Fulde-Ferrell-Larkin-Ovchinnikov pairing as leading instability on the square lattice

Jan Gukelberger, Sebastian Lienert, Evgeny Kozik, Lode Pollet, and Matthias Troyer

Phys. Rev. B 94, 075157 – Published 31 August 2016

Abstract

We study attractively interacting spin- $\frac{1}{2}$ fermions on the square lattice subject to a spin population imbalance. Using unbiased diagrammatic Monte Carlo simulations we find an extended region in the parameter space where the Fermi liquid is unstable towards formation of Cooper pairs with nonzero center-of-mass momentum, known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In contrast to earlier mean-field and quasi-classical studies we provide quantitative and well-controlled predictions on the existence and location of the relevant Fermi-liquid instabilities. The highest temperature where the FFLO instability can be observed is about half of the superfluid transition temperature in the unpolarized system.

Received 16 September 2015
Revised 25 April 2016

DOI:https://doi.org/10.1103/PhysRevB.94.075157

Physics Subject Headings (PhySH)

FFLO

2-dimensional systems

Monte Carlo methods Quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jan Gukelberger^1,*, Sebastian Lienert¹, Evgeny Kozik², Lode Pollet³, and Matthias Troyer¹

¹Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
²Physics Department, King's College London, Strand, London WC2R 2LS, United Kingdom
³Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, University of Munich, Theresienstrasse 37, 80333 Munich, Germany

^*Corresponding author: gukelberger@phys.ethz.ch

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 94, Iss. 7 — 15 August 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Phase diagram for $U / t = - 4$ at quarter filling: The white region is a Fermi liquid. In the blue shaded region, the Fermi liquid is unstable towards conventional ( $Q = 0$ ) pairing. In the red shaded region there is an exclusive FFLO instability with finite pair momentum $Q_{*}$ . Open symbols indicate whether zero- (blue circles) or finite-momentum pairing (red diamonds) is dominant (black squares: no significant difference). The black dotted line separates the two regimes. All lines are guides to the eye.
Reuse & Permissions
Figure 2
(top) Temperature dependence of the leading pairing eigenvalues for zero momentum (open symbols/dashed lines) and finite momentum $Q_{*}$ (filled symbols/solid lines) for different polarizations $P$ . (center) Estimates of the critical polarization for the two channels from varying diagram order cutoff $N_{*}$ for temperatures $T = 0.5$ (black), $T = 0.1$ (green), and $T = 0.025$ (cyan). The left-most data points show our extrapolations $N_{*} \to \infty$ . (bottom) Difference between FFLO and conventional pairing eigenvalues for varying polarization. The corresponding temperatures are indicated to the right of the curves. Circles and diamonds on the curves indicate the critical polarization where zero- and finite-momentum eigenvalues respectively cross unity. Also shown is the pair momentum magnitude $Q_{*}$ (red dots).
Reuse & Permissions
Figure 3
Influence of density shown for $n = 0.8$ (top row) and $n = 0.1$ (center row) with polarization $P = 0.3$ and temperature $T = 0.025$ . Left panels show majority spin momentum distribution (colors, from blue=unoccupied to red=occupied) and minority FS (dashed contour), as well as the latter shifted by the optimal pair momentum $Q_{*}$ (solid contour). The other panels illustrate the dependence of the one-particle propagator product $χ (Q)$ on the pair momentum $Q$ . (bottom) Dependence of the optimal pair momentum $Q_{*}$ , extracted from the one-particle propagator product $χ (Q)$ , on density $n$ and polarization $P$ . Dotted lines indicate the weak-coupling form for an isotropic dispersion, dashed lines for a square-shaped Fermi surface.
Reuse & Permissions
Figure 4
Pairing eigenvalues for different channels at quarter filling and polarization $P = 0.2$ . Shown are the singlet pairing eigenvalues with pair momenta $Q = 0, Q_{*}$ (i.e., on the coordinate axis) and $Q_{\times}$ (on the BZ diagonal) as well as the $p$ -wave triplet eigenvalues for zero-momentum pairing of the majority ( $p^{↓ ↓}$ ) and minority ( $p^{↑ ↑}$ ) species, respectively. The latter have been multiplied by a factor of ten.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics