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Physical Review Letters

Parity violation and superconductivity in two-dimensional correlated electronic systems

Paul B. Wiegmann

Published Oct 15, 1990• 44 citations
Publisher

Abstract

It is shown that the parity-violated ground state of two-dimensional strongly correlated electronic systems (commensurate flux state) provides a physical realization of the anyon mechanism of superconductivity. The electromagnetic response of the commensurate flux state is calculated. It is found that the superconducting ground state is accompanied by the restoration of parity and time-reversal symmetry: the parity-violation signal is very small at low energies and momentum, and vanishes in the static limit as well as in the uniform limit.

DOI
10.1103/physrevlett.65.2070

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It is shown that the parity-violated ground state of two-dimensional strongly correlated electronic systems (commensurate flux state) provides a physical realization of the anyon mechanism of superconductivity. The electromagnetic response of the commensurate flux state is calculated. It is found that the superconducting ground state is accompanied by the restoration of parity and time-reversal symmetry: the parity-violation signal is very small at low energies and momentum, and vanishes in the static limit as well as in the uniform limit.
We consider electromagnetic response and kinetic properties of a strongly correlated two-dimensional electron system having parity- and time-reversal symmetry violating ground state. An important example of such a state is presented by a generalized flux phase of the doped Mott insulator with a fictitious magnetic field commensurate with filling. We observe that electromagnetic response functions of the compressible flux states exhibit no superconducting behaviour. Processes of spinon and holon scattering by fluctuations of a fictitious magnetic field produce a relaxation of the system. On the basis of the quantum kinetic equation we find frequency- and momentum-dependent electrical and thermal conductivities and thermopower of a generalized flux phase.
We study parity violating states of strongly correlated two-dimensional electronic systems. On the basis of mean field theory for the SU(2N)-symmetric generalization of the system involved we give the arguments supporting the existence of these states at a filling number different from one-half. We derive an effective Lagrangian describing the long wavelength dynamics of magnetic excitations and their interaction with charged spinless holes. We establish that the ground state of a doped system is superconducting and discuss the phenomenological manifestations of the parity violation.
Using a large-N slave-boson formulation of the t-J model on the square lattice that has explicit spinon-holon decoupling of the correlated electron, we study the stability and electromagnetic response of the commensurate flux phase in the limit near half filling. A region of stability for the flux phase is found located between a dimer phase region near half filling and a fluxless metallic phase region far from half filling. The commensurate flux phase itself is found to be a superconductor of the anyon type. Furthermore, it is shown that the parity--time-reversal--violating characteristic of this phase results in a frequency-dependent Faraday effect. This effect manifests itself as a zero-field Hall effect in the low-frequency limit, where the off-diagonal conductance scales with the hole concentration. Associated with this result, it is also found that the commensurate flux phase supports a series of optical absorption peaks at energies on the order of J. Lastly, inclusion of instanton tunneling events in the effective gauge-field action results in the confinement of the spinon and holon degrees of freedom. This confinement effect, however, weakens exponentially as one approaches the Mott transition. The present results are discussed in the context of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting oxides.
We study parity violating states of strongly correlated two-dimensional electronic systems. On the basis of mean field theory for the SU (2N)-symmetric generalization of the system involved we give the arguments supporting the existence of these states at a filling number different from one-half. We derive an effective Lagrangian describing the long wavelength dynamics of magnetic excitations and their interaction with charged spinless holes. We establish that the ground state of a doped system is superconducting and discuss the phenomenological manifestations of the parity violation.
The discovery of high temperature superconductivity inspired a number of novel proposals, one of which, put forward by C.M.Varma, involves the breaking of time-reversal symmetry to explain the physics of the underdoped pseudogap phase. It was proposed that time-reversal symmetry is spontaneously broken as a result of strong repulsion between the Cu-O electrons to form loop-currents in the system. In this work, we developed a general theory to study the quantum phase transitions in the 2 dimensional strongly interacting electronic systems in which time-reversal symmetry is spontaneously broken in the ground state. We first applied the theory of magnetic groups to identify electronic current-loop patterns in two physically relevant systems: (i) 2-band model involving spinless electrons on a honeycomb lattice with next-nearest-neighbor interactions; (ii) 3-band CuO2CuO_{2}CuO2​ model with and without lattice distortions. Next, by examining the correlation function within the standard ring and ladder Dyson series approximations, we identify the effective Hamiltonian with the relevant interactions responsible for creating low-energy fluctuations near the quantum critical point. The mean-field analysis of this effective Hamiltonian elucidated the fact that time-reversal symmetry breaking in a 2-band model is in the same universality class as the interband particle-hole pair condensation instability which occurs in the semi-conductors under large enough particle-hole attraction. Using Hubbard-Stratonovich transformation and functional integral method, we are able to investigate this instability and the static susceptibility in the condensed phase both in half-filling and doped case. Away from half-filling, because the condensates are metallic and couple to the gapless collective intraband particle-hole excitations, we find that the static susceptibility is generically negative as a result of this coupling, which implies that the condensates are unstable.
The nature of superfluid, superconducting, and magnetic ordering is elucidated for mesoscopic systems in which the single-particle level spacing is much larger than both the temperature and the critical temperature of ordering. Ordering is defined as a spontaneous violation of symmetry, the gauge invariance and time reversal being by definition symmetries violated in superfluidity (superconductivity) and magnetism contexts, respectively. Superfluidity and superconductivity are realized in thermodynamic equilibrium states with a non-integral average number of particles and are accompanied by the spontaneous violation of time homogeneity. In Fermi systems two types of superfluidity and superconductivity are possible which are characterized by the presence of pair or single-particle 'condensates'. The latter is remarkable in that spontaneous violation of fundamental symmetries such as spatial 2? rotation and double time reversal takes place. Possible experiments on metallic nanoparticles and ultracold atomic gases in magnetic traps are discussed.