Electrodynamic duality and vortex unbinding in driven-dissipative condensates

Editors' Suggestion

Electrodynamic duality and vortex unbinding in driven-dissipative condensates

G. Wachtel, L. M. Sieberer, S. Diehl, and E. Altman

Phys. Rev. B 94, 104520 – Published 27 September 2016

Abstract

We investigate the superfluid properties of two-dimensional driven Bose liquids, such as polariton condensates, using their long-wavelength description in terms of a compact Kardar-Parisi-Zhang (KPZ) equation for the phase dynamics. We account for topological defects (vortices) in the phase field through a duality mapping between the compact KPZ equation and a theory of nonlinear electrodynamics coupled to charges. Using the dual theory, we derive renormalization group equations that describe vortex unbinding in these media. When the nonequilibirum drive is turned off, the KPZ nonlinearity $λ$ vanishes and the RG flow gives the usual Kosterlitz-Thouless (KT) transition. On the other hand, with nonlinearity $λ > 0$ vortices always unbind, even if the same system with $λ = 0$ is superfluid. We predict the finite-size scaling behavior of the superfluid stiffness in the crossover governed by vortex unbinding showing its clear distinction from the scaling associated with the KT transition.

Received 2 May 2016

DOI:https://doi.org/10.1103/PhysRevB.94.104520

Physics Subject Headings (PhySH)

BKT transition Polaritons

2-dimensional systems

Kardar–Parisi–Zhang equation Renormalization group

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. Wachtel^1,2, L. M. Sieberer^1,3, S. Diehl⁴, and E. Altman^1,3

¹Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
²Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
³Department of Physics, University of California, Berkeley, California 94720, USA
⁴Institute of Theoretical Physics, University of Cologne, D-50937 Cologne, Germany

Lattice duality for the compact Kardar-Parisi-Zhang equation

L. M. Sieberer, G. Wachtel, E. Altman, and S. Diehl

Phys. Rev. B 94, 104521 (2016)

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 94, Iss. 10 — 1 September 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Finite-size phase diagram for a 2D driven-dissipative condensate. $T$ is the “vortex temperature,” i.e., the strength of the noise acting on topological defects, and $L$ is the system size measured here in units of a microscopic cutoff scale $a$ . In thermal equilibrium (blue, dashed line), close to the critical temperature $T_{c}$ , the phase boundary behaves as $ln (L / a) \sim 1 / \sqrt{T_{c} - T}$ . Out of equilibrium (red, solid line), algebraic order is destroyed at any noise strength in the thermodynamic limit. For small values of $T$ , the phase boundary approaches a value on the order of the bare screening length $L_{v}$ . The phase boundaries are obtained by integrating the renormalization group flow equations (52) up to $y = 1$ , starting from an initial value of $y = 0.1$ .
Reuse & Permissions
Figure 2
RG flow lines as described by Eqs. (52). Dashed line: $λ = 0$ , KT flow; solid line: $λ^{2} / D^{2} = 0.4$ .
Reuse & Permissions
Figure 3
Renormalized dilectric constant in a finite-size system, obtained by integrating the RG flow equations (52). (a) 2D superfluid in thermal equilibrium, i.e., with $λ = 0$ . From top to bottom, the lines correspond to increasing system sizes. $l = 2, 3, ..., 8, \infty$ denotes the logarithmic system size $l = ln (L / a)$ . In the thermodynamic limit, the dielectric constant undergoes a discontinuous jump at the critical temperature from zero to the universal value $1 / (ɛ T) = 4$ . (b) Nonequilibrium RG flow with $λ^{2} / D^{2} = 0.15$ . The qualitative behavior of $1 / (ɛ T)$ closely resembles the equilibrium one of panel (a) up to moderate system sizes. For small values of $λ / D$ , the agreement is even quantitative, and in finite-size systems equilibrium and driven-dissipative cases are practically indistinguishable. The nonequilibrium character of the underlying dynamics becomes manifest only in the thermodynamic limit, when $1 / (ɛ T)$ is renormalized to zero. In both panels, $T$ is the bare value of the temperature, while $ɛ$ is the renormalized dielectric constant.
Reuse & Permissions
Figure 4
Finite-size phase diagram as a function of (a) the dimensionless pumping strength $x$ and (b) the vortex fugacity $y$ . In both panels, the red, solid line denotes the boundary between disordered and algebraic order phases for $\bar{γ} = 0.1$ and $\bar{u} = 0.14$ , the green, dotted-dashed line denotes the same boundary with $\bar{γ} = 0.5$ , and the blue, dashed line is the KT phase boundary. In exciton-polaritons, the microscopic scale $a$ can be estimated as the healing length, which is typically $a \approx 1 μ m$ , while typical system sizes are on the order of $L \approx 100 μ m$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics