Denis R. Candido, M. E. Flatté, J. Carlos Egues
We investigate the electronic and transport properties of topological and trivial InAs$_{1-x}$Bi$_x$ quantum dots (QDs). By considering the rapid band gap change within valence band anticrossing theory for InAs$_{1-x}$Bi$_x$, we predicted that Bi-alloyed quantum wells become $\sim 30$meV gapped 2D topological insulators for well widths $d>6.9$nm $(x = 0.15)$ and obtain the $\boldsymbol{k.p}$ parameters of the corresponding Bernevig-Hughes-Zhang (BHZ) model. We analytically solve this model for cylindrical confinement via modified Bessel functions. For non-topological dots we find "geometrically protected" discrete helical edge-like states, i.e., Kramers pairs with spin-angular-momentum locking, in stark contrast with ordinary InAs QDs. For a conduction window with four edge states, we find that the two-terminal conductance ${\cal G}$ vs. the QD radius $R$ and the gate $V_g$ controlling its levels shows a double peak at $2e^2/h$ for both topological and trivial QDs. In contrast, when bulk and edge-state Kramers pairs coexist and are degenerate, a single-peak resonance emerges. Our results blur the boundaries between topological and non-topological phenomena for conductance measurements in small systems such as QDs. Bi-based BHZ QDs should also prove important as hosts to edge spin qubits.
Henrique J. P. Freire, J. Carlos Egues
Here we investigate the spin-dependent subband structure of newly-developed Mn-based modulation-doped quantum wells. In the presence of an external magnetic field, the s-d exchange coupling between carriers and localized d electrons of the Mn impurities gives rise to large spin splittings resulting in a magnetic-field dependent subband structure. Within the framework of the effective-mass approximation, we self-consistently calculate the subband structure at zero temperature using Density Functional Theory (DFT) with a Local Spin Density Approximation (LSDA). We present results for the magnetic-field dependence of the subband structure of shallow ZnSe/ZnCdMnSe modulation doped quantum wells. Our results show a significant contribution to the self-consistent potential due to the exchange-correlation term. These calculations are the first step in the study of a variety of interesting spin-dependent phenomena, e.g., spin-resolved transport and many-body effects in polarized two-dimensional electron gases.
Alexander Khaetskii, J. Carlos Egues
We have studied the edge spin accumulation in a high mobility two-dimensional electron gas formed in a symmetric well with two subbands. This study is strongly motivated by the recent experiment of Hernandez et al. [Phys. Rev. B {\bf 88}, 161305(R) (2013)] who demonstrated the spin accumulation near the edges of a bilayer symmetric GaAs structure in contrast to no effect in a single-layer configuration. The intrinsic mechanism of the spin-orbit interaction we consider arises from the coupling between two subband states of opposite parities. We obtain a parametrically large magnitude of the edge spin density for the two-subband sample as compared to the usual single-subband structure. We show that the presence of a gap in the system, i.e., the energy separation $Δ$ between the two subband bottoms, changes drastically the picture of the edge spin accumulation. Thus one can easily proceed from the regime of weak spin accumulation to the regime of strong one by varying the Fermi energy (electron density) and/or $Δ$. We estimate that by changing the gap $Δ$ from zero up to $1÷2$ K, the magnitude of the effect changes by three orders of magnitude. This opens up the possibility for the design of new spintronic devices.
Miguel J. Carballido, Simon Svab, Rafael S. Eggli, Taras Patlatiuk, Pierre Chevalier Kwon, Jonas Schuff, Rahel M. Kaiser, Leon C. Camenzind, Ang Li, Natalia Ares, Erik P. A. M Bakkers, Stefano Bosco, J. Carlos Egues, Daniel Loss, Dominik M. Zumbühl
Across leading qubit platforms, a common trade-off persists: increasing coherence comes at the cost of operational speed, reflecting the notion that protecting a qubit from its noisy surroundings also limits control over it. This speed-coherence dilemma limits qubit performance across various technologies. Here, we demonstrate a hole spin qubit in a Ge/Si core/shell nanowire that triples its Rabi frequency while simultaneously quadrupling its Hahn-echo coherence time, boosting the Q-factor by over an order of magnitude. This is enabled by the direct Rashba spin-orbit interaction, emerging from heavy-hole-light-hole mixing through strong confinement in two dimensions. Tuning a gate voltage causes this interaction to peak, providing maximum drive speed and a point where the qubit is optimally protected from charge noise, allowing speed and coherence to scale together. Our proof-of-concept shows that careful dot design can overcome a long-standing limitation, offering a new approach towards building high-performance, fault-tolerant qubits.
Denis R. Candido, Maxim Kharitonov, J. Carlos Egues, Ewelina M. Hankiewicz
We present a paradoxical finding that, in the vicinity of a topological phase transition in a quantum anomalous Hall system (Chern insulator), topology nearly always (except when the system obeys charge-conjugation symmetry) results in a significant extension of the edge-state structure beyond the minimal one required to satisfy the Chern numbers. The effect arises from the universal gapless linear-in-momentum Hamiltonian of the nodal semimetal describing the system right at the phase transition, whose form is enforced by the change of the Chern number. Its emergent approximate chiral symmetry results in an edge-state band in the vicinity of the node, in the region of momenta where such form is dominant. Upon opening the gap, this edge-state band is modified in the gap region, becoming "protected" (connected to the valence bulk band with one end and conduction band with the other) in the topologically nontrivial phase and "nonprotected" (connected to either the valence or conduction band with both ends) in the trivial phase. The edge-state band persists in the latter as long as the gap is small enough.
Antonio Zegarra, Denis R. Candido, J. Carlos Egues, Wei Chen
We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase transitions, and using interacting Su-Schrieffer-Heeger model as an example. From the many-body spectral function, we find that closing of the bulk gap remains a defining feature even if the topological phase transition is driven by interactions. The existence of edge state in the presence of interactions can be captured by means of a T-matrix formalism combined with Dyson's equation, and the bulk-edge correspondence is shown to be satisfied even in the presence of interactions. The critical exponent of the edge state decay length is shown to be affiliated with the same universality class as the noninteracting limit.
Minchul Lee, Marco O. Hachiya, E. Bernardes, J. Carlos Egues, Daniel Loss
We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity $σ^z_{xy}$ is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field $B$ and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated $σ^z_{xy}$ exhibits a nonmonotonic behavior and can change its sign as the Fermi energy (the carrier areal density $n_{2D}$) is varied between the subband edges. We determine the magnitude of $σ^z_{xy}$ for realistic InSb quantum wells by performing a self-consistent calculation of the intersubband-induced spin-orbit coupling.
Pirmin J. Weigele, D. C. Marinescu, Florian Dettwiler, Jiyong Fu, Shawn Mack, J. Carlos Egues, David D. Awschalom, Dominik M. Zumbühl
We exploit the high-symmetry spin state obtained for equal Rashba and linear Dresselhaus interactions to derive a closed-form expression for the weak localization magnetoconductivity -- the paradigmatic signature of spin-orbit coupling in quantum transport. The small parameter of the theory is the deviation from the symmetry state introduced by the mismatch of the linear terms and by the cubic Dresselhaus term. In this regime, we perform quantum transport experiments in GaAs quantum wells. Top and back gates allow independent tuning of the Rashba and Dresselhaus terms in order to explore the broken-symmetry regime where the formula applies. We present a reliable two-step method to extract all parameters from fits to the new expression, obtaining excellent agreement with recent experiments. This provides experimental confirmation of the new theory, and advances spin-orbit coupling towards a powerful resource in emerging quantum technologies.
John Schliemann, J. Carlos Egues, Daniel Loss
We propose a spin field-effect transistor based on spin-orbit (s-o) coupling of both the Rashba and the Dresselhaus types. Differently from earlier proposals, spin transport through our device is tolerant against spin-independent scattering processes. Hence the requirement of strictly ballistic transport can be relaxed. This follows from a unique interplay between the Dresselhaus and the (gate-controlled) Rashba interactions; these can be tuned to have equal strengths thus yielding k-independent eigenspinors even in two dimensions. We discuss implementations with two-dimensional devices and quantum wires. In the latter, our setup presents strictly parabolic dispersions which avoids complications arising from anticrossings of different bands.
J. Carlos Egues, Guido Burkard, Daniel Loss
We consider a two-channel spin transistor with weak spin-orbit induced interband coupling. We show that the coherent transfer of carriers between the coupled channels gives rise to an \textit{additional} spin rotation. We calculate the corresponding spin-resolved current in a Datta-Das geometry and show that a weak interband mixing leads to enhanced spin control.
Sigurdur I. Erlingsson, J. Carlos Egues
We show that electrons in ordinary III-V semiconductor double wells with an in-plane modulating periodic potential and inter well spin-orbit interaction are tunable Topological Insulators (TIs). Here the essential TI ingredients, namely, band inversion and the opening of an overall bulk gap in the spectrum arise, respectively, from (i) the combined effect of the double well even-odd state splitting $Δ_{SAS}$ together with the superlattice potential and (ii) the interband Rashba spin-orbit coupling $η$. We corroborate our exact diagonalization results by an analytical nearly-free electron description that allows us to derive an effective Bernevig-Hughes-Zhang (BHZ) model. Interestingly, the gate-tunable $Δ_{SAS}$ drives a topological phase transition featuring a discontinuous Chern number at $Δ_{SAS}\sim 5.4$ meV. Finally, we explicitly verify the bulk-edge correspondence by considering a strip configuration and determining not only the bulk bands in the non-topological and topological phases but also the edge states and their Dirac-like spectrum in the topological phase. The edge electronic densities exhibit peculiar spatial oscillations as they decay away into the bulk. For concreteness, we present our results for InAs-based wells with realistic parameters.
J. Carlos Egues, Guido Burkard, D. Saraga, John Schliemann, Daniel Loss
We extend our previous work on shot noise for entangled and spin polarized electrons in a beam-splitter geometry with spin-orbit (\textit{s-o}) interaction in one of the incoming leads (lead 1). Besides accounting for both the Dresselhaus and the Rashba spin-orbit terms, we present general formulas for the shot noise of singlet and triplets states derived within the scattering approach. We determine the full scattering matrix of the system for the case of leads with \textit{two} orbital channels coupled via weak \textit{s-o} interactions inducing channel anticrossings. We show that this interband coupling coherently transfers electrons between the channels and gives rise to an additional modulation angle -- dependent on both the Rashba and Dresselhaus interaction strengths -- which allows for further independent coherent control of the electrons traversing the incoming leads. We derive explicit shot noise formulas for a variety of correlated pairs (e.g., Bell states) and lead spin polarizations. Interestingly, the singlet and \textit{each} of the triplets defined along the quantization axis perpendicular to lead 1 (with the local \textit{s-o} interaction) and in the plane of the beam splitter display distinctive shot noise for injection energies near the channel anticrossings; hence, one can tell apart all the triplets, in addition to the singlet, through noise measurements. We also find that spin-orbit induced backscattering within lead 1 reduces the visibility of the noise oscillations, due to the additional partition noise in this lead. Finally, we consider injection of two-particle wavepackets into leads with multiple discrete states and find that two-particle entanglement can still be observed via noise bunching and antibunching.
Esmerindo S. Bernardes, John Schliemann, Minchul Lee, J. Carlos Egues, Daniel Loss
We investigate the spin-orbit (s-o) interaction in two-dimensional electron gases (2DEGs) in quantum wells with two subbands. From the $8\times 8$ Kane model, we derive a new inter-subband-induced s-o term which resembles the functional form of the Rashba s-o -- but is non-zero even in \emph{symmetric} structures. This follows from the distinct parity of the confined states (even/odd) which obliterates the need for asymmetric potentials. We self-consistently calculate the new s-o coupling strength for realistic wells and find it comparable to the usual Rashba constant. Our new s-o term gives rise to a non-zero ballistic spin-Hall conductivity, which changes sign as a function of the Fermi energy ($ε_F$), and can induce an unusual \emph{zitterbewegung} with cycloidal trajectories \textit{without} magnetic fields.
Esmerindo Bernardes, John Schliemann, J. Carlos Egues, Daniel Loss
Recently, we have introduced a novel inter-subband-induced spin-orbit (s-o) coupling [Phys. Rev. Lett. 99, 076603 (2007); cond-mat/0607218] arising in \textit{symmetric} wells with at least two subbands. This new s-o coupling gives rise to an usual zitterbewegung -- i.e. the semiconductor analog to the relativistic trembling motion of electrons -- with cycloidal motion without magnetic fields. Here we complement these findings by explicitly deriving expressions for the corresponding zitterbewegung in spin space.
Rodrigo A. Dourado, Poliana H. Penteado, J. Carlos Egues
We propose a protocol based only on local conductance measurements for distinguishing trivial from topological phases in realistic three-terminal superconducting nanowires coupled to normal leads, capable of hosting Majorana zero modes (MZMs). By using Green functions and the scattering matrix approach, we calculate the conductance matrix and the local density of states (LDOS) as functions of the asymmetry in the couplings to the left ($Γ_L$) and right ($Γ_R$) leads. In the trivial phase, we find that the zero-bias local conductances are distinctively affected by variations in $Γ_R$ (for fixed $Γ_L$): while $G_{LL}$ is mostly constant, $G_{RR}$ decays exponentially as $Γ_R$ is decreased. In the topological phase, surprisingly, $G_{LL}$ and $G_{RR}$ are both suppressed with $G_{LL} \sim G_{RR}$. This \textit{nonlocal} suppression of $G_{LL}$ with $Γ_R$ scales with the MZM hybridization energy $\varepsilon_m$ and arises from the emergence of a dip in the LDOS near zero energy at the left end of the wire, which affects the local Andreev reflection. We further exploit this nonlocality of the local Andreev processes and the gate-controlled suppression of the LDOS by proposing a Majorana-based transistor. Our results hold for zero and low electron temperatures $T<20$ mK. For $T = 30, 40$ mK, $G_{LL}$ and $G_{RR}$ become less correlated. As an additional nonlocal fingerprint of the topological phase at higher $T$'s, we predict modulations in our \textit{asymmetric} conductance deviation $δG^{asym}_{LL}= G_{LL}^{Γ_R = Γ_L} - G_{LL}^{Γ_R \ll Γ_L}$ that remains commensurate with the Majorana oscillations in $\varepsilon_m$ over the range $30<T< 150~\rm{mK}$.
Igor J. Califrer, Poliana H. Penteado, J. Carlos Egues, Wei Chen
When normal metals (NMs) are attached to topological insulators or topological superconductors, it is conceivable that the quantum states in these finite adjacent materials can intermix. In this case -- and because the NM usually does not possess the same symmetry as the topological material -- it is pertinent to ask whether zero-energy edge states in the topological layer are affected by the presence of the NM. To address this issue, we consider three prototype systems simulated by tight-binding models, namely a Su-Schrieffer-Heeger/NM, a Kitaev/NM, and a Chern insulator/NM. For all junctions investigated, we find that there exist trivial ``fine-tuned'' zero-energy states in the NM layer that can percolate into the topological region, thus mimicking a topological state. These zero-energy states are created by fine-tuning the NM chemical potential such that some of the NM states cross zero energy; they can occur even when the topological material is in the topologically trivial phase, and exist over a large region of the topological phase diagram. Interestingly, the true Majorana end modes of the Kitaev/NM model cannot be crossed by any NM state, as the NM metal layer in this case does not break particle-hole symmetry. On the other hand, when the chiral symmetry of the Su-Schrieffer-Heeger chain is broken by the attached NM, crossings are allowed. In addition, even in Chern insulators that do not preserve nonspatial symmetries, but the topological edge state self-generates a symmetry eigenvalue, such a fine-tuned zero-energy state can still occur. Our results indicate that when a topological material is attached to a metallic layer, one has to be cautious as to identify true topological edge states merely from their energy spectra and wave function profiles near the interface.
Marco O. Hachiya, Guido Burkard, J. Carlos Egues
We investigate the spin relaxation and decoherence in a single-electron graphene quantum dot with Rashba and intrinsic spin-orbit interactions. We derive an effective spin-phonon Hamiltonian via the Schrieffer-Wolff transformation in order to calculate the spin relaxation time T_1 and decoherence time T_2 within the framework of the Bloch-Redfield theory. In this model, the emergence of a non-monotonic dependence of T_1 on the external magnetic field is attributed to the Rashba spin-orbit coupling-induced anticrossing of opposite spin states. A rapid decrease of T_1 occurs when the spin and orbital relaxation rates become comparable in the vicinity of the spin-mixing energy-level anticrossing. By contrast, the intrinsic spin-orbit interaction leads to a monotonic magnetic field dependence of the spin relaxation rate which is caused solely by the direct spin-phonon coupling mechanism. Within our model, we demonstrate that the decoherence time T_2 ~ 2 T_1 is dominated by relaxation processes for the electron-phonon coupling mechanisms in graphene up to leading order in the spin-orbit interaction. Moreover, we show that the energy anticrossing also leads to a vanishing pure spin dephasing rate for these states for a super-Ohmic bath.
R. F. Rossetti, G. D. de Moraes Neto, J. Carlos Egues, M. H. Y. Moussa
Feb 25, 2015·quant-ph·PDF Here we present a protocol for generating Lissajous curves with a trapped ion by engineering Rashba- and the Dresselhaus-type spin-orbit interactions in a Paul trap. The unique anisotropic Rashba $α_{x}$, $α_{y}$ and Dresselhaus $β_{x}$, $β_{y}$ couplings afforded by our setup also enables us to obtain an "unusual" Zitterbewegung, i.e., the semiconductor analog of the relativistic trembling motion of electrons, with cycloidal trajectories in the absence of magnetic fields. We have also introduced bounded SO interactions, confined to an upper-bound vibrational subspace of the Fock states, as an additional mechanism to manipulate the Lissajous motion of the trapped ion. Finally, we accounted for dissipative effects on the vibrational degrees of freedom of the ion and find that the Lissajous trajectories are still robust and well defined for realistic parameters.
Florian Dettwiler, Jiyong Fu, Shawn Mack, Pirmin J. Weigele, J. Carlos Egues, David D. Awschalom, Dominik M. Zumbühl
The Rashba and Dresselhaus spin-orbit (SO) interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly-oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba $α$ and Dresselhaus $β$ couplings to equal $\it{fixed}$ strengths $α=β$, the total SO field becomes unidirectional thus rendering the electron spins immune to dephasing due to momentum scattering. A robust persistent spin helix (PSH) has already been experimentally realized at this singular point $α=β$. Here we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields together with a technique that allows for independent electrical control over the SO couplings via top gate voltage $V_T$ and back gate voltage $V_B$. We demonstrate for the first time the gate control of $β$ and the $\it{continuous\,locking}$ of the SO fields at $α=β$, i.e., we are able to vary both $α$ and $β$ controllably and continuously with $V_T$ and $V_B$, while keeping them locked at equal strengths. This makes possible a new concept: "stretchable PSHs", i.e., helical spin patterns with continuously variable pitches $P$ over a wide parameter range. The extracted spin-diffusion lengths and decay times as a function of $α/β$ show a significant enhancement near $α/β=1$. Since within the continuous-locking regime quantum transport is diffusive (2D) for charge while ballistic (1D) for spin and thus amenable to coherent spin control, stretchable PSHs could provide the platform for the much heralded long-distance communication $\sim 8 - 25$ $μ$m between solid-state spin qubits.
Gerson J. Ferreira, Henrique J. P. Freire, J. Carlos Egues
The longitudinal resistivity $ρ_{xx}$ of two-dimensional electron gases formed in wells with two subbands displays ringlike structures when plotted in a density--magnetic-field diagram, due to the crossings of spin-split Landau levels (LLs) from distinct subbands. Using spin density functional theory and linear response, we investigate the shape and spin polarization of these structures as a function of temperature and magnetic-field tilt angle. We find that (i) some of the rings "break" at sufficiently low temperatures due to a quantum Hall ferromagnetic phase transition, thus exhibiting a high degree of spin polarization ($\sim 50 $%) within, consistent with the NMR data of Zhang \textit{et al.} [Phys. Rev. Lett. {\bf 98}, 246802 (2007)], and (ii) for increasing tilting angles the interplay between the anticrossings due to inter-LL couplings and the exchange-correlation (XC) effects leads to a collapse of the rings at some critical angle $θ_c$, in agreement with the data of Guo \textit{et al.} [Phys. Rev. B {\bf 78}, 233305 (2008)].