Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.

arXiv:1801.03495Physical Review LettersSep 24, 20189 citations

Deconfined quantum critical point in fermionic systems

Zixiang Li, Hong Yao

Bulletin of the American Physical SocietyMar 8, 20180 citations

Collisionless transport close to a fermionic quantum critical point

Bitan Roy, Vladimir Juričić

We here report the scaling of optical conductivity (OC) in the \emph{collisionless} regime ( $\hbar \omega \gg k_B T$ ) in the vicinity of a relativistic quantum critical point, separating two-dimensional massless Dirac fermions from a fully gapped insulator. Inside the critical regime gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC according to $\sigma^{\rm IB}_0 [1-N_b/(2N_f)]$ for $N_f \gg 1$ as $T \to 0$ to the leading order in $\epsilon$ -expansion, where $N_f (N_b)$ is the fermionic(bosonic) flavor number, $\sigma^{\rm IB}_0$ is the OC of a non-interacting Dirac fluid, and $\epsilon=3-d$ . Furthermore, the weight of the Drude peak inside the critical regime also gets suppressed following a universal scaling function, while maintaining its delta function profile. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalization of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented.We here report the scaling of optical conductivity (OC) in the \emph{collisionless} regime ($\hbar \omega \gg k_B T$) in the vicinity of a relativistic quantum critical point, separating two-dimensional massless Dirac fermions from a fully gapped insulator. Inside the critical regime gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC according to $\sigma^{\rm IB}_0 [1-N_b/(2N_f)]$ for $N_f \gg 1$ as $T \to 0$ to the leading order in $\epsilon$-expansion, where $N_f (N_b)$ is the fermionic(bosonic) flavor number, $\sigma^{\rm IB}_0$ is the OC of a non-interacting Dirac fluid, and $\epsilon=3-d$. Furthermore, the weight of the Drude peak inside the critical regime also gets suppressed following a universal scaling function, while maintaining its delta function profile. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalization of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented.

Jan 10, 20182 citations

Fermion-induced quantum criticality with two length scales in Dirac systems

Emilio Mínguez Torres, Laura Classen, Igor F. Herbut +1 more

The recently discovered fermion-induced quantum critical points of Dirac materials present a new opportunity to revisit and extend the standard paradigms of quantum criticality. The appearance of a second diverging length scale at a continuous quantum phase transition is one such extension. The authors present a functional renormalization group study of fermion-induced quantum critical points in the broken-symmetry phase, in which the presence of gapless fermions and discrete symmetry breaking provide the natural setup for this phenomenon to occur.The recently discovered fermion-induced quantum critical points of Dirac materials present a new opportunity to revisit and extend the standard paradigms of quantum criticality. The appearance of a second diverging length scale at a continuous quantum phase transition is one such extension. The authors present a functional renormalization group study of fermion-induced quantum critical points in the broken-symmetry phase, in which the presence of gapless fermions and discrete symmetry breaking provide the natural setup for this phenomenon to occur.

arXiv:1802.00364Physical review. B./Physical review. BMar 22, 201843 citations

Fermion-induced quantum critical points: beyond Landau criterion

Hong Yao, Zixiang Li, Yi‐Fan Jiang +1 more

Bulletin of the American Physical SocietyMar 16, 20160 citations

We here report the scaling of optical conductivity (OC) in the \emph{collisionless} regime (

\hbar \omega \gg k_B T

) in the vicinity of a relativistic quantum critical point, separating two-dimensional massless Dirac fermions from a fully gapped insulator. Inside the critical regime gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC according to

\sigma^{\rm IB}_0 [1-N_b/(2N_f)]

for

N_f \gg 1

T \to 0

to the leading order in

\epsilon

-expansion, where

N_f (N_b)

is the fermionic(bosonic) flavor number,

\sigma^{\rm IB}_0

is the OC of a non-interacting Dirac fluid, and

\epsilon=3-d

. Furthermore, the weight of the Drude peak inside the critical regime also gets suppressed following a universal scaling function, while maintaining its delta function profile. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalization of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented.