Spin Relaxation and Decoherence of Holes in Quantum Dots

Abstract

We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is two times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) g-factor.Spin physics has become one of the most rapidly developing branches of condensed matter physics. Spin physics is very important, not only from a fundamental point of view, but also for the fabrication of novel electronic devices, for the experimental realization of quantum computation, and for the development of spin electronics (spintronics) [1]. Quantum dots (QDs) are most attractive candidates for these applications because of their reduced dimensionality, leading to long-lived spin states and allowing single spin manipulation [2].Recent experiments [3,4,5] show that electrons in QDs have a long spin relaxation time (up to 20 ms [5]) and it is now possible to prepare a single electron spin state with a well-defined orientation, read the spin state out, and store the information about the spin orientation for a long time [5]. There are two main spin relaxation mechanisms for electron spins in QDs: that due to the electron-phonon interaction [6,7,8,9] and that due to the hyperfine interaction with surrounding nuclear spins [10,11,12]. Since the valence band has p symmetry, the hyperfine interaction of holes with lattice nuclei is suppressed with respect to that of the conduction band (electrons). This has led to an increased interest in hole spins as carries of long-lived quantum information. It was shown that in thin quantum wells (QWs) the hole spin relaxation is slower than that in the bulk case [13,14]. Nevertheless, the hole spin relaxation time is several orders of magnitude smaller than that for electrons. This is due to the fact that, in addition to existing spin-orbit (SO) couplings for electrons due to bulk inversion asymmetry (BIA) (Dresselhaus spin-orbit (DSO) coupling [15]) and structure inversion asymmetry (SIA) (the Rashba spinorbit (RSO) coupling [16]) there is strong SO coupling between the heavy-hole (HH) and light-hole (LH) subbands [17].Very recently, investigation of hole spin relaxation in QDs was reported [18,19]. In these works only one SO mechanism was considered, the SO coupling between HHs and LHs. It was shown that the hole spin relaxation time in QDs is longer than that in QWs but still shorter by several orders of magnitude than that for electrons in QDs. Furthermore, it was found that SO coupling between HHs and LHs is negligible for two-dimensional (2D) QDs if the energy splitting between the HH and LH subbands is much larger than the level spacing in those subbands [19]. Up to now ...

Consequences of Spin-Orbit Coupling at the Single Hole Level: Spin-Flip Tunneling and the Anisotropic g Factor

“…The early prediction of greatly reduced hyperfine interaction between hole and nuclear spins, and concomitant increased coherence times [14,15], were confirmed experimentally in systems with small HH-LH mixing realized as selfassembled dots (SADs) [16][17][18] or nanowires [19]. In this regime the strong anisotropy of the hole g-factor is expected [12]. To date, however, only partial anisotropy was demonstrated, e.g., in InAs SADs [20] and silicon nanowires [21].…”

“…The hole properties are traced to the amount of HH-LH subband mixing [12,13], which is related to the details of quantum confinement, strain, and the spin-orbit interaction. The early prediction of greatly reduced hyperfine interaction between hole and nuclear spins, and concomitant increased coherence times [14,15], were confirmed experimentally in systems with small HH-LH mixing realized as selfassembled dots (SADs) [16][17][18] or nanowires [19].…”

Hole-spin initialization and relaxation times in InAs/GaAs quantum dots

“…That is why the electron spin relaxation and decoherence sources in QDs have been intensively studied in the last few years; some more limited number of studies have centered on the hole spin. The main conclusions of these studies are that in moderate magnetic fields (1-10 T) and at low temperature, the electron T e 1 and the hole T h 1 spin-relaxation times are governed by the same mechanism, i.e., the spin-orbitmediated single-phonon scattering, [4][5][6][7][8] which leads to relatively slow relaxation times in the range of milliseconds [9][10][11][12][13] with T h 1 five or ten times smaller than T e 1 . 12 However, the electron-and hole-spin coherence times T e,h 2 have been found to be in the microsecond range up to 15 K, [14][15][16][17] and for higher temperatures T e 2 has shown a sharp decrease 16 related to the modulation by phonons of the hyperfine (hf) interaction with the random fluctuating host nuclear spins.…”

Hole spin relaxation in InAs/GaAs quantum dot molecules

“…[28] Several works have theoretically addressed the hole spin relaxation in single QDs taking into account different SOI mechanisms and have showed that one or another prevail depending on the QD traits. [20,29,30,31,32] By comparison, the spin relaxation of holes in DQDs is still poorly understood. This is inspite of their promising prospects for the development of quantum information architectures.…”

“…[16,17,18,19] Using the spin of holes in qubits requires control over the hole spin relaxation (T 1 ) and decoherence (T 2 ) times, the latter being related to the former at low temperatures. [20] In the presence of external magnetic fields, the main mechanism of spin relaxation for the valence band is usually phonon scattering mediated by spin-orbit interaction (SOI). [21,22] Indeed, the strong SOI of holes is responsible for some of its characteristic properties, e.g.…”