Supersolidity in electron-hole bilayers with a large density - - PowerPoint PPT Presentation
Supersolidity in electron-hole bilayers with a large density imbalance Francesca Maria Marchetti ICSCE-5, 8 February 2011 In collaboration with Meera Parish & Peter Littlewood Cavendish Laboratory, University of Cambridge, UK [1] arxiv >
ICSCE-5, 8 February 2011
Supersolidity in imbalanced electron-hole bilayers Meera Parish & Peter Littlewood Cavendish Laboratory, University of Cambridge, UK [1] arxiv > cond.mat > 1009.1420 Previous related work on imbalanced Fermi gases: [2] Nature Physics 3, 124 (2007) [3] Phys. Rev. Lett. 98 98, 160402 (2007)
Supersolidity in imbalanced electron-hole bilayers BEC BCS ✧ Tunable interactions ✧ BEC-BCS crossover
Supersolidity in imbalanced electron-hole bilayers BEC BCS ✧ Tunable interactions ✧ BEC-BCS crossover
[Zwierlein et al. Nature (2005)]
Supersolidity in imbalanced electron-hole bilayers BEC BCS Can superfluidity persist in presence of a population imbalance? ✧ Tunable interactions ✧ BEC-BCS crossover ✧ Density imbalance frustrates pairing
Supersolidity in imbalanced electron-hole bilayers
[Parish, Marchetti et al. Nature Physics (2007)] [Sheehy et al. PRL (2006)]
BEC BCS
[Shin et al. PRL (2006)]
N N SF Fully paired SF phase Macroscpic spatial phase separation between SF and N (inhomogeneous) Polarised SF or 1FS breached pairing (space homogeneous) Bose-Fermi mixture
Supersolidity in imbalanced electron-hole bilayers
[Parish, Marchetti et al. Nature Physics (2007)] [Sheehy et al. PRL (2006)]
BEC BCS FFLO phase Fully paired SF phase Macroscpic spatial phase separation between SF and N (inhomogeneous)
[Shin et al. PRL (2006)]
N N SF Polarised SF or 1FS breached pairing (space homogeneous) Bose-Fermi mixture SUPERSOLID PHASE
Supersolidity in imbalanced electron-hole bilayers ✧ Experiments (Rice & MIT): FFLO elusive Displacement of Fermi surface: …allows the system to polarise …allows Fermi surface nesting Phase separation dominates over FFLO However …it costs kinetic energy …nesting is partial
[Liao et al. Nature (2010)]
FFLO FFLO phase
Supersolidity in imbalanced electron-hole bilayers Magnetised superconductors QCD and neutron stars
Supersolidity in imbalanced electron-hole bilayers Magnetised superconductors QCD and neutron stars Electron-hole systems (N.B. here the density is varied) BEC BCS
BEC of bound excitons exciton insulator
Supersolidity in imbalanced electron-hole bilayers Magnetised superconductors QCD and neutron stars Electron-hole systems (N.B. here the density is varied) BEC BCS
BEC of bound excitons exciton insulator
Supersolidity in imbalanced electron-hole bilayers
e- e- e- e- e- e- h+ h+ 1 h+ h+ h+
3D 2D 1D valence band conduction band position QW1 QW2 electron-hole bilayers: better route to achieve FFLO!
Supersolidity in imbalanced electron-hole bilayers e- e- e- e- e- e- h+ h+ 1 h+ h+ h+ Novel ‘bosonic’ limit of FFLO valence band conduction band position QW1 QW2
electron-hole bilayers: better route to achieve FFLO!
3D 2D 1D
Supersolidity in imbalanced electron-hole bilayers Optically pumped coupled quantum wells
[Butov et al. Nature (2002)] [Snoke et al. Nature (2002)] […and many more…]
⇒ Equilibrium phase diagram Individually contacted doped layers
[Croxall et al. PRL (2008)] [Seamons et al. PRL (2009)]
e- e- e- e- e- e- h+ h+ 1 h+ h+ h+ valence band conduction band position QW1 QW2
Supersolidity in imbalanced electron-hole bilayers 1 1 1 1 1 1 1 2 2 2 2 2 ⇒ No spin (spin polarised) bare intra-layer Coulomb interaction bare inter-layer
Supersolidity in imbalanced electron-hole bilayers 1 1 1 1 1 1 1 2 single particle in the 2nd layer + Fermi see in the 1st layer (SF) (FFLO) relative k CoM Q Good description of both low and high density limit
Supersolidity in imbalanced electron-hole bilayers 1 1 1 1 1 1 1 2 Good description of both low and high density limit (N) Interpolate by screening the interactions (within RPA) = dress with density fluctuations, including particle-hole excitations (SF) single particle in the 2nd layer + Fermi see in the 1st layer relative k CoM Q
Supersolidity in imbalanced electron-hole bilayers
Read also as mean-field (linearised) gap equation
SF & FFLO Parameters: exciton Bohr radius ⇒ interlayer distance ⇒ dimensionless density ⇒ mass ratio
[Yamashita et al. J Phys Soc Japan (2010)] [Pieri et al. PRB (2007)] [Subasi et al. PRB (2010)]
⇒ Current theories ⇒ … some neglect screening ⇒ … some neglect finite Q FFLO (next talk)
Supersolidity in imbalanced electron-hole bilayers
Read also as mean-field (linearised) gap equation
[Yamashita et al. J Phys Soc Japan (2010)] [Pieri et al. PRB (2007)] [Subasi et al. PRB (2010)]
Parameters: exciton Bohr radius ⇒ Current theories ⇒ … some neglect screening ⇒ … some neglect finite Q FFLO (next talk) SF & FFLO ⇒ interlayer distance ⇒ dimensionless density ⇒ mass ratio
Supersolidity in imbalanced electron-hole bilayers
[arxiv/cond.mat/1009.1420]
high density low density ⇒ interlayer distance ⇒ dimensionless density ⇒ mass ratio GaAs:
FFLO region enhanced if minority particle lighter
Supersolidity in imbalanced electron-hole bilayers Unscreened case ⇒ Numerically ⇒ Analytically
Supersolidity in imbalanced electron-hole bilayers Unscreened case ⇒ Numerically ⇒ Analytically
Supersolidity in imbalanced electron-hole bilayers
Supersolidity in imbalanced electron-hole bilayers Normal phase: ⇒ repulsive and dipolar : the dilute gas is a Fermi liquid 1 2 effective interaction between two unbound minority particles (RPA) Excitonic phase: 1 2 ⇒ also repulsive and dipolar : no phase separation (biexciton formation suppressed for single spin species & ) well separated excitons (dipoles)
Supersolidity in imbalanced electron-hole bilayers 1 2 Landau theory for = exciton density chemical potential minimum energy at
Supersolidity in imbalanced electron-hole bilayers 1 2 Landau theory for = exciton density (weak crystalisation theory) Complex order parameter chemical potential minimum energy at Minimal energy solution ⇒ supersolid: exciton condesate with 2D spatial modulation (diagonal and off-diagonal order)
Supersolidity in imbalanced electron-hole bilayers Exciton binding energy in GaAs = upper bound for the FFLO critical temperature
(electron hole recombining): finite momentum pairing ( ) GaAs 1 2
Supersolidity in imbalanced electron-hole bilayers Electron-hole bilayers: promising for observing exotic pairing phenomena Evidence of FFLO phase at large imbalance: finite-Q exciton in presence of a fermi sea Dilute gas of finite-Q excitons: condensation with 2D spatial modulation (a supersolid) Prospects for experimental observation ⇒ bosonic limit of FFLO
Supersolidity in imbalanced electron-hole bilayers Magnetised superconductors SC Zeeman term
Supersolidity in imbalanced electron-hole bilayers Interpolate between high and low density via RPA 1 1 1 1 1 1 1 2 Full imbalance limit: Screening between 12 through 11 = + + … = + 1 1 1 1 1 = + + … = + 1 1 1 polarisation operator (Linhard function)
Supersolidity in imbalanced electron-hole bilayers
Read also as mean-field (linearised) gap equation (BEC-BCS crossover)
SF & FFLO ⇒ minority particle chemical potential
[Yamashita et al. J Phys Soc Japan (2010)] [Pieri et al. PRB(2007)] [Subasi et al. PRB (2010)]
Supersolidity in imbalanced electron-hole bilayers Our approach + screened Coulomb interactions (infinite particle-hole excitations) bound state unbound state In cold atoms (majority Fermi sea non-interacting and interspecies interaction short range): POLARON ANSATZ add a single particle-hole excitation Not profitable to just excite one particle-hole pair when interactions are long-range and the majority Fermi sea is interacting
Supersolidity in imbalanced electron-hole bilayers
[arxiv/cond.mat/1009.1420]
high density low density Low density: Q=0 exciton (SF) (two-body limit) High density: screening causes unbinding (N) Intermediate density: Significant region of FFLO FFLO region enhanced if minority particle lighter
Supersolidity in imbalanced electron-hole bilayers FFLO region enhanced if minority particle lighter
[arxiv/cond.mat/1009.1420]
A Q=0 exciton requires a minority particle to sit above the Fermi sea ⇒ Kinetic cost increases for lighter m2 favouring FFLO
Supersolidity in imbalanced electron-hole bilayers Second order phase transitions at the FFLO-N transition
Supersolidity in imbalanced electron-hole bilayers
[Yamashita et al. J Phys Soc Japan (2010)]
At the unbinding transitions ( ) the integral is divergent for , so the exciton with is always bound ( ) Unscreened case ⇒ Numerically ⇒ Analytically:
Supersolidity in imbalanced electron-hole bilayers Normal phase: effective interaction between two unbound minority particles (RPA) + 1 1 = ⇒ repulsive and dipolar : the dilute gas is a Fermi liquid Well separated excitons (dipoles) 1 2 1 2 ⇒ also repulsive and dipolar : no phase separation (biexciton formation suppressed for single spin species & )
Supersolidity in imbalanced electron-hole bilayers