# SIMES Publications

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**"Resonant magneto-optic Kerr effect in the magnetic topological insulator Cr:(Sb**_{x},Bi_{1−x})_{2}Te_{3}_{"} — Shreyas Patankar: J. P. Hinton, Joel Griesmar, J. Orenstein, J. S. Dodge, Xufeng Kou, Lei Pan, Kang L. Wang, A. J. Bestwick, E. J. Fox, D. Goldhaber-Gordon, Jing Wang, and Shou-Cheng Zhang; Physical Review B, 12/31/15.

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J. P. Hinton, Joel Griesmar, J. Orenstein, J. S. Dodge, Xufeng Kou, Lei Pan, Kang L. Wang, A. J. Bestwick, E. J. Fox, D. Goldhaber-Gordon, Jing Wang, and Shou-Cheng Zhang

**Abstract**

We report measurements of the polar Kerr effect, proportional to the out-of-plane component of the magnetization, in thin films of the magnetically doped topological insulator (Cr0.12Bi0.26Sb0.62)2Te3. Measurements of the complex Kerr angle ΘK were performed as a function of photon energy in the range 0.8eV<ℏω<3.0eV. We observed a peak in the real part of ΘK(ω) and zero crossing in the imaginary part that we attribute to a resonant interaction with a spin-orbit avoided crossing located ≈1.6 eV above the Fermi energy. The resonant enhancement allows measurement of the temperature and magnetic field dependence of ΘK in the ultrathin film limit, d≥2 quintuple layers (QL). We find a sharp transition to zero remanent magnetization at 6 K for d<8 QL, consistent with theories of the dependence of impurity spin interactions on film thickness and their location relative to topological insulator surfaces.

**"Erratum: Kerr effect as evidence of gyrotropic order in the cuprates [Phys. Rev. B 87 , 115116 (2013)]"** — Hosur, Pavan: A. Kapitulnik, S. A. Kivelson, J. Orenstein, S. Raghu, W. Cho, and A. Fried; Physical Review B, 01/26/15.

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A. Kapitulnik, S. A. Kivelson, J. Orenstein, S. Raghu, W. Cho, and A. Fried

**Abstract**

Recent analysis has confirmed earlier general arguments that the Kerr response vanishes in any time-reversal invariant system which satisfies the Onsager relations. Thus, the widely cited relation between natural optical activity (gyrotropy) and the Kerr response, employed in our original paper, is incorrect. However, there is increasingly clear experimental evidence that, as argued in our paper, the onset of an observable Kerr signal in the cuprates reflects point-group symmetry rather than time-reversal symmetry breaking.

**"Kerr effect as evidence of gyrotropic order in the cuprates"** — Pavan Hosur: A. Kapitulnik, S. A. Kivelson, J. Orenstein and S. Raghu; Physical Review B, 03/11/13.

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A. Kapitulnik, S. A. Kivelson, J. Orenstein and S. Raghu

**Abstract**

The Kerr effect can arise in a time-reversal invariant dissipative medium that is “gyrotropic,” i.e., one that breaks inversion (I) and all mirror symmetries. Examples of such systems include electron analogs of cholesteric liquid crystals and their descendants, such as systems with chiral charge ordering. We present arguments that the striking Kerr onset seen in the pseudogap phase of a large number of cuprate high-temperature superconductors is an evidence of chiral charge ordering. We discuss additional experimental consequences of a phase transition to a gyrotropic state, including the appearance of a zero-field Nernst effect.

**"Doppler velocimetry of spin propagation in a two-dimensional electron gas"** — Luyi Yang: J. D. Koralek, J. Orenstein, D. R. Tibbetts, J. L. Reno and M. P. Lilly; Nature Physics , 12/11/11.

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J. D. Koralek, J. Orenstein, D. R. Tibbetts, J. L. Reno and M. P. Lilly

**Abstract**

Controlling the flow of electrons by manipulating their spin is a key to the development of spin-based electronics. Recent demonstrations of electrical-gate control in spin-transistor configurations have shown great promise, but operation at room temperature remains elusive. Further progress requires a deeper understanding of the propagation of spin polarization, particularly in the high-mobility semiconductors used for devices. Here we report the application of Doppler velocimetry to resolve the motion of spin-polarized electrons in GaAs quantum wells driven by a drifting Fermi sea. We find that the spin mobility tracks the high electron mobility precisely as a function of temperature. However, we also observe that the coherent precession of spins driven by spin–orbit interaction, which is essential for the operation of a broad class of spin logic devices, breaks down at temperatures above 150 K, for reasons that are not yet understood theoretically.

**"From a Single-Band Metal to a High-Temperature Superconductor via Two Thermal Phase Transitions"** — Rui-Hua He: M. Hashimoto, H. Karapetyan, J. D. Koralek, J. P. Hinton, J. P. Testaud, V. Nathan, Y. Yoshida, Hong Yao, K. Tanaka, W. Meevasana, R. G. Moore, D. H. Lu, S.-K. Mo, M. Ishikado, H. Eisaki, Z. Hussain, T. P. Devereaux, S. A. Kivelson, J. Orenstein, A. Kapitulnik; Science, 03/25/11.

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M. Hashimoto, H. Karapetyan, J. D. Koralek, J. P. Hinton, J. P. Testaud, V. Nathan, Y. Yoshida, Hong Yao, K. Tanaka, W. Meevasana, R. G. Moore, D. H. Lu, S.-K. Mo, M. Ishikado, H. Eisaki, Z. Hussain, T. P. Devereaux, S. A. Kivelson, J. Orenstein, A. Kapitulnik

**Abstract**

The nature of the pseudogap phase of cuprate high-temperature superconductors is a major unsolved problem in condensed matter physics. We studied the commencement of the pseudogap state at temperature T* using three different techniques (angle-resolved photoemission spectroscopy, polar Kerr effect, and time-resolved reflectivity) on the same optimally doped Bi2201 crystals. We observed the coincident, abrupt onset at T* of a particle-hole asymmetric antinodal gap in the electronic spectrum, a Kerr rotation in the reflected light polarization, and a change in the ultrafast relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (Tc), entangled in an energy-momentum–dependent manner with the preexisting pseudogap features, ushering in a ground state with coexisting orders.

**"Random walk approach to spin dynamics in a two-dimensional electron gas with spin-orbit coupling"** — Luyi Yang: J. Orenstein, and Dung-Hai Lee ; Phys. Rev. B, 10/26/10.

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J. Orenstein, and Dung-Hai Lee

**Abstract**

We introduce and solve a semiclassical random walk (RW) model that describes the dynamics of spin polarization waves in zinc-blende semiconductor quantum wells. We derive the dispersion relations for these waves, including the Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the effects of an electric field applied parallel to the spin polarization wave vector. In agreement with calculations based on quantum kinetic theory [ P. Kleinert and V. V. Bryksin Phys. Rev. B 76 205326 (2007)], the RW approach predicts that spin waves acquire a phase velocity in the presence of the field that crosses zero at a nonzero wave vector, q_{0}. In addition, we show that the spin-wave decay rate is independent of field at q_{0} but increases as (q−q_{0})^{2} for q≠q_{0}. These predictions can be tested experimentally by suitable transient spin grating experiments.

**"Emergence of the persistent spin helix in semiconductor quantum wells"** — J. D. Koralek: C. P. Weber, J. Orenstein, B. A. Bernevig, Shou-Cheng Zhang, S. Mack & D. D. Awschalom; Nature , 04/02/09.

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C. P. Weber, J. Orenstein, B. A. Bernevig, Shou-Cheng Zhang, S. Mack & D. D. Awschalom

**Abstract**

According to Noether’s theorem^{1}, for every symmetry in nature there is a corresponding conservation law. For example, invariance with respect to spatial translation corresponds to conservation of momentum. In another well-known example, invariance with respect to rotation of the electron’s spin, or SU(2) symmetry, leads to conservation of spin polarization. For electrons in a solid, this symmetry is ordinarily broken by spin–orbit coupling, allowing spin angular momentum to flow to orbital angular momentum. However, it has recently been predicted that SU(2) can be achieved in a two-dimensional electron gas, despite the presence of spin–orbit coupling^{2}. The corresponding conserved quantities include the amplitude and phase of a helical spin density wave termed the ‘persistent spin helix’^{2}. SU(2) is realized, in principle, when the strengths of two dominant spin–orbit interactions, the Rashba^{3} (strength parameterized by ) and linear Dresselhaus^{4} ( _{1}) interactions, are equal. This symmetry is predicted to be robust against all forms of spin-independent scattering, including electron–electron interactions, but is broken by the cubic Dresselhaus term ( _{3}) and spin-dependent scattering. When these terms are negligible, the distance over which spin information can propagate is predicted to diverge as approaches _{1}. Here we report experimental observation of the emergence of the persistent spin helix in GaAs quantum wells by independently tuning and _{1}. Using transient spin-grating spectroscopy^{5}, we find a spin-lifetime enhancement of two orders of magnitude near the symmetry point. Excellent quantitative agreement with theory across a wide range of sample parameters allows us to obtain an absolute measure of all relevant spin–orbit terms, identifying _{3} as the main SU(2)-violating term in our samples. The tunable suppression of spin relaxation demonstrated in this work is well suited for application to spintronics^{6, }^{7}.