Band geometry, Berry curvature, and superfluid weight

Liang, Long; Vanhala, Tuomas I.; Peotta, Sebastiano; Siro, Topi; Harju, Ari; Törmä, Païvi

doi:10.1103/physrevb.95.024515

Cited by 194 publications

(293 citation statements)

References 69 publications

(132 reference statements)

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“…A flat band, which can be represented by δ function in the energy spectrum, is even more singular than a Van Hove singularity and leads to correlation induced novel phases which are qualitatively different from the phases appearing in presence of a Van Hove singularity [4]. Influence of the flat bands or quasiflat bands on different emergent novel phases of interacting lattice fermions, such as ferromagnetism [5][6][7][8], flat-band superfluidity [9][10][11], high-T c superconductivity of electron-doped compounds [12], non-Fermi-liquid behavior [13,14], and topological phases [15] have been explored theoretically. Experimentally, effects of flat bands have been reported in various real materials such as tetragonal La 4 Ba 2 Cu 2 O 10 [4], LaCo 5 and CePt 5 [16], and can be realized using ultracold atoms [17][18][19][20], where lattice geometry, and thus the singularities, can be well controlled.…”

Section: Introductionmentioning

confidence: 99%

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

2017

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The properties of a phase at finite interactions can be significantly influenced by the underlying dispersion of the noninteracting Hamiltonian. We demonstrate this by studying the repulsive Hubbard model on the twodimensional Lieb lattice, which has a flat band for vanishing interaction U . We perform real-space dynamical mean-field theory calculations at different temperatures and dopings using a continuous-time quantum Monte Carlo impurity solver. Studying the frequency dependence of the self-energy, we find that a nonmagnetic metallic region at finite temperature displays non-Fermi-liquid behavior, which is a concomitant of the flat-band singularity. At half-filling, we also find a magnetically ordered region, where the order parameter varies linearly with the interaction strength, and a strongly correlated Mott insulating phase. The double occupancy decreases sharply for small U , highlighting the flat-band contribution. Away from half-filling, we observe the stripe order, i.e., an inhomogeneous spin and charge density wave of finite wavelength, which turns into a sublattice ordering at higher temperatures.

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Section: Introductionmentioning

confidence: 99%

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

2017

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“…Now, the current operators (12), (13), the Green's function and the Hamiltonian all have the same structure as those for conventional BCS theory developed in [55]. Thus one can compute, by applying the Matsubara formalism and analytic continuation, the currentcurrent response function in a similar fashion as done in [55]. One starts from (11), inserts the expressions (12), (13) for the current operators, deploys the Matsubara formalism, applies the diagrammatic expansion up to first order diagrams and obtains , which vanishes at zero temperature if the quasiparticle spectrum is gapped.…”

Section: Derivation Of the Superfluid Weight In The Presence Of Soc Fmentioning

confidence: 99%

“…In [54,55] it was shown that in case of conventional BCS states the superfluid weight can be divided to two parts: the so-called conventional and geometric contributions, = + comprises the geometric properties of the Bloch functions. In a similar fashion than in [55], also in our case the superfluid weight can be split to conventional and geometric parts so that…”

Section: Derivation Of the Superfluid Weight In The Presence Of Soc Fmentioning

confidence: 99%

“…Additionally, we compare the superfluid weight components in orthogonal spatial directions. We also compute the so-called geometric superfluid weight component which is just recently found new superfluid contribution that depends on the geometric properties of the single-particle Bloch functions [54,55].In our study we discard the existence of LO phases as the LO ansatzes break the translational invariance which is required for deriving the superfluid weight in a simple form. Ignoring LO states, however, is not an issue because we are interested in the stability and BKT transition temperatures of exotic superfluid states: if there exists more stable LO states than FF states that we find, it implies the BKT transition temperatures of these LO states being higher than the temperatures we obtain for FF states.…”

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Superfluid weight and Berezinskii–Kosterlitz–Thouless temperature of spin-imbalanced and spin–orbit-coupled Fulde–Ferrell phases in lattice systems

2018

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We study the superfluid weight D s and Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures T BKT in case of exotic Fulde-Ferrell (FF) superfluid states in lattice systems. We consider spinimbalanced systems with and without spin-orbit coupling (SOC) accompanied with in-plane Zeeman field. By applying mean-field theory, we derive general equations for D s and T BKT in the presence of SOC and the Zeeman fields for 2D Fermi-Hubbard lattice models, and apply our results to a 2D square lattice. We show that conventional spin-imbalanced FF states without SOC can be observed at finite temperatures and that FF phases are further stabilized against thermal fluctuations by introducing SOC. We also propose how topologically non-trivial SOC-induced FF phases could be identified experimentally by studying the total density profiles. Furthermore, the relative behavior of transverse and longitudinal superfluid weight components and the role of the geometric superfluid contribution are discussed.performed with quasi-one-dimensional population-imbalanced atomic gases have shown to be consistent with the existence of the FFLO state [33] but unambiguous proof is still missing.In addition to conventional spin-imbalanced quantum gas experiments, recently also synthetic SOC and Zeeman fields have been realized in ultracold gas experiments [34][35][36][37][38] which makes it possible to investigate SOC-induced FFLO states as well. As SOC-induced FFLO states have been predicted to be stable in larger parameter regime than conventional spin-imbalanced FFLO phases [10], synthetic SOC could provide a way to realize FFLO experimentally in ultracold gas systems [15].Low dimensionality has been predicted to favor 40]. However, in two and lower dimensional systems thermal phase fluctuations of the Cooper pair wave functions prevent the formation of true superfluid long range order as stated by the Mermin-Wagner theorem [41]. Instead, only quasi-long range order is possible. In two-dimensions, the phase transition from a normal Fermi gas to a superfluid state of quasi-long range order is determined by the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T BKT [42]. Below T BKT the system is a superfluid and above T BKT superfluidity is lost.In recent years, SOC-induced FFLO phases in two-dimensional systems have gained considerable attention [7,10,13,14,20,21,25]. In these systems it has been argued that SOC accompanied with the in-plane Zeeman field would yield FFLO states. Furthermore, in [13,14] it was predicted that in the presence of the out-of-plane Zeeman field, i.e. spin-imbalance, SOC-induced FFLO states could be topologically non-trivial and support Majorana fermions. Such topological FFLO states are conceptually new and exotic superconductive phases of matter. However, these studies were performed by applying mean-field theories which do not consider the stability of FFLO states against thermal phase fluctuations in terms of the BKT transition. Superfluidity and BKT transition temperatures of BCS phases in spin-...

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Pair density wave facilitated by Bloch quantum geometry in nearly flat band multiorbital superconductors

Chen

Wen

2023

Sci. China Phys. Mech. Astron.

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Band geometry, Berry curvature, and superfluid weight

Cited by 194 publications

References 69 publications

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

Temperature and doping induced instabilities of the repulsive Hubbard model on the Lieb lattice

Superfluid weight and Berezinskii–Kosterlitz–Thouless temperature of spin-imbalanced and spin–orbit-coupled Fulde–Ferrell phases in lattice systems

Pair density wave facilitated by Bloch quantum geometry in nearly flat band multiorbital superconductors

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