Excitonic condensation in a double-layer graphene system

Abstract

The possibility of excitonic condensation in a recently proposed electrically biased double-layer graphene system is studied theoretically. The main emphasis is put on obtaining a reliable analytical estimate for the transition temperature into the excitonic state. As in a double-layer graphene system the total number of fermionic "flavors" is equal to N = 8 due to two projections of spin, two valleys, and two layers, the large-N approximation appears to be especially suitable for theoretical investigation of the system. On the other hand, the large number of flavors makes screening of the bare Coulomb interactions very efficient, which, together with the suppression of backscattering in graphene, leads to an extremely low energy of the excitonic condensation. It is shown that the effect of screening on the excitonic pairing is just as strong in the excitonic state as it is in the normal state. As a result, the value of the excitonic gap ∆ is found to be in full agreement with the previously obtained estimate for the mean-field transition temperature T c , the maximum possible value ∆ max , T max c ∼ 10 −7 ǫ F (ǫ F is the Fermi energy) of both being in 1mK range for a perfectly clean system. This proves that the energy scale ∼ 10 −7 ǫ F really sets the upper bound for the transition temperature and invalidates the recently expressed conjecture about the high-temperature first-order transition into the excitonic state. These findings suggest that, unfortunately, the excitonic condensation in graphene double-layers can hardly be realized experimentally.

AA-stacked bilayer graphene in an applied electric field: Tunable antiferromagnetism and coexisting exciton order parameter

“…Under such conditions, according to Ref. [36], the exciton gap becomes exponentially small around 1 mK. In this case, a small amount of disorder makes exciton condensation impossible [37].…”

“…References [25][26][27][28][29]36] considered a system with two graphene layers separated by an insulating layer. The dielectric barrier between the layers completely suppresses the interlayer tunneling and destroys the AFM order.…”

Strong Coulomb drag and broken symmetry in double-layer graphene

“…These features suggest a unique venue for searching for 1 new interaction phenomena. Accordingly, double-layer graphene has attracted significant theoretical interest and has already become a subject of intense debates about predictions for both Coulomb drag [22][23][24][25][26][27][28] and excitonic superfluidity 15,29 . As for experiment, a recent publication 16 reported Coulomb drag in double-layer graphene in zero magnetic field B by using devices in which the layers were separated by a several-nanometre-thick alumina barrier and had charge carrier mobilities µ ∼ 10,000 cm 2 V −1 s −1 .…”

Superfluidity of a dilute gas of electron-hole pairs in a bilayer system

“…Quite recently a suggestion has been made to use graphene layers as components of bilayer systems [14][15][16][17][18]. Further investigations revealed that a serious problem in this case is screening of Coulomb interaction between the electron and the hole [19,20]. The screening effect is most dangerous in the regime of weak coupling, when the size of electron-hole pairs significantly exceeds the average interparticle distance (BCS regime).…”