Abstract
Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.
Highlights
Vortices in superfluids are characterized by the quantized circulation of superfluid velocity and manifest quantum mechanics on macroscopic scales
The softness of the Tkachenko mode implies that true off-diagonal long-range U(1) order is destroyed by quantum fluctuations in two-dimensional vortex crystals at vanishing temperature and the system exhibits only algebraically decaying U(1) order [28,29,30]
The Abrikosov mean-field theory predicts a direct second-order transition between the vortex crystal in a superconductor and the normal phase [13], fluctuations are expected to invalidate this result [34]. It was proposed already in [35] that, at a sufficiently large temperature, a vortex crystal in a two-dimensional superconductor should melt into a vortex fluid via a pair of BKT-like phase transitions triggered by unbinding of dislocation and disclination defects of the crystal
Summary
Vortices in superfluids are characterized by the quantized circulation of superfluid velocity and manifest quantum mechanics on macroscopic scales. The Abrikosov mean-field theory predicts a direct second-order transition between the vortex crystal in a superconductor and the normal phase [13], fluctuations are expected to invalidate this result [34] It was proposed already in [35] that, at a sufficiently large temperature, a vortex crystal in a two-dimensional superconductor should melt into a vortex fluid via a pair of BKT-like phase transitions triggered by unbinding of dislocation and disclination defects of the crystal. Since it is expected that dislocations and disclinations play an important role in thermal and quantum melting of two-dimensional vortex crystals, it is desirable to develop a theory, where these topological defects are naturally incorporated. A bound state of two dislocations of opposite charge carries the vortex number charge and cannot unbind without condensing vortices These two observations imply that a conventional continuous dislocation-assisted quantum melting transition between the vortex crystal and a hexatic or smectic phase is not allowed [71]. We investigate two different possible Higgs transitions and derive the effective gauge theories of resulting quantum nematic and smectic phases
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