A PHP Error was encountered

Severity: Warning

Message: fopen(/var/lib/php/sessions/ci_sessiond9avr3j713dbeeuh3p7sp6akeiu2be18): Failed to open stream: No space left on device

Filename: drivers/Session_files_driver.php

Line Number: 177

Backtrace:

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_start(): Failed to read session data: user (path: /var/lib/php/sessions)

Filename: Session/Session.php

Line Number: 137

Backtrace:

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "choices"

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated

Filename: models/Detail_model.php

Line Number: 71

Backtrace:

File: /var/www/html/application/models/Detail_model.php
Line: 71
Function: strpos

File: /var/www/html/application/controllers/Detail.php
Line: 252
Function: insertAPISummary

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated

Filename: helpers/my_audit_helper.php

Line Number: 8919

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 8919
Function: str_replace

File: /var/www/html/application/controllers/Detail.php
Line: 255
Function: formatAIDetailSummary

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "choices"

Filename: controllers/Detail.php

Line Number: 256

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 256

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 256

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 257

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 257

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 258

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 258

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 259

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 259
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 259

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 259
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 260

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 260

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 260

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_get_contents(https://...@gmail.com&api_key=61f08fa0b96a73de8c900d749fcb997acc09): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests

Filename: helpers/my_audit_helper.php

Line Number: 143

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 143
Function: file_get_contents

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 209
Function: simplexml_load_file_from_url

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3098
Function: getPubMedXML

File: /var/www/html/application/controllers/Detail.php
Line: 574
Function: pubMedSearch_Global

File: /var/www/html/application/controllers/Detail.php
Line: 488
Function: pubMedGetRelatedKeyword

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Attempt to read property "Count" on bool

Filename: helpers/my_audit_helper.php

Line Number: 3100

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3100
Function: _error_handler

File: /var/www/html/application/controllers/Detail.php
Line: 574
Function: pubMedSearch_Global

File: /var/www/html/application/controllers/Detail.php
Line: 488
Function: pubMedGetRelatedKeyword

File: /var/www/html/index.php
Line: 316
Function: require_once

Magnetoresistance and valley degree of freedom in bulk bismuth. | LitMetric

Magnetoresistance and valley degree of freedom in bulk bismuth.

J Phys Condens Matter

Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China.

Published: August 2018

AI Article Synopsis

Article Abstract

In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.

Download full-text PDF

Source
http://dx.doi.org/10.1088/1361-648X/aaced7DOI Listing

Publication Analysis

Top Keywords

magnetic field
24
quantum limit
12
bulk bismuth
8
theoretical understanding
8
orientation magnetic
8
will discuss
8
valley
6
magnetic
6
field
6
magnetoresistance valley
4

Similar Publications

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!