Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session W23: Focus Session: Anderson Localization |
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Sponsoring Units: DCOMP Chair: Mark Jarrell, Louisiana State University Room: 202B |
Thursday, March 5, 2015 2:30PM - 3:06PM |
W23.00001: Anderson localization for chemically realistic systems Invited Speaker: Hanna Terletska Disorder which is ubiquitous for most materials can strongly effect their properties. It may change their electronic structures or even cause their localization, known as Anderson localization. Although, substantial progress has been achieved in the description of the Anderson localization, a proper mean-field theory of this phenomenon for more realistic systems remains elusive. Commonly used theoretical methods such as the coherent potential approximation and its cluster extensions [1] fail to describe the Anderson transition, as the average density of states (DOS) employed in such theories is not critical at the transition. However, near the transition, due to the spatial confinement of carriers, the local DOS becomes highly skewed with a log-normal distribution, for which the most probable and the typical values differ noticeably from the average value. Dobrosavljevic et.al., incorporated such ideas in their typical medium theory (TMT), and showed that the typical (not average) DOS is critical at the transition. While the TMT is able to capture the localized states, as a local single site theory it still has several drawbacks. For the disorder Anderson model in three dimension it underestimates the critical disorder strength, and fails to capture the re-entrance behavior of the mobility edge. We have recently developed a cluster extension of the TMT, which addresses these drawbacks by systematically incorporating non-local corrections. This approach converges quickly with cluster size and allows us to incorporate the effect of interactions and realistic electronic structure. As the first steps towards realistic material modeling, we extended our TMDCA formalisms to systems with the off diagonal disorder and multiple bands structures. We also applied our TMDCA scheme to systems with both disorder and interactions and found that correlations effects tend to stabilize the metallic behavior even in two dimensions. [1] M. Jarrell and H. R. Krishnamurthy, Phys. Rev. B 63, 125102 (2001). [2] V. Dobrosavljevic et. al, Eur. Phys. Lett. 62, 76 (2003). [3] C. E. Ekuma et.al., Phys. Rev. B89, 081107 (2014). [Preview Abstract] |
Thursday, March 5, 2015 3:06PM - 3:18PM |
W23.00002: Weakly Interacting Disordered Electron Systems C.E. Ekuma, H. Terletska, S. Yang, K.-M. Tam, N.S. Vidhyadhiraja, J. Moreno, M. Jarrell We report on the interplay of interactions and disorder within the typical medium dynamical cluster approximation using the Anderson-Hubbard model. By the systematical incorporation of non-local spatial correlations and the diagonal disorder on an equal footing, we study the initial effects of electron interactions ($U$) in one (1D), two (2D), and three (3D) dimensions. Treating the interacting non-local cluster self-energy ($\Sigma^{(SOPT)}_c[{\cal\tilde{G}}](i,j\neq i)$) up to $\mathcal{O}\left[U^2\right]$ order in the perturbation expansion, we obtain the ground-state phase diagram in 3D for the disorder induced paramagnetic metal to insulator transition in the presence of weak interactions. We find that the critical disorder strength ($W_c$), required to localize all states, increases with increasing $U$; implying that the metallic phase is stabilized by interactions. In 2D, our results agree with previous findings on the destruction of the insulating phase by $U$, while in 1D, we find strong competition between both phases. [Preview Abstract] |
Thursday, March 5, 2015 3:18PM - 3:30PM |
W23.00003: Typical Medium Dynamical Cluster Approximation For Disordered Superconductors Elisha Siddiqui, Hanna Terletska, Chinedu Ekuma, N.S. Vidhyadhiraja, Juana Moreno, Mark Jarrell We study the effect of disorder on a three-dimensional attractive Hubbard model using the typical medium dynamical cluster approximation with the Bogoliubov-de Gennes approach as a cluster solver. We explore the effect of disorder for a fixed interaction strength on the diagonal and the off-diagonal typical density of states. As the disorder strength is increased, the pairing parameter or the off-diagonal typical density of states decreases and vanishes at a critical disorder strength while the spectral gap remains finite. This indicates the transition from a superconducting to a super-resistive phase. Also, we find that the critical disorder increases as the interaction strength decreases. A further increase in the disorder strength causes the diagonal typical density of states to vanish. This indicates the transition from a super-resistive to the Anderson insulator phase. Finally, using this analysis for various parameter regimes, we are able to construct a complete disorder vs. interaction strength phase diagram where the three different phases are identified. [Preview Abstract] |
Thursday, March 5, 2015 3:30PM - 3:42PM |
W23.00004: Study of multiband disordered systems using the typical medium dynamical cluster approximation Yi Zhang, Hanna Terletska, Conrad Moore, Chinedu Ekuma, Ka Ming Tam, Juana Moreno, Mark Jarrell We generalize the typical medium dynamical cluster approximation to disordered systems with multiple bands. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states and the mobility edge of the Anderson localized states. We apply our method to the three dimensional multiband Anderson model with both inter- and intra-band hopping and disorder potential and find fast convergence with increasing cluster size. Our results are consistent with the ones obtained by the transfer matrix and the kernel polynomial methods. Our findings show that the typical medium dynamical cluster approximation method can be used to study the Anderson localization in real materials. [Preview Abstract] |
Thursday, March 5, 2015 3:42PM - 3:54PM |
W23.00005: Benchmarking Multiband Cluster Typical Medium Theory Conrad Moore, Yi Zhang, Ka Ming Tam, Juana Moreno, Mark Jarrell We perform transfer matrix calculations on a non-interacting multiple band disordered system with diagonal and off-diagonal disorder. The mobility edge is determined by finite size scaling. We compare with mobility edge predictions from the Typical Medium Dynamical Cluster Approximation (TMDCA). From these results, we discuss the applicability of TMDCA to study localization in realistic disordered systems. [Preview Abstract] |
Thursday, March 5, 2015 3:54PM - 4:06PM |
W23.00006: Disorder Problem In Diluted Magnetic Semiconductors Ryky Nelson, Chinedu Ekuma, Hanna Terletska, Vidhyadhiraja Sudhindra, Juana Moreno, Mark Jarrell Motivated by experimental studies [1-4] addressing the role of impurity disorder in diluted magnetic semiconductors (DMS), we investigate the effects of disorder using a simple tight-binding Hamiltonian with random impurity potential and spin-fermion exchange which is self-consistently solved using the typical medium theory. Adopting the typical density of states (TDoS) as the order parameter, we find that the TDoS vanishes below a critical concentration of the impurity, which indicates an Anderson localization transition in the system. Our results qualitatively explain why at concentrations lower than a critical value DMS are insulating and paramagnetic, while at larger concentrations are ferromagnetic. We also compare several simple models to explore the interplay between ferromagnetic order and disorder induced insulating behavior, and the role of the spin-orbit interaction on this competition. We apply our findings to (Ga,Mn)As and (Ga,Mn)N to compare and contrast their phase diagrams.\\[4pt] [1] A. Richardella et al., Science 327, 665 (2010).\\[0pt] [2] M. Dobrowolska et al., Nature Mater. 11, 444-449 (2012).\\[0pt] [3] N. Samarth, Nature Mater. 11, 360-361 (2012).\\[0pt] [4] M. E. Flatt\'e, Nature Phys. 7, 285-286 (2011). [Preview Abstract] |
Thursday, March 5, 2015 4:06PM - 4:18PM |
W23.00007: Encoding the structure of many-body localization with matrix product operators David Pekker, Bryan K. Clark Anderson insulators are non-interacting disordered systems which have localized single particle eigenstates. The interacting analogue of Anderson insulators are the Many-Body Localized (MBL) phases. The natural language for representing the spectrum of the Anderson insulator is that of product states over the single-particle modes. We show that product states over Matrix Product Operators of small bond dimension is the corresponding natural language for describing the MBL phases. In this language all of the many-body eigenstates are encode by Matrix Product States (i.e. DMRG wave function) consisting of only two sets of low bond-dimension matrices per site: the $G_i$ matrix corresponding to the local ground state on site i and the $E_i$ matrix corresponding to the local excited state. All $2n$ eigenstates can be generated from all possible combinations of these matrices. [Preview Abstract] |
Thursday, March 5, 2015 4:18PM - 4:30PM |
W23.00008: Typical density of states as an order parameter for the Anderson localization Ka-Ming Tam, Conrad Moore, Juana Moreno, Mark Jarrell The typical medium theory and its recently proposed extensions for models with off-diagonal disorder and multiple bands are significant progress towards the study of localization phenomenon in real materials. The fundamental assumption of these methods is that the typical density of states can be treated as an order parameter. However, its justifications in lattice model is largely lacking. This is predominantly due to two factors. First, the lattice sizes amenable for exact diagonalization is rather limited. Second, the small lattice sizes lead to a very sensitive dependence on the broadening factor. In this work, we use the kernel polynomial method to perform simulation for large system sizes. By adapting the method for the study of criticality, we find that the typical density of states has a well defined finite size scaling behavior. In particular, from the kurtosis, Binder ratio, of the distribution of the density of states for different lattice sizes, we find a clear crossing to identify the critical point. This provides further support that the typical density of states can be used as an order parameter for the localization transition. [Preview Abstract] |
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