metal and quantum criticality in two dimensions: Theory and application to organic superconductors, Phys. Rev. B 93, 085112 (2016).
  75. D. Pimenov, I. Mandal, F. Piazza, and M. Punk, Non-Fermi liquid at the FFLO quantum critical point, Phys. Rev. B 98, 024510 (2018).
  76. T. Holder and W. Metzner, Fermion loops and improved power-counting in two-dimensional critical metals with singular forward scattering, Phys. Rev. B 92, 245128 (2015).
  77. M. Bauer, M. M. Parish, and T. Enss, Universal equation of state and pseudogap in the two-dimensional Fermi gas, Phys. Rev. Lett. 112, 135302 (2014).
  78. P. Bloom, Two-dimensional Fermi gas, Phys. Rev. B 12, 125 (1975).
  79. G. Bertaina and S. Giorgini, BCS-BEC crossover in a two-dimensional Fermi gas, Phys. Rev. Lett. 106, 110403 (2011).
  80. Q. CHEN, J. Stajic, S. Tan, and K. Levin, BCS–BEC crossover: From high temperature superconductors to ultracold superfluids, Phys. Rep. 412, 1 (2005).
  81. J. M. Luttinger, Fermi surface and some simple equilibrium properties of a system of interacting fermions, Phys. Rev. 119, 1153 (1960).
  82. P. Pieri and G. C. Strinati, Luttinger theorem and imbalanced Fermi systems, Eur. Phys. J. B 90, 68 (2017).
  83. M. Randeria, J.-M. Duan, and L.-Y. Shieh, Bound states, Cooper pairing, and Bose condensation in two dimensions, Phys. Rev. Lett. 62, 981 (1989).
  84. J. Levinsen and M. M. Parish, Strongly interacting two-dimensional Fermi gases, in Annual Review of Cold Atoms and Molecules (World Scientific, Singapore, 2015), Chap. 1, Vol. 3, pp. 1–75.
  85. L. Salasnich and F. Toigo, Composite bosons in the two-dimensional BCS-BEC crossover from Gaussian fluctuations, Phys. Rev. A 91, 011604 (2015).
  86. L. He, H. Lü, G. Cao, H. Hu, and X.-J. Liu, Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases, Phys. Rev. A 92, 023620 (2015).
  87. I. Boettcher, L. Bayha, D. Kedar, P. A. Murthy, M. Neidig, M. G. Ries, A. N. Wenz, G. Zürn, S. Jochim, and T. Enss, Equation of state of ultracold fermions in the 2D BEC-BCS crossover region, Phys. Rev. Lett. 116, 045303 (2016).
  88. E. Vitali, H. Shi, M. Qin, and S. Zhang, Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations, Phys. Rev. A 96, 061601 (2017).
  89. T. Zielinski, B. Ross, and A. Gezerlis, Pairing in two-dimensional Fermi gases with a coordinate-space potential, Phys. Rev. A 101, 033601 (2020).
  90. L. Sobirey, N. Luick, M. Bohlen, H. Biss, H. Moritz, and T. Lompe, Observation of superfluidity in a strongly correlated two-dimensional Fermi gas, Science 372, 844 (2021).
  91. S. Van Loon and C. A. R. Sá de Melo, Effects of quantum fluctuations on the low-energy collective modes of two-dimensional superfluid Fermi gases from the BCS to the Bose limit, Phys. Rev. Lett. 131, 113001 (2023).
  92. L. Pisani, P. Bovini, F. Pavan, and P. Pieri, Boson-fermion pairing and condensation in two-dimensional Bose-Fermi mixtures, SciPost Phys. 18, 076 (2025).
  93. A. Tartari, Phase diagram of a two-component Fermi gas with density imbalance throughout the BCS-BEC crossover, Ph.D. thesis, University of Camerino, 2011.
  94. W. Schneider, V. B. Shenoy, and M. Randeria, Theory of radio frequency spectroscopy of polarized Fermi gases, arXiv:0903.3006.
  95. I. Dzyaloshinskii, Some consequences of the Luttinger theorem:   The Luttinger surfaces in non-Fermi liquids and Mott insulators, Phys. Rev. B 68, 085113 (2003).
  96. R. Combescot, S. Giraud, and X. Leyronas, Analytical theory of the dressed bound state in highly polarized Fermi gases, Europhys. Lett. 88, 60007 (2009).
  97. M. Punk, P. T. Dumitrescu, and W. Zwerger, Polaron-to-molecule transition in a strongly imbalanced Fermi gas, Phys. Rev. A 80, 053605 (2009).
  98. E. Fratini and P. Pieri, Mass imbalance effect in resonant Bose-Fermi mixtures, Phys. Rev. A 85, 063618 (2012).
  99. M. M. Parish, Polaron-molecule transitions in a two-dimensional Fermi gas, Phys. Rev. A 83, 051603(R) (2011).
  100. D. Durel and M. Urban, Application of the renormalized random-phase approximation to polarized Fermi gases, Phys. Rev. A 101, 013608 (2020).
  101. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Dover Publications, Mineola, NY, 2003).
  102. J. M. Luttinger and J. C. Ward, Ground-state energy of a many-fermion system. II, Phys. Rev. 118, 1417 (1960).
  103. S. Takada and T. Izuyama, Superconductivity in a molecular field. I, Prog. Theor. Phys. 41, 635 (1969).
  104. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Dover Publications, New York, 1975).
  105. P. Nozières, Theory of Interacting Fermi Systems (W. A. Benjamin, New York, 1964).
  106. J. Gan and E. Wong, Non-Fermi-liquid behavior in quantum critical systems, Phys. Rev. Lett. 71, 4226 (1993).
  107. S. Schmitt-Rink, C. M. Varma, and A. E. Ruckenstein, Pairing in two dimensions, Phys. Rev. Lett. 63, 445 (1989).
  108. N. Dupuis, Field Theory of Condensed Matter and Ultracold Gases (World Scientific, Singapore, 2023), Vol. 1.
  109. P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435 (1977).
  110. A. J. Millis, Effect of a nonzero temperature on quantum critical points in itinerant fermion systems, Phys. Rev. B 48, 7183 (1993).
  111. V. Oganesyan, S. A. Kivelson, and E. Fradkin, Quantum theory of a nematic Fermi fluid, Phys. Rev. B 64, 195109 (2001).
  112. W. Metzner, D. Rohe, and S. Andergassen, Soft Fermi surfaces and breakdown of Fermi-liquid behavior, Phys. Rev. Lett. 91, 066402 (2003).
  113. L. Dell'Anna and W. Metzner, Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions, Phys. Rev. B 73, 045127 (2006).
  114. P. Wölfle and A. Rosch, Fermi liquid near a quantum critical point, J. Low Temp. Phys. 147, 165 (2007).
  115. P. A. Lee, Gauge field, Aharonov-Bohm flux, and high-Tc superconductivity, Phys. Rev. Lett. 63, 680 (1989).
  116. M. A. Metlitski and S. Sachdev, Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order, Phys. Rev. B 82, 075127 (2010).
  117. D. Belitz, T. R. Kirkpatrick, A. J. Millis, and T. Vojta, Nonanalytic magnetization dependence of the magnon effective mass in itinerant quantum ferromagnets, Phys. Rev. B 58, 14155 (1998).
  118. J. Rech, C. Pépin, and A. V. Chubukov, Quantum critical behavior in itinerant electron systems: Eliashberg theory and instability of a ferromagnetic quantum critical point, Phys. Rev. B 74, 195126 (2006).
  119. D. Dalidovich and S.-S. Lee, Perturbative non-Fermi liquids from dimensional regularization, Phys. Rev. B 88, 245106 (2013).
  120. I. Mandal and S.-S. Lee, Ultraviolet/infrared mixing in non-Fermi liquids, Phys. Rev. B 92, 035141 (2015).
  121. S. Sur and S.-S. Lee, Quasilocal strange metal, Phys. Rev. B 91, 125136 (2015).
  122. R. Küchler, P. Gegenwart, J. Custers, O. Stockert, N. Caroca-Canales, C. Geibel, J. G. Sereni, and F. Steglich, Quantum criticality in the cubic heavy-fermion system CeIn3−xSnx, Phys. Rev. Lett. 96, 256403 (2006).
  123. E. Fawcett, Spin-density-wave antiferromagnetism in chromium, Rev. Mod. Phys. 60, 209 (1988).
  124. J. A. Hertz and M. A. Klenin, Fluctuations in itinerant-electron paramagnets, Phys. Rev. B 10, 1084 (1974).
  125. A. Abanov, A. V. Chubukov, and J. Schmalian, Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis, Adv. Phys. 52, 119 (2003).
  126. P. Pieri and G. C. Strinati, Strong-coupling limit in the evolution from BCS superconductivity to Bose-Einstein condensation, Phys. Rev. B 61, 15370 (2000).
  127. F. Pistolesi and G. C. Strinati, Evolution from BCS superconductivity to Bose condensation: Calculation of the zero-temperature phase coherence length, Phys. Rev. B 53, 15168 (1996).
  128. S.-S. Lee, Stability of the U(1) spin liquid with a spinon Fermi surface in 2+1 dimensions, Phys. Rev. B 78, 085129 (2008).
  129. J. Polchinski, Low-energy dynamics of the spinon-gauge system, Nucl. Phys. B 422, 617 (1994).
  130. M. A. Metlitski and S. Sachdev, Quantum phase transitions of metals in two spatial dimensions. II. Spin density wave order, Phys. Rev. B 82, 075128 (2010).
  131. S. A. Maier and P. Strack, Universality in antiferromagnetic strange metals, Phys. Rev. B 93, 165114 (2016).
  132. P. Lunts, A. Schlief, and S.-S. Lee, Emergence of a control parameter for the antiferromagnetic quantum critical metal, Phys. Rev. B 95, 245109 (2017).
  133. A. Schlief, P. Lunts, and S.-S. Lee, Exact critical exponents for the antiferromagnetic quantum critical metal in two dimensions, Phys. Rev. X 7, 021010 (2017).
  134. P. Lunts, M. S. Albergo, and M. Lindsey, Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable hybrid Monte Carlo, Nat. Commun. 14, 2547 (2023).
  135. Y. B. Bazaliy, R. Ramazashvili, Q. Si, and M. R. Norman, Magnetotransport near a quantum critical point in a simple metal, Phys. Rev. B 69, 144423 (2004).
  136. I. Mandal, Stable non-Fermi liquid fixed point at the onset of incommensurate 2kF charge density wave order, Nucl. Phys. B 1005, 116586 (2024).
  137. Y. Sagi, T. E. Drake, R. Paudel, R. Chapurin, and D. S. Jin, Breakdown of the Fermi liquid description for strongly interacting fermions, Phys. Rev. Lett. 114, 075301 (2015).
  138. C. Feng, T. Hartke, Y.-Y. He, B. Oreg, C. Turnbaugh, N. Jia, M. Zwierlein, and S. Zhang, In search of exotic pairing in the Hubbard model: Many-body computation and quantum gas microscopy, Proc. Natl. Acad. Sci. USA 123, e2600303123 (2026).
  139. C. A. Regal, M. Greiner, and D. S. Jin, Observation of resonance condensation of fermionic atom pairs, Phys. Rev. Lett. 92, 040403 (2004).
  140. M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, Observation of pair condensation in the quasi-2D BEC-BCS crossover, Phys. Rev. Lett. 114, 230401 (2015).
  141. P. Dyke, A. Hogan, I. Herrera, C. C. N. Kuhn, S. Hoinka, and C. J. Vale, Dynamics of a Fermi gas quenched to unitarity, Phys. Rev. Lett. 127, 100405 (2021).
  142. P. Wang, Z. Fu, L. Huang, and J. Zhang, Momentum-resolved Raman spectroscopy of a noninteracting ultracold Fermi gas, Phys. Rev. A 85, 053626 (2012).
  143. Z. Fu, P. Wang, L. Huang, Z. Meng, and J. Zhang, Momentum-resolved Raman spectroscopy of bound molecules in ultracold Fermi gas, Phys. Rev. A 86, 033607 (2012).
  144. C. Shkedrov, G. Ness, Y. Florshaim, and Y. Sagi, In situ momentum-distribution measurement of a quantum degenerate Fermi gas using Raman spectroscopy, Phys. Rev. A 101, 013609 (2020).
  145. O. K. Diessel, J. von Milczewski, A. Christianen, and R. Schmidt, Probing molecular spectral functions and unconventional pairing using Raman spectroscopy, Phys. Rev. Res. 6, 023239 (2024).
  146. F. Pirolo, L. Pisani, and P. Pieri, Data for “FFLO transition and quantum criticality in polarized Fermi gases”, Zenodo Repository, 2026, https://doi.org/10.5281/zenodo.21699968.
  147. S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Continuous quantum phase transitions, Rev. Mod. Phys. 69, 315 (1997).
  148. M. E. Fisher and R. J. Burford, Theory of critical-point scattering and correlations. I. The Ising model, Phys. Rev. 156, 583 (1967).
  149. B. L. Altshuler, L. B. Ioffe, and A. J. Millis, Critical behavior of the T=02kF density-wave phase transition in a two-dimensional Fermi liquid, Phys. Rev. B 52, 5563 (1995).
  150. S.-S. Lee, Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions, Phys. Rev. B 80, 165102 (2009).
  151. M. Drechsler and W. Zwerger, Crossover from BCS-superconductivity to Bose-condensation, Ann. Phys. 504, 15 (1992).
  152. J. D'Alberto, L. Cardarelli, D. E. Galli, G. Bertaina, and P. Pieri, Quantum Monte Carlo and perturbative study of two-dimensional Bose-Fermi mixtures, Phys. Rev. A 109, 053302 (2024).

Outline

Information

Phys. Rev. B 114, 254507– Published 6 November, 2026
  • Received 31 July 2026
  • Revised 14 October 2026
  • Accepted 26 October 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation