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Novel phases of silicene and inducement of tunable super-current transport
Partha Goswami
Deshbandhu College, University of Delhi, Kalkaji, New Delhi-110019, India
[email protected]
Abstract Our aim is to discuss theoretically the electric field and the spin-orbit coupling tunable
topological phase transitions in silicene. We start with single-particle silicene Hamiltonian [1,2,3]
comprising of the kinetic energy, a buckling induced staggered sub-lattice potential between silicon atoms
at A sites and B sites for an applied electric field (E z) perpendicular to its plane, the intrinsic spin-orbit
coupling (ISOC) tso(~ 4 meV) stronger than that in graphene, the intrinsic/extrinsic Rashba spin-orbit
coupling(RSOC), and the exchange coupling. We report the effect of the non-magnetic impurity scattering
on stand-alone, mono-layer silicene (MLS) first taking into account intra- and inter-valley scattering
processes. Our investigation have shown that, as long as the impurity strength parameter V 0 is moderate ,
i.e. V0 is of the same order as tso, the electric field (Ez = Ec )driven valley spin polarized metallic (VSPM)
phase transition of the silicene is protected (see Figure 1). For V 0 >> tso, however, one sees the
disappearance of this phase due to accentuated intra- and inter-valley scattering processes. In fact, we
utilize a model for screened scattering centers (SSC) of the Gaussian shape for this purpose, with the
screening length (L) spanning the range varying smoothly on the scale of the lattice constant(a), as the
facilitator of the former ( requires non-local SSC with ,say, L equals 10a ) as well as that of the latter (local
SSC with, say, L equals a). The local potentials allow us to go beyond the scope of the single-valley
scattering problem. Obviously, the ISOC induced quantum spin Hall effect (a quantized response of a
transverse spin current to an electric field) is realizable in this system. The intrinsic Rashba coupling does
not cause the disappearance of this phase. The VSPM phase is also found to be robust against this
coupling. We next examine the case where the exchange field(M), and the tunable extrinsic RSOC
parameter are present only. The tuning of the latter pushes the MLS from a conventional quantum
anomalous Hall (QAHE) phase (characterized by a quantized charge Hall conductance in an insulating
state) to a novel valley-polarized quantum anomalous Hall phase with a band gap. The new phase
provides a good platform for designing the dissipation-less valleytronics.
The combination of a s-wave superconducting proximity effect with VSPM is another issue discussed
here with the focus on the signature of both local and crossed Andreev reflection processes. We show
that the super-current flowing in the superconductor/normal/ superconductor junction is in pure VSPM
state and completely tunable by Ez. This finding, together with the fact that the Andreev reflection process
is fully valley-spin polarized, show that silicene/germanene provide a remarkable platform for tunable
super-current transport.
References
[1] M Ezawa New J Phys 14 (2012) 033003.
[2] M Ezawa Phys Rev Lett 109 (2012) 055502.
[3] M Ezawa Phys Rev Lett 110 (2013) 026603.
3
1.2
Impurity Potential
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TOPOLOGICAL INSULATOR
TOPOLOGICAL PHASE TRANSITION
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0.8
VSPM STATE
BAND INSULATOR
1.5
0.6
1
0.4
0.5
0.2
0
0
0.5
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Electric Field
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Figure 1. The contour plot of the ‘spin down’ upon the ‘spin-up’ band gap ratio as a function of (Ez / Ec)
and V0 / tso. The deep blue region corresponds to VSPM phase characterized by zero band-gap ratio.