Electric field tuning of spin splitting in topological insulator quantum dots doped with a single magnetic ion

Abstract

We investigate theoretically the electron spin states in a disk-shaped topological insulator quantum dot (TIQD) containing a single magnetic Mn 2+ ion. We demonstrate that the energy spectra and the density distributions of the symmetry-protected edge states in a HgTe TIQD can be modulated effectively by a single magnetic impurity Mn 2+ . Additionally, when an in-plane external electric field is applied., it not only tunes the spin splittings of edge states via the s ( p )- d exchange interaction between the electron (hole) and the magnetic Mn 2+ ion respectively, but also gives rise to the bright-to-dark transitions in the optical transition spectrum. Such spin properties of TIQDs with single Mn 2+ ion as illustrated in this work could offer a new platform for topological electro-optical devices.

Formation of bound states from the edge states of 2D topological insulator by macroscopic magnetic barriers

“…In figure 3 state energy and decreases from l 1 ∼ 4 nm at V 0 ∼ 0.2 eV to l 2 ∼ 2 nm at V 0 > 0.4 eV, and slowly varies for higher values of V 0 . Such values of the penetration depth into the magnet are in agreement of the other studies of the exchange interaction models with the same values of the exchange integral [31][32][33].…”

“…Since typically it exceeds the lattice constant by a factor of 3 … 5, the value of N a > 1 which is greater than N 0 = 1 being the value for a single magnet. As a result, the value of the exchange integral in ( 14) is greater than for a single magnet and can reach the amplitudes in the range of 5 … 40 meV in accordance with previously published estimates [31][32][33].…”

“…The amplitude of the exchange interaction between the edge states and the magnetic impurities differs in various setups and under different estimates. It is expected to reach up to 40 meV in [31], up to 100 meV in [32], and up to 400 meV in [33]. The magnetic proximity effects causing the gap opening up to 90 meV near the Dirac point of the TI spectrum have been experimentally observed in other TI for the Bi 2 Se 3 3D TI capped with the MnSe bi-layers [34].…”

“…For the infinitively high barriers the equation ( 36) can be solved analytically [9], but for a more realistic situation with finite values of the barrier height M 1 и M 2 only the numerical solution is possible for a general case. After obtaining the energy E of a discrete level one may normalize the wavefunction ( 31)- (33) to unity in the usual way: after setting, for example, C 1 = 1, one obtains the normalized eigenstate as…”

Interference effect in the electronic transport of a topological insulator quantum dot

“…Numerical studies indicate that surface states are still robust against disorder in a TIQD [6]. Unique electronic [4][5][6][7][8][9][10][11][12][13][14][15][16][17] and optical properties [18][19][20][21][22] due to surface levels have been predicted and potential applications suggested [23][24][25][26][27]. For the moment, QDs of Bi 2 Se 3 [28][29][30] and Bi 2 Te 3 [31] have been fabricated experimentally.…”