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arXiv:0712.1043 · Physical Review B

Nonequilibrium-induced metal-superconductor quantum phase transition in graphene

So Takei, Yong Baek Kim

Published Oct 2, 2008• 15 citations
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Abstract

We study the effects of dissipation and time-independent nonequilibrium drive on an open superconducting graphene. In particular, we investigate how dissipation and nonequilibrium effects modify the semi-metal-BCS quantum phase transition that occurs at half filling in equilibrium graphene with attractive interactions. Our system consists of a graphene sheet sandwiched by two semi-infinite three-dimensional Fermi-liquid reservoirs, which act both as a particle pump/sink and a source of decoherence. A steady-state charge current is established in the system by equilibrating the two reservoirs at different but constant chemical potentials. The graphene sheet is described using the attractive Hubbard model in which the interaction is decoupled in the $s$-wave channel. The nonequilibrium BCS superconductivity in graphene is formulated using the Keldysh path-integral formalism, and we obtain generalized gap and number density equations valid for both zero and finite voltages. The behavior of the gap is discussed as a function of both attractive interaction strength and electron densities for various graphene-reservoir couplings and voltages. We discuss how tracing out the dissipative environment (with or without voltage) leads to decoherence of Cooper pairs in the graphene sheet, hence, to a general suppression of the gap order parameter at all densities. For weak enough attractive interactions we show that the gap vanishes even for electron densities away from half filling and illustrate the possibility of a dissipation-induced metal-superconductor quantum phase transition. We find that the application of small voltages does not alter the essential features of the gap as compared to the case when the system is subject to dissipation alone (i.e., zero voltage). The possibility of tuning the system through the metal-superconductor quantum critical point using voltage is presented.

DOI
10.1103/physrevb.78.165401

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We study the effects of dissipation and time-independent nonequilibrium drive on an open superconducting graphene. In particular, we investigate how dissipation and nonequilibrium effects modify the semi-metal-BCS quantum phase transition that occurs at half filling in equilibrium graphene with attractive interactions. Our system consists of a graphene sheet sandwiched by two semi-infinite three-dimensional Fermi-liquid reservoirs, which act both as a particle pump/sink and a source of decoherence. A steady-state charge current is established in the system by equilibrating the two reservoirs at different but constant chemical potentials. The graphene sheet is described using the attractive Hubbard model in which the interaction is decoupled in the sss-wave channel. The nonequilibrium BCS superconductivity in graphene is formulated using the Keldysh path-integral formalism, and we obtain generalized gap and number density equations valid for both zero and finite voltages. The behavior of the gap is discussed as a function of both attractive interaction strength and electron densities for various graphene-reservoir couplings and voltages. We discuss how tracing out the dissipative environment (with or without voltage) leads to decoherence of Cooper pairs in the graphene sheet, hence, to a general suppression of the gap order parameter at all densities. For weak enough attractive interactions we show that the gap vanishes even for electron densities away from half filling and illustrate the possibility of a dissipation-induced metal-superconductor quantum phase transition. We find that the application of small voltages does not alter the essential features of the gap as compared to the case when the system is subject to dissipation alone (i.e., zero voltage). The possibility of tuning the system through the metal-superconductor quantum critical point using voltage is presented.
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Two-band electronic structures with a valence and a conduction band separated by a tunable energy gap and with pairing of electrons in different channels can be relevant to investigate the properties of two-dimensional multiband superconductors and electron-hole superfluids, such as monolayer FeSe, recently discovered superconducting bilayer graphene, and double-bilayer graphene electron-hole systems. This electronic configuration also allows us to study the coexistence of superconductivity and charge-density waves in connection with underdoped cuprates and transition metal dichalcogenides. By using a mean-field approach to study the system mentioned above, we have obtained numerical results for superconducting gaps, chemical potential, condensate fractions, coherence lengths, and superconducting mean-field critical temperature, considering a tunable band gap and different fillings of the conduction band, for a parametric choice of the pairing interactions. By tuning these quantities, the electrons redistribute among valence and conduction band in a complex way, leading to a new physics with respect to single-band superconductors, such as density-induced and band-selective BCS-BEC crossover, quantum phase transitions, and hidden criticalities. At finite temperature, this phenomenon is also responsible for the nonmonotonic behavior of the superconducting gaps resulting in a superconducting-normal state reentrant transition, without the need of disorder or magnetic effects.
Within the time-dependent Gutzwiller approximation applied to the negative-UUU Hubbard model, we investigate the dynamics of a superconductor after an interaction quench for different values of the final interaction from weak to strong coupling. The equilibrium BCS-BEC crossover becomes a sharp transition in the out-of-equilibrium dynamics between weak- and strong-coupling dynamical phases. Two different frequencies (${\mathrm{\ensuremath{\Omega}}}_{J}<{\mathrm{\ensuremath{\Omega}}}_{U}$) dominate the order parameter dynamics. In the weak coupling phase, ${\mathrm{\ensuremath{\Omega}}}_{J}$ follows twice the asymptotic average value of the gap (${\mathrm{\ensuremath{\Omega}}}_{J}\ensuremath{\approx}2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\infty}}$) and ${\mathrm{\ensuremath{\Omega}}}_{U}$ is much larger but hardy visible in the anomalous density. At long times the BCS dynamics is recovered but surprisingly differences remain during the transient phase. In the strong coupling phase, the dynamics decouples from the asymptotic value of the order parameter except at exactly half filling and close to the dynamical transition where ${\mathrm{\ensuremath{\Omega}}}_{U}\ensuremath{\approx}2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\infty}}$. The out-of-equilibrium transient spectral density and optical conductivity are presented and discussed in relation to pump probe experiments. Both ${\mathrm{\ensuremath{\Omega}}}_{J}$ and ${\mathrm{\ensuremath{\Omega}}}_{U}$ give rise to a complex structure of self-driven slow Rabi oscillations which are visible in the nonequilibrium optical conductivity where also sidebands appear due to the modulation of the double occupancy by superconducting amplitude oscillations. Analogous results apply to CDW and SDW systems. Our results show that in systems with long coherence times, pump-probe experiments allow us to characterize the regime (BCS vs preformed pairs) through very specific out-of-equilibrium fingerprints.
We study the competing charge-density-wave and superconducting order in the attractive Hubbard model under a voltage bias, using steady-state nonequilibrium dynamical mean-field theory. We show that the charge-density wave is suppressed in a current-carrying nonequilibrium steady state. This effect is beyond a simple Joule-heating mechanism and a ``supercooled'' metallic state is stabilized at a nonequilibrium temperature lower than the equilibrium superconducting Tc{T}_{c}Tc​. On the other hand, a current-carrying superconducting state is dissipationless and thus not subject to the same nonthermal suppression, and can therefore nucleate out of the supercooled metal, e.g., in a resistive switching experiment. The fact that an electric current can change the relative stability of different phases compared to thermal equilibrium, even when a system appears locally thermal due to electron-electron scattering, provides a general perspective to control intertwined orders out of equilibrium.
We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic $\ensuremath{\pi}$ flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the U(1)U(1)U(1) symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the sss-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekul\'e valence bond solid, where an emergent U(1)U(1)U(1) symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].
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