Upper bound on the superfluid stiffness in disordered Bose and Fermi systems

We derive several upper bounds for the superfluid stiffness ${D}_{s}$ for Bose and Fermi systems in terms of expectation values of local operators using linear response theory and variational methods. These give insight into the nontrivial dependence of ${D}_{s}$ on parameters such as disorder and interaction in systems with broken continuous translational invariance. Our best variational bound for disordered systems is obtained by allowing the phase twist applied at the boundary to be distributed inhomogeneously within the system. Path integral quantum Monte Carlo simulations are used to quantitatively compare the bounds and ${D}_{s}$ for disordered interacting Bose systems.We derive several upper bounds for the superfluid stiffness ${D}_{s}$ for Bose and Fermi systems in terms of expectation values of local operators using linear response theory and variational methods. These give insight into the nontrivial dependence of ${D}_{s}$ on parameters such as disorder and interaction in systems with broken continuous translational invariance. Our best variational bound for disordered systems is obtained by allowing the phase twist applied at the boundary to be distributed inhomogeneously within the system. Path integral quantum Monte Carlo simulations are used to quantitatively compare the bounds and ${D}_{s}$ for disordered interacting Bose systems.

arXiv:cond-mat/9801053Physical review. B, Condensed matterMay 1, 199839 citations

Superconductivity is boundless

Johannes Stephan Hofmann, Debanjan Chowdhury, Steven Allan Kivelson +1 more

What limits the value of the superconducting transition temperature ( $T_c$ ) is a question of great fundamental and practical importance. Various upper bounds on $T_c$ have been proposed, expressed as fractions of the Fermi temperature, $T_F$ , the zero-temperature superfluid stiffness, $\rho_s(0)$ , or a characteristic Debye frequency, $\omega_0$ . We show that while these bounds are physically motivated and are certainly useful in many relevant situations, none of them serve as a rigorous bound on $T_c$ . To demonstrate this, we provide explicit models where $T_c/T_F$ (with an appropriately defined $T_F$ ), $T_c/\rho_s(0)$ , and $T_c/\omega_0$ are unbounded.What limits the value of the superconducting transition temperature ($T_c$) is a question of great fundamental and practical importance. Various upper bounds on $T_c$ have been proposed, expressed as fractions of the Fermi temperature, $T_F$, the zero-temperature superfluid stiffness, $\rho_s(0)$, or a characteristic Debye frequency, $\omega_0$. We show that while these bounds are physically motivated and are certainly useful in many relevant situations, none of them serve as a rigorous bound on $T_c$. To demonstrate this, we provide explicit models where $T_c/T_F$ (with an appropriately defined $T_F$), $T_c/\rho_s(0)$, and $T_c/\omega_0$ are unbounded.

May 19, 20210 citations

Lattice effects on the superfluid stiffness

Matthias Hecker, Jörg Schmalian

Verhandlungen der Deutschen Physikalischen GesellschaftJan 1, 20170 citations

Bounds on the Superconducting Transition Temperature: Applications to Twisted Bilayer Graphene and Cold Atoms

Tamaghna Hazra, Nishchhal Verma, Mohit Randeria

Understanding the material parameters that control the superconducting transition temperature T c is a problem of fundamental importance.In many novel superconductors phase fluctuations determine T c , rather than the collapse of the pairing amplitude.We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension.This in turn leads to an upper bound on T c in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry.Our bound is particularly useful for the strongly correlated regime of low-density and narrowband systems, where mean-field theory fails.For a simple parabolic band in 2D with Fermi energy E F , we find that k B T c ≤ E F =8, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases.Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum T c to be close to the experimentally observed value.Finally, we discuss the question of deriving rigorous upper bounds on T c in 3D.Understanding the material parameters that control the superconducting transition temperature T c is a problem of fundamental importance.In many novel superconductors phase fluctuations determine T c , rather than the collapse of the pairing amplitude.We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension.This in turn leads to an upper bound on T c in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry.Our bound is particularly useful for the strongly correlated regime of low-density and narrowband systems, where mean-field theory fails.For a simple parabolic band in 2D with Fermi energy E F , we find that k B T c ≤ E F =8, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases.Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum T c to be close to the experimentally observed value.Finally, we discuss the question of deriving rigorous upper bounds on T c in 3D.

arXiv:1811.12428Physical Review XSep 17, 201992 citations

We derive several upper bounds for the superfluid stiffness

{D}_{s}

for Bose and Fermi systems in terms of expectation values of local operators using linear response theory and variational methods. These give insight into the nontrivial dependence of

{D}_{s}

on parameters such as disorder and interaction in systems with broken continuous translational invariance. Our best variational bound for disordered systems is obtained by allowing the phase twist applied at the boundary to be distributed inhomogeneously within the system. Path integral quantum Monte Carlo simulations are used to quantitatively compare the bounds and

{D}_{s}

for disordered interacting Bose systems.

What limits the value of the superconducting transition temperature (

T_c

) is a question of great fundamental and practical importance. Various upper bounds on

T_c

have been proposed, expressed as fractions of the Fermi temperature,

T_F

, the zero-temperature superfluid stiffness,

\rho_s(0)

, or a characteristic Debye frequency,

\omega_0

. We show that while these bounds are physically motivated and are certainly useful in many relevant situations, none of them serve as a rigorous bound on

T_c

. To demonstrate this, we provide explicit models where

T_c/T_F

(with an appropriately defined

T_F

T_c/\rho_s(0)

, and

T_c/\omega_0

are unbounded.